diff --git a/.gitignore b/.gitignore
index f2aa3e6..6e41586 100644
--- a/.gitignore
+++ b/.gitignore
@@ -14,4 +14,7 @@ Cargo.lock
 *.pdb
 
 # KZG PARAMS
-params
\ No newline at end of file
+params
+
+# Python virtual environment
+.venv/
\ No newline at end of file
diff --git a/README.md b/README.md
index 348b00b..876ad9e 100644
--- a/README.md
+++ b/README.md
@@ -16,14 +16,23 @@ python3 scripts/circuit_sk.py -n 4096 -qis '[
 ]' -t 65537
 ```
 
+To generate the parameters for the public key proof of encryption circuit run the following command:
+
+```bash
+python3 scripts/circuit_pk.py -n 4096 -qis '[                                      
+    27424203952895201, 
+    27424203952895203
+]' -t 65537
+```
+
 Where `-n` is the degree of the cyclotomic polynomial that defines the ring, `-qis` is the list of moduli qis such that qis[i] is the modulus of the i-th CRT basis of the modulus q of the ciphertext space, `-t` is the plaintext modulus. The value of `𝜎` for the gaussian distribution is set to 3.2 by default.
 
 You can modify these parameters to fit your needs. Note that the python script used to generate the inputs is largely unoptimized and can take a while to run for parameters with large `n`, since the polynomial multiplication is not done using NTT.
 
 As a result:
-- A file `./src/data/sk_enc_{n}_{qis_len}x{qis_bitsize}_{t}.json` is generated including the input to the circuit that can be used for testing for those specific parameters. It includes a random secret key, a random plaintext message and the corresponding ciphertext encrypted under the secret key.
-- A file `./src/data/sk_enc_{n}_{qis_len}x{qis_bitsize}_{t}_zeroes.json` is generated. In this file all the coefficients of the input polynomials are set to zero. This input is used at key generation time, when the actual inputs are not known.
-- A file `./src/constants/sk_enc_constants_{n}_{qis_len}x{qis_bitsize}_{t}.rs` is generated including the generic constants for the circuit. Note that we separate them from the input because these should be known at compile time.
+- A file `./src/data/{p|s}k_enc_{n}_{qis_len}x{qis_bitsize}_{t}.json` is generated including the input to the circuit that can be used for testing for those specific parameters. It includes a random secret key, a random plaintext message and the corresponding ciphertext encrypted under the secret key.
+- A file `./src/data/{p|s}k_enc_{n}_{qis_len}x{qis_bitsize}_{t}_zeroes.json` is generated. In this file all the coefficients of the input polynomials are set to zero. This input is used at key generation time, when the actual inputs are not known.
+- A file `./src/constants/{p|s}k_enc_constants_{n}_{qis_len}x{qis_bitsize}_{t}.rs` is generated including the generic constants for the circuit. Note that we separate them from the input because these should be known at compile time.
 
 On top of that, the console will print an estimatation of the number of advice cells needed to compile the circuit in halo2 considering a single advice column and a lookup table of size 2^8. Spoiler: around 90% of the constraints are generated by the range checks on the polynomial coefficients.
 
diff --git a/scripts/circuit_pk.py b/scripts/circuit_pk.py
new file mode 100644
index 0000000..b3aba16
--- /dev/null
+++ b/scripts/circuit_pk.py
@@ -0,0 +1,664 @@
+import os
+from bfv.crt import CRTModuli
+from bfv.bfv import BFVCrt
+from bfv.discrete_gauss import DiscreteGaussian
+from bfv.polynomial import Polynomial, poly_div
+from random import randint
+import copy
+from utils import assign_to_circuit
+import argparse
+import json
+
+
+
+def main(args): 
+    
+    '''
+    ENCRYPTION PHASE - performed outside the circuit.
+    '''
+
+    n = args.n
+    qis = args.qis
+    qis = json.loads(qis)
+    t = args.t
+
+    crt_moduli = CRTModuli(qis)
+    sigma = 3.2
+    discrete_gaussian = DiscreteGaussian(sigma)
+    bfv_crt = BFVCrt(crt_moduli, n, t, discrete_gaussian)
+
+    # Perform encryption of m in each CRT basis
+    s = bfv_crt.SecretKeyGen()
+    e = bfv_crt.bfv_q.rlwe.SampleFromErrorDistribution()
+    ais = []
+    
+    for i in range(len(crt_moduli.qis)):
+        ais.append(bfv_crt.bfv_qis[i].rlwe.Rq.sample_polynomial())
+    
+    # Generate Public key 
+    pub_key = bfv_crt.PublicKeyGen(s,e,ais)
+ 
+    
+    m = bfv_crt.bfv_q.rlwe.Rt.sample_polynomial()
+    e0 = bfv_crt.bfv_q.rlwe.SampleFromErrorDistribution()
+    e1 = bfv_crt.bfv_q.rlwe.SampleFromErrorDistribution()
+    u = bfv_crt.bfv_q.rlwe.SampleFromTernaryDistribution()
+
+    ciphertext = bfv_crt.PubKeyEncrypt(pub_key,m,e0,e1,u)
+
+    # Sanity check for valid decryption    
+    message_prime = bfv_crt.Decrypt(s, ciphertext)
+
+    assert m == message_prime
+
+    # k1 = [QM]t namely the scaled message polynomial
+    k1 = m.scalar_mul(crt_moduli.q)
+    k1.reduce_coefficients_by_modulus(t)
+
+    # `p` is the modulus of the prime field of the circuit
+    p = 21888242871839275222246405745257275088548364400416034343698204186575808495617
+
+    # `r2is` are the polynomials r2i for each i-th CRT basis.
+    r2is = []
+
+    # `r1is` are the polynomials r1i for each i-th CRT basis.
+    r1is = []
+
+    # `k0is` are the negative multiplicative inverses of t modulo each qi.
+    k0is = []
+
+    # `ct0is` are the polynomials ct0i for each CRT basis. 
+    ct0is = []
+
+    # `ct0is_hat` are the polynomials ct0i_hat for each CRT basis.
+    ct0is_hat = []
+
+    # `ct1is` are the polynomials ct0i for each CRT basis. 
+    ct1is = []
+
+    # `ct1is_hat` are the polynomials ct0i_hat for each CRT basis.
+    ct1is_hat = []
+
+    # `pk0is` are the polynomials pk0 for each i-th CRT basis
+    pk0is = [] 
+
+    # `pk1is` are the polynomials pk0 for each i-th CRT basis
+    pk1is = []  
+
+    # `p1is` are the polynomials p1i for each i-th CRT basis.
+    p1is = []
+
+    # `p2is` are the polynomials p2i for each i-th CRT basis.
+    p2is = []
+
+
+
+    '''
+    SETUP PHASE - performed outside the circuit
+    For each CRT basis, we need to compute the polynomials r1i and r2i (check this doc for more details: https://hackmd.io/@gaussian/r1W98Kqqa)
+    '''
+    pk_array = []
+    pk1_array = []
+
+
+    for i,pk in enumerate(pub_key):
+        pk_array.append(pk[0].coefficients)
+        pk1_array.append(pk[1].coefficients)
+
+    
+        
+    cyclo = [1] + [0] * (n - 1) + [1]
+    cyclo = Polynomial(cyclo)
+
+    for i, cti in enumerate(ciphertext):
+
+        ct0i = cti[0]
+        ct1i = cti[1]
+
+        # k0i = -t^{-1} namely the multiplicative inverse of t modulo qi
+        k0i = pow(-t, -1, qis[i])
+
+        # ct0i_hat = pk0 *u + e0 + k0*k1
+        pk0 = Polynomial(pk_array[i])
+        pk1 = Polynomial(pk1_array[i])
+        
+        ct0i_hat= pk0 * u + e0 + k1.scalar_mul(k0i)
+        assert(len(ct0i_hat.coefficients) - 1 == 2 * n - 2)
+
+
+        # pk0i * u + e0 + k0i * k1 = ct0i mod Rqi
+        # assert that ct0i_hat = ct0i mod Rqi
+        ct0i_hat_clone = copy.deepcopy(ct0i_hat)
+        # mod Rqi means that we need to:
+        # - reduce the coefficients of ct0i_hat_clone by the cyclotomic polynomial
+        # - reduce the coefficients of ct0i_hat_clone by the modulus
+        ct0i_hat_clone.reduce_coefficients_by_cyclo(cyclo.coefficients)
+        ct0i_hat_clone.reduce_coefficients_by_modulus(qis[i])
+        assert ct0i_hat_clone == ct0i
+
+        # Calculate r2i
+        # divide ct0i - ct0i_hat by the cyclotomic polynomial over Zqi to get r2i
+        num = ct0i + ct0i_hat.scalar_mul(-1)
+        # reduce the coefficients of num by the modulus qi 
+        num.reduce_coefficients_by_modulus(qis[i])
+        (quotient, rem) = poly_div(num.coefficients, cyclo.coefficients)
+        # assert that the remainder is zero
+        assert rem == []
+        r2i = Polynomial(quotient)
+        # assert that the degree of r2i is equal to n - 2
+        assert len(r2i.coefficients) - 1 == n - 2
+
+        # Assert that ct0i - ct0i_hat = r2i * cyclo mod Zqi
+        lhs = ct0i + ct0i_hat.scalar_mul(-1)
+        rhs = r2i * cyclo
+        # reduce the coefficients of lhs by the modulus qi
+        lhs.reduce_coefficients_by_modulus(qis[i])
+        assert lhs == rhs 
+        
+        # Calculate r1i
+        # divide ct0i - ct0i_hat - r2i * cyclo by the modulus qi to get r1i
+        num = ct0i + ct0i_hat.scalar_mul(-1) + (r2i * cyclo).scalar_mul(-1)
+        (quotient, rem) = poly_div(num.coefficients, [qis[i]])
+        # assert that the remainder is zero
+        assert rem == []
+        r1i = Polynomial(quotient)
+        # assert that the degree of r1i is 2n - 2
+        assert len(r1i.coefficients) - 1 == 2 * n - 2
+
+        # Assert that ct0i = ct0i_hat + r1i * qi + r2i * cyclo mod Zp
+        lhs = ct0i
+        rhs = ct0i_hat + (r1i.scalar_mul(qis[i])) + (r2i * cyclo)
+
+        # remove the leading zeroes from rhs until the length of rhs.coefficients is equal to n
+        while len(rhs.coefficients) > n and rhs.coefficients[0] == 0:
+            rhs.coefficients.pop(0)
+
+        assert lhs == rhs
+
+        # ct1_hat = pk1 * u + e1 
+        ct1i_hat = pk1 * u + e1
+        assert(len(ct1i_hat.coefficients) - 1 == 2 * n - 2)
+
+        ct1i_hat_clone = copy.deepcopy(ct1i_hat)
+
+        ct1i_hat_clone.reduce_coefficients_by_cyclo(cyclo.coefficients)
+        ct1i_hat_clone.reduce_coefficients_by_modulus(qis[i])
+        assert ct1i_hat_clone == ct1i
+
+        #Calculating the p2i and p1i for ct1i is same as we calculating the r2i and r1i 
+        num = ct1i + ct1i_hat.scalar_mul(-1)
+        num.reduce_coefficients_by_modulus(qis[i])
+
+        (quotient,rem) = poly_div(num.coefficients,cyclo.coefficients)
+        assert rem == []
+
+        p2i = Polynomial(quotient)
+        assert len(p2i.coefficients) - 1 == n - 2
+
+        #assert ct1i - ct1i_hat = p2i * cyclo mod zqi
+        lhs = ct1i + ct1i_hat.scalar_mul(-1) 
+        rhs = p2i * cyclo
+
+        #reduce the coefficients of lhs by modulus qi 
+        lhs.reduce_coefficients_by_modulus(qis[i])
+        assert lhs == rhs
+
+        num = ct1i + ct1i_hat.scalar_mul(-1) + (p2i * cyclo).scalar_mul(-1)
+        (quotient,rem) = poly_div(num.coefficients,[qis[i]])
+
+        assert rem == []
+        p1i = Polynomial(quotient)
+
+        lhs = ct1i
+        rhs = ct1i_hat + (p1i * Polynomial([qis[i]]) + (p2i * cyclo))
+
+        for j in range(len(rhs.coefficients)):
+            if rhs.coefficients[j] != 0:
+                rhs.coefficients = rhs.coefficients[j:]
+                break
+
+        assert lhs == rhs
+
+        pk1is.append(pk1)
+        p2is.append(p2i)
+        p1is.append(p1i)
+        ct1is.append(ct1i)
+        ct1is_hat.append(ct1i_hat)
+        r2is.append(r2i)
+        r1is.append(r1i)
+        k0is.append(k0i)
+        ct0is.append(ct0i)
+        ct0is_hat.append(ct0i_hat)
+        pk0is.append(pk0)
+
+    # `r1_bounds` are the bounds for the coefficients of r1i for each CRT basis
+    r1_bounds = []
+
+    # `r2_bounds` are the bounds for the coefficients of r2i for each CRT basis
+    r2_bounds = []
+
+    # `p1_bounds` are the bounds for the coefficients of p1i for each CRT basis
+    p1_bounds = []
+
+    # `p2_bounds` are the bounds for the coefficients of p2i for each CRT basis
+    p2_bounds = []    
+
+    '''
+    CIRCUIT - PHASE 0 - ASSIGNMENT
+    '''
+
+    # Every assigned value must be an element of the field Zp. Negative coefficients `-z` are assigned as `p - z`
+    pk0i_assigned = []
+    pk1i_assigned = []
+
+    for i,pk0i in enumerate(pk0is):
+        pk0i_assigned.append(assign_to_circuit(pk0i,p))
+        pk1i_assigned.append(assign_to_circuit(pk1is[i],p))
+    
+
+    e0_assigned = assign_to_circuit(e0, p)
+    e1_assigned = assign_to_circuit(e1,p)
+    k1_assigned = assign_to_circuit(k1, p)
+    u_assigned = assign_to_circuit(u,p)
+
+    r1is_assigned = []
+    r2is_assigned = []
+    p1is_assigned = []
+    p2is_assigned = []
+    ct0is_assigned = []
+    ct1is_assigned = []
+
+    for i in range(len(ciphertext)):
+        r1i_assigned = assign_to_circuit(r1is[i], p)
+        r2i_assigned = assign_to_circuit(r2is[i], p)
+        p1i_assigned = assign_to_circuit(p1is[i],p)
+        p2i_assigned = assign_to_circuit(p2is[i],p)
+        ct0_assigned = assign_to_circuit(ct0is[i],p)
+        ct1_assigned = assign_to_circuit(ct1is[i],p)
+        p1is_assigned.append(p1i_assigned)
+        p2is_assigned.append(p2i_assigned)
+        r1is_assigned.append(r1i_assigned)
+        r2is_assigned.append(r2i_assigned)
+        ct0is_assigned.append(ct0_assigned)
+        ct1is_assigned.append(ct1_assigned)
+
+
+
+    # For the sake of simplicity, we generate a random challenge here
+    gamma = randint(0, 1000)
+
+    '''
+    CIRCUIT - PHASE 1 - ASSIGNMENT
+    '''
+
+    # Every assigned value must be an element of the field Zp. Negative coefficients `-z` are assigned as `p - z`
+    qi_constants = []
+    k0i_constants = []
+
+
+
+    for i in range(len(ciphertext)):
+       
+
+        qi_constants.append(qis[i])
+
+        k0i_constant = assign_to_circuit(Polynomial([k0is[i]]), p).coefficients[0]
+        k0i_constants.append(k0i_constant)
+
+    cyclo_at_gamma = cyclo.evaluate(gamma)
+    cyclo_at_gamma_assigned = assign_to_circuit(Polynomial([cyclo_at_gamma]), p).coefficients[0]
+
+
+    '''
+    CIRCUIT - PHASE 1 - RANGE CHECK
+    '''
+
+    lookup_bits = 8
+
+
+    b = int(discrete_gaussian.z_upper)
+    # constraint. The coefficients of e should be in the range [-B, B] where B is the upper bound of the discrete Gaussian distribution
+    assert all(coeff >= -b and coeff <= b for coeff in e.coefficients)
+    # After the circuit assignement, the coefficients of e_assigned must be in [0, B] or [p - B, p - 1]
+    assert all(coeff in range(0, b+1) or coeff in range(p - b, p) for coeff in e0_assigned.coefficients)
+    # To perform a range check with a smaller lookup table, we shift the coefficients of e_assigned to be in [0, 2B] (the shift operation is constrained inside the circuit)
+    e0_shifted = Polynomial([(coeff + b) % p for coeff in e0_assigned.coefficients])
+    assert all(coeff >= 0 and coeff <= 2*b for coeff in e0_shifted.coefficients)
+
+    # constraint. The coefficients of e1 should be in the range [-B, B] where B is the upper bound of the discrete Gaussian distribution
+    assert all(coeff >= -b and coeff <= b for coeff in e1.coefficients)
+    # After the circuit assignement, the coefficients of e1_assigned must be in [0, B] or [p - B, p - 1]
+    assert all(coeff in range(0, b+1) or coeff in range(p - b, p) for coeff in e1_assigned.coefficients)
+    # To perform a range check with a smaller lookup table, we shift the coefficients of e1_assigned to be in [0, 2B] (the shift operation is constrained inside the circuit)
+    e1_shifted = Polynomial([(coeff + b) % p for coeff in e1_assigned.coefficients])
+    assert all(coeff >= 0 and coeff <= 2*b for coeff in e1_shifted.coefficients)
+
+    u_bound = 1
+    # constraint. The coefficients of s should be in the range [-1, 0, 1]
+    assert all(coeff >= -u_bound and coeff <= u_bound for coeff in s.coefficients)
+    # After the circuit assignement, the coefficients of u_assigned must be in [0, 1, p - 1]
+    assert all(coeff in range(0, u_bound+1) or coeff in range(p - u_bound, p) for coeff in u_assigned.coefficients)
+    # To perform a range check with a smaller lookup table, we shift the coefficients of u_assigned to be in [0, 1, 2] (the shift operation is constrained inside the circuit)
+    u_shifted = Polynomial([(coeff + 1) % p for coeff in u_assigned.coefficients])
+    assert all(coeff >= 0 and coeff <= 2*u_bound for coeff in u_shifted.coefficients)
+
+    # constraint. The coefficients of k1 should be in the range [-(t-1)/2, (t-1)/2]
+    k1_bound = int((t - 1) / 2)
+    assert all(coeff >= -k1_bound and coeff <= k1_bound for coeff in k1.coefficients)
+    # After the circuit assignement, the coefficients of k1_assigned must be in [0, k1_bound] or [p - k1_bound, p - 1] 
+    assert all(coeff in range(0, int(k1_bound) + 1) or coeff in range(p - int(k1_bound), p) for coeff in k1_assigned.coefficients)
+    # To perform a range check with a smaller lookup table, we shift the coefficients of k1_assigned to be in [0, 2*k1_bound] (the shift operation is constrained inside the circuit)
+    k1_shifted = Polynomial([(coeff + int(k1_bound)) % p for coeff in k1_assigned.coefficients])
+    assert all(coeff >= 0 and coeff <= 2*k1_bound for coeff in k1_shifted.coefficients)
+   
+    e0_at_gamma_assigned = e0_assigned.evaluate(gamma)
+
+    e1_at_gamma_assigned = e1_assigned.evaluate(gamma)
+
+    k1_at_gamma_assigned = k1_assigned.evaluate(gamma)
+
+    u_at_gamma_assigned = u_assigned.evaluate(gamma)
+
+    pk_bound = []
+
+    for i in range(len(ciphertext)):
+      # sanity check. The coefficients of ct0i and ct1i should be in the range [-(qi-1)/2, (qi-1)/2]
+        bound = int((qis[i] - 1) / 2)
+        assert all(coeff >= -bound and coeff <= bound for coeff in ct0is[i].coefficients)
+        assert all(coeff >= -bound and coeff <= bound for coeff in ct1is[i].coefficients)
+
+
+        # sanity check. The coefficients of ai should be in the range [-(qi-1)/2, (qi-1)/2]
+        bound = int((qis[i] - 1) / 2)
+        assert all(coeff >= -bound and coeff <= bound for coeff in ais[i].coefficients)
+
+        # sanity check. The coefficients of ai * s should be in the range $[-N \cdot \frac{q_i - 1}{2}, N \cdot \frac{q_i - 1}{2}]$
+        bound = int((qis[i] - 1) / 2) * n
+        res = ais[i] * s
+        assert all(coeff >= -bound and coeff <= bound for coeff in res.coefficients)
+
+
+        # sanity check. The coefficients of pk0 = ai * s + e should be in the range $- (N \cdot \frac{q_i - 1}{2} + B), N \cdot \frac{q_i - 1}{2} + B]$
+        bound = int(n * ((qis[i] - 1) / 2) + b)
+        res = ais[i] * s + e
+        assert all(coeff >= -bound and coeff <= bound for coeff in res.coefficients)
+
+
+        #constraint .The coefficient of pk0i_assigned and pk1i_assigned should be in range [-(qi-1)/2 , (qi-1)/2 ]
+        pk0_bound = int((qis[i] - 1) / 2)
+        pk_bound.append(pk0_bound)
+
+
+        assert all(coeff >= -pk0_bound and coeff <= pk0_bound for coeff in pk0is[i].coefficients)
+        assert all(coeff >= -pk0_bound and coeff <= pk0_bound for coeff in pk1is[i].coefficients)
+
+
+        # After the circuit assignement, the coefficients of pk0i_assigned[i] and pk1i_assigned[i] must be in [0, pk0_bound] or [p - pk0_bound, p - 1] 
+        assert all(coeff in range(0, int(pk0_bound) + 1) or coeff in range(p - int(pk0_bound), p) for coeff in pk0i_assigned[i].coefficients)
+        assert all(coeff in range(0, int(pk0_bound) + 1) or coeff in range(p - int(pk0_bound), p) for coeff in pk1i_assigned[i].coefficients)
+
+        # To perform a range check with a smaller lookup table, we shift the coefficients of pk0i_assigned and pk1i_assigned to be in [0, 2*pk0_bound] (the shift operation is constrained inside the circuit)
+        pk0i_shifted = Polynomial([(coeff + int(pk0_bound)) % p for coeff in pk0i_assigned[i].coefficients])
+        assert all(coeff >= 0 and coeff <= 2*pk0_bound for coeff in pk0i_shifted.coefficients)
+
+        pk1i_shifted = Polynomial([(coeff + int(pk0_bound)) % p for coeff in pk1i_assigned[i].coefficients])
+        assert all(coeff >= 0 and coeff <= 2*pk0_bound for coeff in pk1i_shifted.coefficients)
+
+        #sanity check . the coefficient of pk0is[i] * u should be in range [(-n*(qis-1)/2),(n*(qis-1)/2)]
+        bound = int((qis[i] - 1) /2 ) * n
+        res = pk0is[i] * u
+        assert all(coeff >= -bound and coeff <= bound for coeff in res.coefficients)
+
+        #sanity check , the coefficient of pk0is[i] * u + e0 should be in range [(-n*(qis-1)/2) + b,(n*(qis-1)/2) + b]
+        bound = int((qis[i] - 1) / 2) * n + b
+        res = pk0is[i] * u + e0
+        assert all(coeff >= -bound and coeff <= bound for coeff in res.coefficients)
+
+        # sanity check. The coefficients of ct0i_hat (pk0is[i] * u + e0 + k1 * k0i) should be in the range $[- (N \cdot \frac{q_i - 1}{2} + B +\frac{t - 1}{2} \cdot |K_{0,i}|), N \cdot \frac{q_i - 1}{2} + B + \frac{t - 1}{2} \cdot |K_{0,i}|]$
+        bound = int((qis[i] - 1) / 2) * n + b + int((t - 1) / 2) * abs(k0is[i])
+        assert all(coeff >= -bound and coeff <= bound for coeff in ct0is_hat[i].coefficients)
+
+
+        # constraint. The coefficients of r2i should be in the range [-(qi-1)/2, (qi-1)/2]
+        r2i_bound = int((qis[i] - 1) / 2)
+        r2_bounds.append(r2i_bound)
+        assert all(coeff >= -r2i_bound and coeff <= r2i_bound for coeff in r2is[i].coefficients)
+        # After the circuit assignement, the coefficients of r2i_assigned must be in [0, r2i_bound] or [p - r2i_bound, p - 1] 
+        assert all(coeff in range(0, int(r2i_bound) + 1) or coeff in range(p - int(r2i_bound), p) for coeff in r2is_assigned[i].coefficients)
+        # To perform a range check with a smaller lookup table, we shift the coefficients of r2i_assigned to be in [0, 2*r2i_bound] (the shift operation is constrained inside the circuit)
+        r2i_shifted = Polynomial([(coeff + int(r2i_bound)) % p for coeff in r2is_assigned[i].coefficients])
+        assert all(coeff >= 0 and coeff <= 2*r2i_bound for coeff in r2i_shifted.coefficients)
+
+        # constraint. The coefficients of (ct0i - ct0i_hat - r2i * cyclo) / qi = r1i should be in the range $[\frac{- ((N+2) \cdot \frac{q_i - 1}{2} + B +\frac{t - 1}{2} \cdot |K_{0,i}|)}{q_i}, \frac{(N+2) \cdot \frac{q_i - 1}{2} + B + \frac{t - 1}{2} \cdot |K_{0,i}|}{q_i}]$
+        r1i_bound = (int((qis[i] - 1) / 2) * (n + 2) + b + int((t - 1) / 2) * abs(k0is[i])) / qis[i]
+        # round bound to the nearest integer
+        r1i_bound = int(r1i_bound)
+        r1_bounds.append(r1i_bound)
+        assert all(coeff >= -r1i_bound and coeff <= r1i_bound for coeff in r1is[i].coefficients)
+        # After the circuit assignement, the coefficients of r1i_assigned must be in [0, r1i_bound] or [p - r1i_bound, p - 1]
+        assert all(coeff in range(0, int(r1i_bound) + 1) or coeff in range(p - int(r1i_bound), p) for coeff in r1is_assigned[i].coefficients)
+        # To perform a range check with a smaller lookup table, we shift the coefficients of r1i_assigned to be in [0, 2*r1i_bound] (the shift operation is constrained inside the circuit)
+        r1i_shifted = Polynomial([(coeff + int(r1i_bound)) % p for coeff in r1is_assigned[i].coefficients])
+        assert all(coeff >= 0 and coeff <= 2*r1i_bound for coeff in r1i_shifted.coefficients)
+
+        # constraint. The coefficients of p2i should be in the range [-(qi-1)/2, (qi-1)/2]
+        p2i_bound = int((qis[i] - 1) / 2)
+        p2_bounds.append(p2i_bound)
+        assert all(coeff >= -p2i_bound and coeff <= p2i_bound for coeff in p2is[i].coefficients)
+        # After the circuit assignement, the coefficients of p2i_assigned must be in [0, p2i_bound] or [p - p2i_bound, p - 1] 
+        assert all(coeff in range(0, int(p2i_bound) + 1) or coeff in range(p - int(p2i_bound), p) for coeff in p2is_assigned[i].coefficients)
+        # To perform a range check with a smaller lookup table, we shift the coefficients of p2i_assigned to be in [0, 2*p2i_bound] (the shift operation is constrained inside the circuit)
+        p2i_shifted = Polynomial([(coeff + int(p2i_bound)) % p for coeff in p2is_assigned[i].coefficients])
+        assert all(coeff >= 0 and coeff <= 2*p2i_bound for coeff in p2i_shifted.coefficients)
+
+        # constraint. The coefficients of (ct1i - ct1i_hat - p2i * cyclo) / qi = p1i should be in the range $[\frac{- ((N+2) \cdot \frac{q_i - 1}{2} + B)}{q_i}, \frac{(N+2) \cdot \frac{q_i - 1}{2} + B}{q_i}]$
+        p1i_bound = (int((qis[i] - 1) / 2) * (n + 2) + b ) / qis[i]
+        # round bound to the nearest integer
+        p1i_bound = int(p1i_bound)
+        p1_bounds.append(p1i_bound)
+        assert all(coeff >= -p1i_bound and coeff <= p1i_bound for coeff in p1is[i].coefficients)
+        # After the circuit assignement, the coefficients of p1i_assigned must be in [0, p1i_bound] or [p - p1i_bound, p - 1]
+        assert all(coeff in range(0, int(p1i_bound) + 1) or coeff in range(p - int(p1i_bound), p) for coeff in p1is_assigned[i].coefficients)
+        # To perform a range check with a smaller lookup table, we shift the coefficients of p1i_assigned to be in [0, 2*p1i_bound] (the shift operation is constrained inside the circuit)
+        p1i_shifted = Polynomial([(coeff + int(p1i_bound)) % p for coeff in p1is_assigned[i].coefficients])
+        assert all(coeff >= 0 and coeff <= 2*p1i_bound for coeff in p1i_shifted.coefficients)
+
+        # sanity check. The coefficients of r2i * cyclo should be in the range [-(qi-1)/2, (qi-1)/2]
+        bound = int((qis[i] - 1) / 2)
+        res = r2is[i] * cyclo
+        assert all(coeff >= -bound and coeff <= bound for coeff in res.coefficients)
+
+        # sanity check. The coefficients of k1 * k0i should be in the range $[-\frac{t - 1}{2} \cdot |K_{0,i}|, \frac{t - 1}{2} \cdot |K_{0,i}|]$
+        bound = int((t - 1) / 2) * abs(k0is[i])
+        res = k1.scalar_mul(k0is[i])
+        assert all(coeff >= -bound and coeff <= bound for coeff in res.coefficients)    
+
+        # sanity check. The coefficients of ct0i - ct0i_hat should be in the range $ [- ((N+1) \cdot \frac{q_i - 1}{2} + B +\frac{t - 1}{2} \cdot |K_{0,i}|), (N+1) \cdot \frac{q_i - 1}{2} + B + \frac{t - 1}{2} \cdot |K_{0,i}|]$
+        bound = int((qis[i] - 1) / 2) * (n + 1) + b + int((t - 1) / 2) * abs(k0is[i])
+        sub = ct0is[i] + (ct0is_hat[i].scalar_mul(-1))
+        assert all(coeff >= -bound and coeff <= bound for coeff in sub.coefficients)
+
+        # sanity check. The coefficients of ct0i - ct0i_hat - r2i * cyclo should be in the range $[- ((N+2) \cdot \frac{q_i - 1}{2} + B +\frac{t - 1}{2} \cdot |K_{0,i}|), (N+2) \cdot \frac{q_i - 1}{2} + B + \frac{t - 1}{2} \cdot |K_{0,i}|]$
+        bound = ((qis[i] - 1) / 2) * (n + 2) + b + ((t - 1) / 2) * abs(k0is[i])
+        sub = ct0is[i]  + (ct0is_hat[i].scalar_mul(-1)) + (r2is[i] * cyclo).scalar_mul(-1)
+        assert all(coeff >= -bound and coeff <= bound for coeff in sub.coefficients)
+
+        # sanity check. The coefficients of p2is[i] * cyclo should be in the range [-(qi-1)/2, (qi-1)/2]
+        bound = int((qis[i] - 1) / 2)
+        res = p2is[i] * cyclo
+        assert all(coeff >= -bound and coeff <= bound for coeff in res.coefficients)
+
+        # sanity check. The coefficients of ct1i[i] - ct1i_hat[i] should be in the range $ [- ((N+1) \cdot \frac{q_i - 1}{2} + B), (N+1) \cdot \frac{q_i - 1}{2} + B]$
+        bound = int((qis[i] - 1) / 2) * (n + 1) + b
+        sub = ct1is[i] + ct1is_hat[i].scalar_mul(-1)
+        assert all(coeff >= -bound and coeff <= bound for coeff in sub.coefficients)
+
+        # sanity check. The coefficients of ct1i[i] - ct1i_hat[i] - p2is[i] * cyclo should be in the range $[- ((N+2) \cdot \frac{q_i - 1}{2} + B), (N+2) \cdot \frac{q_i - 1}{2} + B]$
+        bound = int((qis[i] - 1) / 2) * (n + 2) + b
+        sub = ct1is[i] + (ct1is_hat[i].scalar_mul(-1)) +  (p2is[i] * cyclo).scalar_mul(-1)
+        assert all(coeff >= -bound and coeff <= bound for coeff in sub.coefficients)
+
+
+
+
+        '''
+        CIRCUIT - PHASE 1 - EVALUATION AT GAMMA CONSTRAINT
+        '''
+
+        r1i_gamma_assigned = r1is_assigned[i].evaluate(gamma)
+        r2i_gamma_assigned = r2is_assigned[i].evaluate(gamma)
+
+        pk0i_at_gamma = pk0is[i].evaluate(gamma)
+        pk0i_at_gamma_assigned = assign_to_circuit(Polynomial([pk0i_at_gamma]),p).coefficients[0]
+
+        p1i_gamma_assigned = p1is_assigned[i].evaluate(gamma)
+        p2i_gamma_assigned = p2is_assigned[i].evaluate(gamma)
+
+        pk1i_at_gamma = pk1is[i].evaluate(gamma)
+        pk1i_at_gamma_assigned = assign_to_circuit(Polynomial([pk1i_at_gamma]),p).coefficients[0]
+
+
+        '''
+        CIRCUIT - PHASE 1 - CORRECT ENCRYPTION CONSTRAINT
+        '''
+
+        lhs = ct0is_assigned[i].evaluate(gamma)
+        rhs = (pk0i_at_gamma_assigned * u_at_gamma_assigned + e0_at_gamma_assigned + (k1_at_gamma_assigned * k0i_constants[i]) + (r1i_gamma_assigned * qi_constants[i]) + (r2i_gamma_assigned * cyclo_at_gamma_assigned))
+
+        assert lhs % p == rhs % p
+
+        lhs = ct1is_assigned[i].evaluate(gamma)
+        rhs = (pk1i_at_gamma_assigned * u_at_gamma_assigned + e1_at_gamma_assigned + p2i_gamma_assigned * cyclo_at_gamma_assigned + p1i_gamma_assigned * qi_constants[i])
+
+        assert lhs % p == rhs % p
+        '''
+        VERIFICATION PHASE
+        '''
+
+        cyclo_at_gamma = cyclo.evaluate(gamma)
+        cyclo_at_gamma_assigned_expected = assign_to_circuit(Polynomial([cyclo_at_gamma]), p).coefficients[0]
+        assert cyclo_at_gamma_assigned == cyclo_at_gamma_assigned_expected
+
+        
+        pk0i_gamma = pk0is[i].evaluate(gamma)
+        pk0i_gamma_assigned_expected = assign_to_circuit(Polynomial([pk0i_gamma]), p).coefficients[0]
+        assert pk0i_at_gamma_assigned == pk0i_gamma_assigned_expected
+
+        ct0i_gamma = ciphertext[i][0].evaluate(gamma)
+        ct0i_gamma_assigned_expected = assign_to_circuit(Polynomial([ct0i_gamma]), p).coefficients[0]
+        assert ct0is_assigned[i].evaluate(gamma) % p == ct0i_gamma_assigned_expected
+
+        pk1i_gamma = pk1is[i].evaluate(gamma)
+        pk1i_gamma_assigned_expected = assign_to_circuit(Polynomial([pk1i_gamma]), p).coefficients[0]
+        assert pk1i_at_gamma_assigned == pk1i_gamma_assigned_expected 
+
+        ct1i_gamma = ciphertext[i][1].evaluate(gamma)
+        ct1i_gamma_assigned_expected = assign_to_circuit(Polynomial([ct1i_gamma]), p).coefficients[0]
+        assert ct1is_assigned[i].evaluate(gamma) % p == ct1i_gamma_assigned_expected
+
+
+        assert qis[i] == qi_constants[i]
+
+        k0i_assigned_expected = assign_to_circuit(Polynomial([k0is[i]]), p).coefficients[0]
+        assert k0i_constants[i] == k0i_assigned_expected
+
+    #  ct0is and ct1is need to be parsed such that their coefficients are in the range [0, p - 1]
+    ct0is_in_p = [assign_to_circuit(ct0i, p) for ct0i in ct0is]
+    ct1is_in_p = [assign_to_circuit(ct1i, p) for ct1i in ct1is]
+    
+    # Parse the inputs into a JSON format such this can be used as input for the (real) circuit
+    json_input = {
+        "pk0i": [[str(coef) for coef in pk0i.coefficients] for pk0i in pk0i_assigned],
+        "pk1i": [[str(coef) for coef in pk1i.coefficients] for pk1i in pk1i_assigned],
+        "u": [str(coef) for coef in u_assigned.coefficients],
+        "e0": [str(coef) for coef in e0_assigned.coefficients],
+        "e1": [str(coef) for coef in e1_assigned.coefficients],
+        "k1": [str(coef) for coef in k1_assigned.coefficients],
+        "r2is": [[str(coef) for coef in r2i.coefficients] for r2i in r2is_assigned],
+        "r1is": [[str(coef) for coef in r1i.coefficients] for r1i in r1is_assigned],
+        "p2is": [[str(coef) for coef in p2i.coefficients] for p2i in p2is_assigned],
+        "p1is": [[str(coef) for coef in p1i.coefficients] for p1i in p1is_assigned],
+        "ct0is": [[str(coef) for coef in ct0i_in_p.coefficients] for ct0i_in_p in ct0is_in_p],
+        "ct1is": [[str(coef) for coef in ct0i_in_p.coefficients] for ct0i_in_p in ct1is_in_p],
+    }
+
+    # Calculate the bit size of the largest qi in qis for the filename
+    qis_bitsize = max(qis).bit_length()
+    qis_len = len(qis)
+
+    # Construct the dynamic filename
+    filename = f"pk_enc_{args.n}_{qis_len}x{qis_bitsize}_{args.t}.json"
+
+    output_path = os.path.join("src", "data","pk_enc_data", filename)
+
+    with open(output_path, 'w') as f:
+        json.dump(json_input, f)
+
+    # Initialize a structure to hold polynomials with zero coefficients. This will be used at key generation.
+    json_input_zeroes = {
+        "pk0i":[["0" for _ in pk0i.coefficients] for pk0i in pk0i_assigned],
+        "pk1i":[["0" for _ in pk1i.coefficients] for pk1i in pk1i_assigned],
+        "u": ["0" for _ in u_assigned.coefficients],
+        "e0": ["0" for _ in e0_assigned.coefficients],
+        "e1": ["0" for _ in e1_assigned.coefficients],
+        "k1": ["0" for _ in k1_assigned.coefficients],
+        "r2is": [["0" for _ in r2i.coefficients] for r2i in r2is_assigned],
+        "r1is": [["0" for _ in r1i.coefficients] for r1i in r1is_assigned],
+        "p2is": [["0" for _ in p2i.coefficients] for p2i in p2is_assigned],
+        "p1is": [["0" for _ in p1i.coefficients] for p1i in p1is_assigned],
+        "ct0is": [["0" for _ in ct0i_in_p.coefficients] for ct0i_in_p in ct0is_in_p],
+        "ct1is": [["0" for _ in ct1i_in_p.coefficients] for ct1i_in_p in ct1is_in_p],
+    }
+
+    output_path = os.path.join("src", "data","pk_enc_data", f"pk_enc_{args.n}_{qis_len}x{qis_bitsize}_{args.t}_zeroes.json")
+
+    with open(output_path, 'w') as f:
+        json.dump(json_input_zeroes, f)
+
+    output_path = os.path.join("src", "constants","pk_enc_constants", f"pk_enc_constants_{args.n}_{qis_len}x{qis_bitsize}_{args.t}.rs")
+
+    with open(output_path, 'w') as f:
+        f.write(f"/// `N` is the degree of the cyclotomic polynomial defining the ring `Rq = Zq[X]/(X^N + 1)`.\n")
+        f.write(f"pub const N: usize = {n};\n")
+        f.write(f"///'The coefficients pf the polynomial 'pk0is` and 'pk1is' should exist in the interval '[-PK_BOUND, PK_BOUND]`.\n")
+        pk_bound_str = ', '.join(map(str,pk_bound))
+        f.write(f"pub const PK_BOUND :[u64; {len(pk_bound)}] = [{pk_bound_str}];\n")
+        f.write(f"///'The coefficients pf the polynomial 'pk1is` should exist in the interval '[-PK0_BOUND, PK0_BOUND]`.\n")
+        f.write(f"/// The coefficients of the polynomial `e` should exist in the interval `[-E_BOUND, E_BOUND]` where `E_BOUND` is the upper bound of the gaussian distribution with 𝜎 = 3.2\n")
+        f.write(f"pub const E_BOUND: u64 = {b};\n")
+        f.write(f"/// The coefficients of the polynomial `s` should exist in the interval `[-S_BOUND, S_BOUND]`.\n")
+        f.write(f"pub const U_BOUND: u64 = {1};\n")
+        f.write(f"/// The coefficients of the polynomials `r1is` should exist in the interval `[-R1_BOUND[i], R1_BOUND[i]]` where `R1_BOUND[i]` is equal to `(qi-1)/2`\n")
+        f.write(f"pub const R1_BOUNDS: [u64; {len(r1_bounds)}] = [{', '.join(map(str, r1_bounds))}];\n")
+        f.write(f"/// The coefficients of the polynomials `r2is` should exist in the interval `[-R2_BOUND[i], R2_BOUND[i]]` where `R2_BOUND[i]` is equal to $\\frac{{(N+2) \\cdot \\frac{{q_i - 1}}{{2}} + B + \\frac{{t - 1}}{{2}} \\cdot |K_{{0,i}}|}}{{q_i}}$\n")
+        f.write(f"pub const R2_BOUNDS: [u64; {len(r2_bounds)}] = [{', '.join(map(str, r2_bounds))}];\n")
+        f.write(f"/// The coefficients of the polynomials `p1is` should exist in the interval `[-P1_BOUND[i], P1_BOUND[i]]` where `P1_BOUND[i]` is equal to (((qis[i] - 1) / 2) * (n + 2) + b ) / qis[i] \n")
+        f.write(f"pub const P1_BOUNDS: [u64; {len(p1_bounds)}] = [{', '.join(map(str, p1_bounds))}];\n")
+        f.write(f"/// The coefficients of the polynomials `p2is` should exist in the interval `[-P2_BOUND[i], P2_BOUND[i]]` where `P2_BOUND[i]` is equal to (qis[i] - 1) / 2  \n")
+        f.write(f"pub const P2_BOUNDS: [u64; {len(p2_bounds)}] = [{', '.join(map(str, p2_bounds))}];\n")
+        f.write(f"/// The coefficients of `k1` should exist in the interval `[-K1_BOUND, K1_BOUND]` where `K1_BOUND` is equal to `(t-1)/2`\n")
+        f.write(f"pub const K1_BOUND: u64 = {k1_bound};\n")
+        qis_str = ', '.join(f'"{q}"' for q in qi_constants)
+        f.write(f"/// List of scalars `qis` such that `qis[i]` is the modulus of the i-th CRT basis of `q` (ciphertext space modulus)\n")
+        f.write(f"pub const QIS: [&str; {len(qi_constants)}] = [{qis_str}];\n")
+        k0is_str = ', '.join(f'"{k0i}"' for k0i in k0i_constants)
+        f.write(f"/// List of scalars `k0is` such that `k0i[i]` is equal to the negative of the multiplicative inverses of t mod qi.\n")
+        f.write(f"pub const K0IS: [&str; {len(k0i_constants)}] = [{k0is_str}];\n")
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser(
+        description="Generate rust constants and json inputs for BFV zk proof of secret key encryption circuit"
+    )
+    parser.add_argument(
+        "-n", type=int, required=True, help="Degree of f(x), must be a power of 2."
+    )
+    parser.add_argument(
+        "-qis", type=str, required=True, help="List of qis such that qis[i] is the modulus of the i-th CRT basis of the modulus q of the ciphertext space."
+    )
+    parser.add_argument(
+        "-t", type=int, required=True, help="Modulus t of the plaintext space."
+    )
+
+    args = parser.parse_args()
+    main(args)
diff --git a/scripts/circuit_sk.py b/scripts/circuit_sk.py
index 7667d51..f6ae9bb 100644
--- a/scripts/circuit_sk.py
+++ b/scripts/circuit_sk.py
@@ -9,6 +9,8 @@
 import argparse
 import json
 
+
+
 def main(args): 
     
     '''
@@ -36,9 +38,9 @@ def main(args):
 
     ctis = bfv_crt.SecretKeyEncrypt(s, ais, e, m)
 
-    # Sanity check for valid decryption    
+    # Sanity check for valid decryption
     message_prime = bfv_crt.Decrypt(s, ctis)
-
+        
     assert m == message_prime
 
     # k1 = [QM]t namely the scaled message polynomial
@@ -290,7 +292,7 @@ def main(args):
         res = ais[i] * s + e
         assert all(coeff >= -bound and coeff <= bound for coeff in res.coefficients)
 
-        # constraint. The coefficients of r2i should be in the range [-(qi-1)/2, (qi-1)/2]
+        # constraint. The coefficients of r`2i should be in the range [-(qi-1)/2, (qi-1)/2]
         r2i_bound = int((qis[i] - 1) / 2)
         r2_bounds.append(r2i_bound)
         assert all(coeff >= -r2i_bound and coeff <= r2i_bound for coeff in r2is[i].coefficients)
@@ -411,7 +413,7 @@ def main(args):
     # Construct the dynamic filename
     filename = f"sk_enc_{args.n}_{qis_len}x{qis_bitsize}_{args.t}.json"
 
-    output_path = os.path.join("src", "data", filename)
+    output_path = os.path.join("src", "data", "sk_enc_data",filename)
 
     with open(output_path, 'w') as f:
         json.dump(json_input, f)
@@ -427,12 +429,12 @@ def main(args):
         "ct0is": [["0" for _ in ct0i_in_p.coefficients] for ct0i_in_p in ct0is_in_p],
     }
 
-    output_path = os.path.join("src", "data", f"sk_enc_{args.n}_{qis_len}x{qis_bitsize}_{args.t}_zeroes.json")
+    output_path = os.path.join("src", "data","sk_enc_data", f"sk_enc_{args.n}_{qis_len}x{qis_bitsize}_{args.t}_zeroes.json")
 
     with open(output_path, 'w') as f:
         json.dump(json_input_zeroes, f)
 
-    output_path = os.path.join("src", "constants", f"sk_enc_constants_{args.n}_{qis_len}x{qis_bitsize}_{args.t}.rs")
+    output_path = os.path.join("src", "constants","sk_enc_constants", f"sk_enc_constants_{args.n}_{qis_len}x{qis_bitsize}_{args.t}.rs")
 
     with open(output_path, 'w') as f:
         f.write(f"/// `N` is the degree of the cyclotomic polynomial defining the ring `Rq = Zq[X]/(X^N + 1)`.\n")
diff --git a/scripts/requirements.txt b/scripts/requirements.txt
index 7aca885..425418c 100644
--- a/scripts/requirements.txt
+++ b/scripts/requirements.txt
@@ -1 +1 @@
-bfv @ git+https://github.com/enricobottazzi/bfv-py.git@e8239e946cab58c5c9fc974ff726010b71d92dbf
\ No newline at end of file
+git+https://github.com/gnosisguild/bfv-py@no-ntt#egg=bfv
\ No newline at end of file
diff --git a/scripts/utils.py b/scripts/utils.py
index c73b492..9a8a45d 100644
--- a/scripts/utils.py
+++ b/scripts/utils.py
@@ -27,7 +27,7 @@ def count_advice_cells_needed_for_poly_range_check(poly: Polynomial, bound: int,
 
     count = 0
 
-    # 4 advice cells for each coefficient needed for the shift addition operation
+    # 4 advice cells for each coefficient needed for the shift addition operation``
     count += 4 * len(poly.coefficients)
 
     # further advice cells for range check inside `check_less_than_safe`
diff --git a/src/constants/mod.rs b/src/constants/mod.rs
index 30230e5..3477ce3 100644
--- a/src/constants/mod.rs
+++ b/src/constants/mod.rs
@@ -1,6 +1,2 @@
-pub mod sk_enc_constants_1024_1x27_65537;
-pub mod sk_enc_constants_16384_8x54_65537;
-pub mod sk_enc_constants_2048_1x53_65537;
-pub mod sk_enc_constants_32768_15x59_65537;
-pub mod sk_enc_constants_4096_2x55_65537;
-pub mod sk_enc_constants_8192_4x55_65537;
+pub mod pk_enc_constants;
+pub mod sk_enc_constants;
diff --git a/src/constants/pk_enc_constants/mod.rs b/src/constants/pk_enc_constants/mod.rs
new file mode 100644
index 0000000..10e90b0
--- /dev/null
+++ b/src/constants/pk_enc_constants/mod.rs
@@ -0,0 +1 @@
+pub mod pk_enc_constants_1024_15x60_65537;
diff --git a/src/constants/pk_enc_constants/pk_enc_constants_1024_15x60_65537.rs b/src/constants/pk_enc_constants/pk_enc_constants_1024_15x60_65537.rs
new file mode 100644
index 0000000..f2f0e22
--- /dev/null
+++ b/src/constants/pk_enc_constants/pk_enc_constants_1024_15x60_65537.rs
@@ -0,0 +1,108 @@
+/// `N` is the degree of the cyclotomic polynomial defining the ring `Rq = Zq[X]/(X^N + 1)`.
+pub const N: usize = 1024;
+///'The coefficients pf the polynomial 'pk0is` and 'pk1is' should exist in the interval '[-PK_BOUND, PK_BOUND]`.
+pub const PK_BOUND: [u64; 15] = [
+    576460752303292416,
+    576460752299360256,
+    576460752298508288,
+    576460752297984000,
+    576460752297820160,
+    576460752296706048,
+    576460752296411136,
+    576460752296214528,
+    576460752294969344,
+    576460752293265408,
+    576460752292773888,
+    576460752291823616,
+    576460752290938880,
+    576460752290709504,
+    576460752290447360,
+];
+///'The coefficients pf the polynomial 'pk1is` should exist in the interval '[-PK0_BOUND, PK0_BOUND]`.
+/// The coefficients of the polynomial `e` should exist in the interval `[-E_BOUND, E_BOUND]` where `E_BOUND` is the upper bound of the gaussian distribution with 𝜎 = 3.2
+pub const E_BOUND: u64 = 19;
+/// The coefficients of the polynomial `s` should exist in the interval `[-S_BOUND, S_BOUND]`.
+pub const U_BOUND: u64 = 1;
+/// The coefficients of the polynomials `r1is` should exist in the interval `[-R1_BOUND[i], R1_BOUND[i]]` where `R1_BOUND[i]` is equal to `(qi-1)/2`
+pub const R1_BOUNDS: [u64; 15] = [
+    32472, 21654, 32101, 32263, 14784, 16206, 30376, 18254, 9343, 14780, 9752, 27859, 2356, 17131,
+    17884,
+];
+/// The coefficients of the polynomials `r2is` should exist in the interval `[-R2_BOUND[i], R2_BOUND[i]]` where `R2_BOUND[i]` is equal to $\frac{(N+2) \cdot \frac{q_i - 1}{2} + B + \frac{t - 1}{2} \cdot |K_{0,i}|}{q_i}$
+pub const R2_BOUNDS: [u64; 15] = [
+    576460752303292416,
+    576460752299360256,
+    576460752298508288,
+    576460752297984000,
+    576460752297820160,
+    576460752296706048,
+    576460752296411136,
+    576460752296214528,
+    576460752294969344,
+    576460752293265408,
+    576460752292773888,
+    576460752291823616,
+    576460752290938880,
+    576460752290709504,
+    576460752290447360,
+];
+/// The coefficients of the polynomials `p1is` should exist in the interval `[-P1_BOUND[i], P1_BOUND[i]]` where `P1_BOUND[i]` is equal to (((qis[i] - 1) / 2) * (n + 2) + b ) / qis[i]
+pub const P1_BOUNDS: [u64; 15] = [
+    513, 513, 513, 513, 513, 513, 513, 513, 513, 513, 513, 513, 513, 513, 513,
+];
+/// The coefficients of the polynomials `p2is` should exist in the interval `[-P2_BOUND[i], P2_BOUND[i]]` where `P2_BOUND[i]` is equal to (qis[i] - 1) / 2  
+pub const P2_BOUNDS: [u64; 15] = [
+    576460752303292416,
+    576460752299360256,
+    576460752298508288,
+    576460752297984000,
+    576460752297820160,
+    576460752296706048,
+    576460752296411136,
+    576460752296214528,
+    576460752294969344,
+    576460752293265408,
+    576460752292773888,
+    576460752291823616,
+    576460752290938880,
+    576460752290709504,
+    576460752290447360,
+];
+/// The coefficients of `k1` should exist in the interval `[-K1_BOUND, K1_BOUND]` where `K1_BOUND` is equal to `(t-1)/2`
+pub const K1_BOUND: u64 = 32768;
+/// List of scalars `qis` such that `qis[i]` is the modulus of the i-th CRT basis of `q` (ciphertext space modulus)
+pub const QIS: [&str; 15] = [
+    "1152921504606584833",
+    "1152921504598720513",
+    "1152921504597016577",
+    "1152921504595968001",
+    "1152921504595640321",
+    "1152921504593412097",
+    "1152921504592822273",
+    "1152921504592429057",
+    "1152921504589938689",
+    "1152921504586530817",
+    "1152921504585547777",
+    "1152921504583647233",
+    "1152921504581877761",
+    "1152921504581419009",
+    "1152921504580894721",
+];
+/// List of scalars `k0is` such that `k0i[i]` is equal to the negative of the multiplicative inverses of t mod qi.
+pub const K0IS: [&str; 15] = [
+    "1124457781908666798",
+    "743839052427601194",
+    "1111422170948171465",
+    "1117121952253736973",
+    "502126104424574846",
+    "552157518114552474",
+    "1050730055179823439",
+    "624214012656257690",
+    "310690856959624444",
+    "501985369079705462",
+    "325081045565655086",
+    "962154749991507364",
+    "64878992155545191",
+    "584702565692244436",
+    "611213585534257079",
+];
diff --git a/src/constants/pk_enc_constants_1024_15x60_65537.rs b/src/constants/pk_enc_constants_1024_15x60_65537.rs
new file mode 100644
index 0000000..b5c4d16
--- /dev/null
+++ b/src/constants/pk_enc_constants_1024_15x60_65537.rs
@@ -0,0 +1,18 @@
+/// `N` is the degree of the cyclotomic polynomial defining the ring `Rq = Zq[X]/(X^N + 1)`.
+pub const N: usize = 1024;
+///'The coefficients pf the polynomial 'pk0is` should exist in the interval '[-PK0_BOUND, PK0_BOUND]`.
+pub const PK0_BOUND:u64 = 590295810345418096640;
+/// The coefficients of the polynomial `e` should exist in the interval `[-E_BOUND, E_BOUND]` where `E_BOUND` is the upper bound of the gaussian distribution with 𝜎 = 3.2
+pub const E_BOUND: u64 = 19;
+/// The coefficients of the polynomial `s` should exist in the interval `[-S_BOUND, S_BOUND]`.
+pub const u_BOUND: u64 = 1;
+/// The coefficients of the polynomials `r1is` should exist in the interval `[-R1_BOUND[i], R1_BOUND[i]]` where `R1_BOUND[i]` is equal to `(qi-1)/2`
+pub const R1_BOUNDS: [u64; 15] = [32472, 21654, 32101, 32263, 14784, 16206, 30376, 18254, 9343, 14780, 9752, 27859, 2356, 17131, 17884];
+/// The coefficients of the polynomials `r2is` should exist in the interval `[-R2_BOUND[i], R2_BOUND[i]]` where `R2_BOUND[i]` is equal to $\frac{(N+2) \cdot \frac{q_i - 1}{2} + B + \frac{t - 1}{2} \cdot |K_{0,i}|}{q_i}$
+pub const R2_BOUNDS: [u64; 15] = [576460752303292416, 576460752299360256, 576460752298508288, 576460752297984000, 576460752297820160, 576460752296706048, 576460752296411136, 576460752296214528, 576460752294969344, 576460752293265408, 576460752292773888, 576460752291823616, 576460752290938880, 576460752290709504, 576460752290447360];
+/// The coefficients of `k1` should exist in the interval `[-K1_BOUND, K1_BOUND]` where `K1_BOUND` is equal to `(t-1)/2`
+pub const K1_BOUND: u64 = 32768;
+/// List of scalars `qis` such that `qis[i]` is the modulus of the i-th CRT basis of `q` (ciphertext space modulus)
+pub const QIS: [&str; 15] = ["1152921504606584833", "1152921504598720513", "1152921504597016577", "1152921504595968001", "1152921504595640321", "1152921504593412097", "1152921504592822273", "1152921504592429057", "1152921504589938689", "1152921504586530817", "1152921504585547777", "1152921504583647233", "1152921504581877761", "1152921504581419009", "1152921504580894721"];
+/// List of scalars `k0is` such that `k0i[i]` is equal to the negative of the multiplicative inverses of t mod qi.
+pub const K0IS: [&str; 15] = ["1124457781908666798", "743839052427601194", "1111422170948171465", "1117121952253736973", "502126104424574846", "552157518114552474", "1050730055179823439", "624214012656257690", "310690856959624444", "501985369079705462", "325081045565655086", "962154749991507364", "64878992155545191", "584702565692244436", "611213585534257079"];
diff --git a/src/constants/sk_enc_constants/mod.rs b/src/constants/sk_enc_constants/mod.rs
new file mode 100644
index 0000000..8b81ed1
--- /dev/null
+++ b/src/constants/sk_enc_constants/mod.rs
@@ -0,0 +1 @@
+pub mod sk_enc_constants_4096_2x55_65537;
diff --git a/src/constants/sk_enc_constants_4096_2x55_65537.rs b/src/constants/sk_enc_constants/sk_enc_constants_4096_2x55_65537.rs
similarity index 100%
rename from src/constants/sk_enc_constants_4096_2x55_65537.rs
rename to src/constants/sk_enc_constants/sk_enc_constants_4096_2x55_65537.rs
diff --git a/src/constants/sk_enc_constants_1024_15x60_65537.rs b/src/constants/sk_enc_constants_1024_15x60_65537.rs
new file mode 100644
index 0000000..b5c4d16
--- /dev/null
+++ b/src/constants/sk_enc_constants_1024_15x60_65537.rs
@@ -0,0 +1,18 @@
+/// `N` is the degree of the cyclotomic polynomial defining the ring `Rq = Zq[X]/(X^N + 1)`.
+pub const N: usize = 1024;
+///'The coefficients pf the polynomial 'pk0is` should exist in the interval '[-PK0_BOUND, PK0_BOUND]`.
+pub const PK0_BOUND:u64 = 590295810345418096640;
+/// The coefficients of the polynomial `e` should exist in the interval `[-E_BOUND, E_BOUND]` where `E_BOUND` is the upper bound of the gaussian distribution with 𝜎 = 3.2
+pub const E_BOUND: u64 = 19;
+/// The coefficients of the polynomial `s` should exist in the interval `[-S_BOUND, S_BOUND]`.
+pub const u_BOUND: u64 = 1;
+/// The coefficients of the polynomials `r1is` should exist in the interval `[-R1_BOUND[i], R1_BOUND[i]]` where `R1_BOUND[i]` is equal to `(qi-1)/2`
+pub const R1_BOUNDS: [u64; 15] = [32472, 21654, 32101, 32263, 14784, 16206, 30376, 18254, 9343, 14780, 9752, 27859, 2356, 17131, 17884];
+/// The coefficients of the polynomials `r2is` should exist in the interval `[-R2_BOUND[i], R2_BOUND[i]]` where `R2_BOUND[i]` is equal to $\frac{(N+2) \cdot \frac{q_i - 1}{2} + B + \frac{t - 1}{2} \cdot |K_{0,i}|}{q_i}$
+pub const R2_BOUNDS: [u64; 15] = [576460752303292416, 576460752299360256, 576460752298508288, 576460752297984000, 576460752297820160, 576460752296706048, 576460752296411136, 576460752296214528, 576460752294969344, 576460752293265408, 576460752292773888, 576460752291823616, 576460752290938880, 576460752290709504, 576460752290447360];
+/// The coefficients of `k1` should exist in the interval `[-K1_BOUND, K1_BOUND]` where `K1_BOUND` is equal to `(t-1)/2`
+pub const K1_BOUND: u64 = 32768;
+/// List of scalars `qis` such that `qis[i]` is the modulus of the i-th CRT basis of `q` (ciphertext space modulus)
+pub const QIS: [&str; 15] = ["1152921504606584833", "1152921504598720513", "1152921504597016577", "1152921504595968001", "1152921504595640321", "1152921504593412097", "1152921504592822273", "1152921504592429057", "1152921504589938689", "1152921504586530817", "1152921504585547777", "1152921504583647233", "1152921504581877761", "1152921504581419009", "1152921504580894721"];
+/// List of scalars `k0is` such that `k0i[i]` is equal to the negative of the multiplicative inverses of t mod qi.
+pub const K0IS: [&str; 15] = ["1124457781908666798", "743839052427601194", "1111422170948171465", "1117121952253736973", "502126104424574846", "552157518114552474", "1050730055179823439", "624214012656257690", "310690856959624444", "501985369079705462", "325081045565655086", "962154749991507364", "64878992155545191", "584702565692244436", "611213585534257079"];
diff --git a/src/constants/sk_enc_constants_16384_8x54_65537.rs b/src/constants/sk_enc_constants_16384_8x54_65537.rs
deleted file mode 100644
index 6794aa1..0000000
--- a/src/constants/sk_enc_constants_16384_8x54_65537.rs
+++ /dev/null
@@ -1,16 +0,0 @@
-/// `N` is the degree of the cyclotomic polynomial defining the ring `Rq = Zq[X]/(X^N + 1)`.
-pub const N: usize = 16384;
-/// The coefficients of the polynomial `e` should exist in the interval `[-E_BOUND, E_BOUND]` where `E_BOUND` is the upper bound of the gaussian distribution with 𝜎 = 3.2
-pub const E_BOUND: u64 = 19;
-/// The coefficients of the polynomial `s` should exist in the interval `[-S_BOUND, S_BOUND]`.
-pub const S_BOUND: u64 = 1;
-/// The coefficients of the polynomials `r1is` should exist in the interval `[-R1_BOUND[i], R1_BOUND[i]]` where `R1_BOUND[i]` is equal to `(qi-1)/2`
-pub const R1_BOUNDS: [u64; 8] = [16113, 24818, 37593, 34517, 12912, 32948, 38917, 29910];
-/// The coefficients of the polynomials `r2is` should exist in the interval `[-R2_BOUND[i], R2_BOUND[i]]` where `R2_BOUND[i]` is equal to $\frac{(N+2) \cdot \frac{q_i - 1}{2} + B + \frac{t - 1}{2} \cdot |K_{0,i}|}{q_i}$
-pub const R2_BOUNDS: [u64; 8] = [6452516132120967, 6452516132120968, 6452516132120969, 6452516132120970, 6452516132120973, 6452516132120975, 6452516132120976, 6452516132120978];
-/// The coefficients of `k1` should exist in the interval `[-K1_BOUND, K1_BOUND]` where `K1_BOUND` is equal to `(t-1)/2`
-pub const K1_BOUND: u64 = 32768;
-/// List of scalars `qis` such that `qis[i]` is the modulus of the i-th CRT basis of `q` (ciphertext space modulus)
-pub const QIS: [&str; 8] = ["12905032264241935", "12905032264241937", "12905032264241939", "12905032264241941", "12905032264241947", "12905032264241951", "12905032264241953", "12905032264241957"];
-/// List of scalars `k0is` such that `k0i[i]` is equal to the negative of the multiplicative inverses of t mod qi.
-pub const K0IS: [&str; 8] = ["3119285534855982", "6547723161734179", "11578631950954274", "10367425251572977", "1858653883183236", "9749317979689080", "12100252264181577", "8552879692347062"];
diff --git a/src/constants/sk_enc_constants_2048_1x53_65537.rs b/src/constants/sk_enc_constants_2048_1x53_65537.rs
deleted file mode 100644
index f74b157..0000000
--- a/src/constants/sk_enc_constants_2048_1x53_65537.rs
+++ /dev/null
@@ -1,16 +0,0 @@
-/// `N` is the degree of the cyclotomic polynomial defining the ring `Rq = Zq[X]/(X^N + 1)`.
-pub const N: usize = 2048;
-/// The coefficients of the polynomial `e` should exist in the interval `[-E_BOUND, E_BOUND]` where `E_BOUND` is the upper bound of the gaussian distribution with 𝜎 = 3.2
-pub const E_BOUND: u64 = 19;
-/// The coefficients of the polynomial `s` should exist in the interval `[-S_BOUND, S_BOUND]`.
-pub const S_BOUND: u64 = 1;
-/// The coefficients of the polynomials `r1is` should exist in the interval `[-R1_BOUND[i], R1_BOUND[i]]` where `R1_BOUND[i]` is equal to `(qi-1)/2`
-pub const R1_BOUNDS: [u64; 1] = [20368];
-/// The coefficients of the polynomials `r2is` should exist in the interval `[-R2_BOUND[i], R2_BOUND[i]]` where `R2_BOUND[i]` is equal to $\frac{(N+2) \cdot \frac{q_i - 1}{2} + B + \frac{t - 1}{2} \cdot |K_{0,i}|}{q_i}$
-pub const R2_BOUNDS: [u64; 1] = [3471589854547519];
-/// The coefficients of `k1` should exist in the interval `[-K1_BOUND, K1_BOUND]` where `K1_BOUND` is equal to `(t-1)/2`
-pub const K1_BOUND: u64 = 32768;
-/// List of scalars `qis` such that `qis[i]` is the modulus of the i-th CRT basis of `q` (ciphertext space modulus)
-pub const QIS: [&str; 1] = ["6943179709095039"];
-/// List of scalars `k0is` such that `k0i[i]` is equal to the negative of the multiplicative inverses of t mod qi.
-pub const K0IS: [&str; 1] = ["4098612896619616"];
diff --git a/src/constants/sk_enc_constants_32768_15x59_65537.rs b/src/constants/sk_enc_constants_32768_15x59_65537.rs
deleted file mode 100644
index bb6ea2e..0000000
--- a/src/constants/sk_enc_constants_32768_15x59_65537.rs
+++ /dev/null
@@ -1,16 +0,0 @@
-/// `N` is the degree of the cyclotomic polynomial defining the ring `Rq = Zq[X]/(X^N + 1)`.
-pub const N: usize = 32768;
-/// The coefficients of the polynomial `e` should exist in the interval `[-E_BOUND, E_BOUND]` where `E_BOUND` is the upper bound of the gaussian distribution with 𝜎 = 3.2
-pub const E_BOUND: u64 = 19;
-/// The coefficients of the polynomial `s` should exist in the interval `[-S_BOUND, S_BOUND]`.
-pub const S_BOUND: u64 = 1;
-/// The coefficients of the polynomials `r1is` should exist in the interval `[-R1_BOUND[i], R1_BOUND[i]]` where `R1_BOUND[i]` is equal to `(qi-1)/2`
-pub const R1_BOUNDS: [u64; 15] = [17449, 44739, 23337, 23971, 38527, 41231, 47178, 25438, 29323, 21130, 36215, 41226, 47080, 20341, 18613];
-/// The coefficients of the polynomials `r2is` should exist in the interval `[-R2_BOUND[i], R2_BOUND[i]]` where `R2_BOUND[i]` is equal to $\frac{(N+2) \cdot \frac{q_i - 1}{2} + B + \frac{t - 1}{2} \cdot |K_{0,i}|}{q_i}$
-pub const R2_BOUNDS: [u64; 15] = [238750987231488128, 238750987231488128, 238750987231488128, 238750987231488128, 238750987231488128, 238750987231488128, 238750987231488128, 238750987231488128, 238750987231488160, 238750987231488160, 238750987231488160, 238750987231488160, 238750987231488160, 238750987231488160, 238750987231488160];
-/// The coefficients of `k1` should exist in the interval `[-K1_BOUND, K1_BOUND]` where `K1_BOUND` is equal to `(t-1)/2`
-pub const K1_BOUND: u64 = 32768;
-/// List of scalars `qis` such that `qis[i]` is the modulus of the i-th CRT basis of `q` (ciphertext space modulus)
-pub const QIS: [&str; 15] = ["477501974462976263", "477501974462976265", "477501974462976267", "477501974462976269", "477501974462976271", "477501974462976277", "477501974462976283", "477501974462976289", "477501974462976293", "477501974462976299", "477501974462976301", "477501974462976307", "477501974462976311", "477501974462976313", "477501974462976317"];
-/// List of scalars `k0is` such that `k0i[i]` is equal to the negative of the multiplicative inverses of t mod qi.
-pub const K0IS: [&str; 15] = ["15519160254606397", "413181248299753132", "101318987089463173", "110550337344198528", "322660099471945682", "362070023329770101", "448729597070750619", "131927434145614106", "188539582116643080", "69158624007851611", "288969678337063080", "361989877431741640", "447294256896967800", "57654044645399264", "32480946673725505"];
diff --git a/src/constants/sk_enc_constants_1024_1x27_65537.rs b/src/constants/sk_enc_constants_4096_2x39_65537.rs
similarity index 81%
rename from src/constants/sk_enc_constants_1024_1x27_65537.rs
rename to src/constants/sk_enc_constants_4096_2x39_65537.rs
index ac52b08..e6a6486 100644
--- a/src/constants/sk_enc_constants_1024_1x27_65537.rs
+++ b/src/constants/sk_enc_constants_4096_2x39_65537.rs
@@ -1,16 +1,16 @@
 /// `N` is the degree of the cyclotomic polynomial defining the ring `Rq = Zq[X]/(X^N + 1)`.
-pub const N: usize = 1024;
+pub const N: usize = 4096;
 /// The coefficients of the polynomial `e` should exist in the interval `[-E_BOUND, E_BOUND]` where `E_BOUND` is the upper bound of the gaussian distribution with 𝜎 = 3.2
 pub const E_BOUND: u64 = 19;
 /// The coefficients of the polynomial `s` should exist in the interval `[-S_BOUND, S_BOUND]`.
 pub const S_BOUND: u64 = 1;
 /// The coefficients of the polynomials `r1is` should exist in the interval `[-R1_BOUND[i], R1_BOUND[i]]` where `R1_BOUND[i]` is equal to `(qi-1)/2`
-pub const R1_BOUNDS: [u64; 1] = [1246];
+pub const R1_BOUNDS: [u64; 2] = [27209, 9723];
 /// The coefficients of the polynomials `r2is` should exist in the interval `[-R2_BOUND[i], R2_BOUND[i]]` where `R2_BOUND[i]` is equal to $\frac{(N+2) \cdot \frac{q_i - 1}{2} + B + \frac{t - 1}{2} \cdot |K_{0,i}|}{q_i}$
-pub const R2_BOUNDS: [u64; 1] = [41319090];
+pub const R2_BOUNDS: [u64; 2] = [180143985099, 180143985291];
 /// The coefficients of `k1` should exist in the interval `[-K1_BOUND, K1_BOUND]` where `K1_BOUND` is equal to `(t-1)/2`
 pub const K1_BOUND: u64 = 32768;
 /// List of scalars `qis` such that `qis[i]` is the modulus of the i-th CRT basis of `q` (ciphertext space modulus)
-pub const QIS: [&str; 1] = ["82638181"];
+pub const QIS: [&str; 2] = ["360287970199", "360287970583"];
 /// List of scalars `k0is` such that `k0i[i]` is equal to the negative of the multiplicative inverses of t mod qi.
-pub const K0IS: [&str; 1] = ["1849798"];
+pub const K0IS: [&str; 2] = ["276643899421", "84380732418"];
diff --git a/src/constants/sk_enc_constants_8192_4x55_65537.rs b/src/constants/sk_enc_constants_8192_4x55_65537.rs
deleted file mode 100644
index 0284096..0000000
--- a/src/constants/sk_enc_constants_8192_4x55_65537.rs
+++ /dev/null
@@ -1,16 +0,0 @@
-/// `N` is the degree of the cyclotomic polynomial defining the ring `Rq = Zq[X]/(X^N + 1)`.
-pub const N: usize = 8192;
-/// The coefficients of the polynomial `e` should exist in the interval `[-E_BOUND, E_BOUND]` where `E_BOUND` is the upper bound of the gaussian distribution with 𝜎 = 3.2
-pub const E_BOUND: u64 = 19;
-/// The coefficients of the polynomial `s` should exist in the interval `[-S_BOUND, S_BOUND]`.
-pub const S_BOUND: u64 = 1;
-/// The coefficients of the polynomials `r1is` should exist in the interval `[-R1_BOUND[i], R1_BOUND[i]]` where `R1_BOUND[i]` is equal to `(qi-1)/2`
-pub const R1_BOUNDS: [u64; 4] = [30180, 5459, 4259, 13207];
-/// The coefficients of the polynomials `r2is` should exist in the interval `[-R2_BOUND[i], R2_BOUND[i]]` where `R2_BOUND[i]` is equal to $\frac{(N+2) \cdot \frac{q_i - 1}{2} + B + \frac{t - 1}{2} \cdot |K_{0,i}|}{q_i}$
-pub const R2_BOUNDS: [u64; 4] = [16838097769646402, 16838097769646404, 16838097769646404, 16838097769646404];
-/// The coefficients of `k1` should exist in the interval `[-K1_BOUND, K1_BOUND]` where `K1_BOUND` is equal to `(t-1)/2`
-pub const K1_BOUND: u64 = 32768;
-/// List of scalars `qis` such that `qis[i]` is the modulus of the i-th CRT basis of `q` (ciphertext space modulus)
-pub const QIS: [&str; 4] = ["33676195539292805", "33676195539292807", "33676195539292809", "33676195539292811"];
-/// List of scalars `k0is` such that `k0i[i]` is equal to the negative of the multiplicative inverses of t mod qi.
-pub const K0IS: [&str; 4] = ["26806019389021282", "1400755436472713", "167001290115052", "9363376949158393"];
diff --git a/src/data/pk_enc_data/pk_enc_1024_15x60_65537.json b/src/data/pk_enc_data/pk_enc_1024_15x60_65537.json
new file mode 100644
index 0000000..2249be4
--- /dev/null
+++ b/src/data/pk_enc_data/pk_enc_1024_15x60_65537.json
@@ -0,0 +1,157902 @@
+{
+  "pk0i": [
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diff --git a/src/data/pk_enc_data/pk_enc_1024_15x60_65537_zeroes.json b/src/data/pk_enc_data/pk_enc_1024_15x60_65537_zeroes.json
new file mode 100644
index 0000000..b5f79bc
--- /dev/null
+++ b/src/data/pk_enc_data/pk_enc_1024_15x60_65537_zeroes.json
@@ -0,0 +1,157902 @@
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+}
diff --git a/src/data/sk_enc_4096_2x55_65537.json b/src/data/sk_enc_4096_2x55_65537.json
deleted file mode 100644
index c6c9db5..0000000
--- a/src/data/sk_enc_4096_2x55_65537.json
+++ /dev/null
@@ -1 +0,0 @@
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\ No newline at end of file
diff --git a/src/data/sk_enc_data/sk_enc_1024_15x60_65537.json b/src/data/sk_enc_data/sk_enc_1024_15x60_65537.json
new file mode 100644
index 0000000..1d50969
--- /dev/null
+++ b/src/data/sk_enc_data/sk_enc_1024_15x60_65537.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/src/data/sk_enc_data/sk_enc_1024_15x60_65537_zeroes.json b/src/data/sk_enc_data/sk_enc_1024_15x60_65537_zeroes.json
new file mode 100644
index 0000000..b8751df
--- /dev/null
+++ b/src/data/sk_enc_data/sk_enc_1024_15x60_65537_zeroes.json
@@ -0,0 +1 @@
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diff --git a/src/data/sk_enc_data/sk_enc_4096_2x39_65537.json b/src/data/sk_enc_data/sk_enc_4096_2x39_65537.json
new file mode 100644
index 0000000..c404557
--- /dev/null
+++ b/src/data/sk_enc_data/sk_enc_4096_2x39_65537.json
@@ -0,0 +1 @@
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diff --git a/src/data/sk_enc_4096_2x55_65537_zeroes.json b/src/data/sk_enc_data/sk_enc_4096_2x39_65537_zeroes.json
similarity index 100%
rename from src/data/sk_enc_4096_2x55_65537_zeroes.json
rename to src/data/sk_enc_data/sk_enc_4096_2x39_65537_zeroes.json
diff --git a/src/data/sk_enc_data/sk_enc_4096_2x55_65537.json b/src/data/sk_enc_data/sk_enc_4096_2x55_65537.json
new file mode 100644
index 0000000..21e1807
--- /dev/null
+++ b/src/data/sk_enc_data/sk_enc_4096_2x55_65537.json
@@ -0,0 +1 @@
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diff --git a/src/data/sk_enc_data/sk_enc_4096_2x55_65537_zeroes.json b/src/data/sk_enc_data/sk_enc_4096_2x55_65537_zeroes.json
new file mode 100644
index 0000000..7b222c6
--- /dev/null
+++ b/src/data/sk_enc_data/sk_enc_4096_2x55_65537_zeroes.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/src/lib.rs b/src/lib.rs
index fe20ed5..ac4e372 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,3 +1,4 @@
 pub mod constants;
+pub mod pk_encryption_circuit;
 pub mod poly;
 pub mod sk_encryption_circuit;
diff --git a/src/pk_encryption_circuit.rs b/src/pk_encryption_circuit.rs
new file mode 100644
index 0000000..5650250
--- /dev/null
+++ b/src/pk_encryption_circuit.rs
@@ -0,0 +1,981 @@
+use axiom_eth::rlc::{
+    chip::RlcChip,
+    circuit::{builder::RlcCircuitBuilder, instructions::RlcCircuitInstructions, RlcCircuitParams},
+};
+use halo2_base::{
+    gates::{circuit::BaseCircuitParams, GateInstructions, RangeChip, RangeInstructions},
+    utils::ScalarField,
+    QuantumCell::Constant,
+};
+use serde::Deserialize;
+
+use crate::{
+    constants::pk_enc_constants::pk_enc_constants_1024_15x60_65537::{
+        E_BOUND, K0IS, K1_BOUND, N, P1_BOUNDS, P2_BOUNDS, PK_BOUND, QIS, R1_BOUNDS, R2_BOUNDS,
+        U_BOUND,
+    },
+    poly::{Poly, PolyAssigned},
+};
+
+/// Helper function to define the parameters of the RlcCircuit. This is a non-optimized configuration that makes use of a single advice column. Use this for testing purposes only.
+pub fn test_params() -> RlcCircuitParams {
+    RlcCircuitParams {
+        base: BaseCircuitParams {
+            k: 22,
+            num_advice_per_phase: vec![1, 1],
+            num_fixed: 1,
+            num_lookup_advice_per_phase: vec![0, 1],
+            lookup_bits: Some(8),
+            num_instance_columns: 1,
+        },
+        num_rlc_columns: 1,
+    }
+}
+/// `BfvPkEncryptionCircuit` is a circuit that checks the correct formation of a ciphertext resulting from BFV public key encryption
+/// All the polynomials coefficients and scalars are normalized to be in the range `[0, p)` where p is the modulus of the prime field of the circuit
+///
+/// pk_q1 = ( pk0i , pk1i )=( [ai*s + E] , -ai )
+/// # Parameters:
+/// * `pk0i`: publicly polynomial created by secret polynomial ([ai*s + E] )
+/// * `pk1i`: publicly polynomial created by polynomial (-[ai])
+/// * `u`: secret polynomial, sampled from ternary distribution.
+/// * `e0`: error polynomial, sampled from discrete Gaussian distribution.
+/// * `e1`: error polynomial, sampled from discrete Gaussian distribution.
+/// * `k1`: scaled message polynomial.
+/// * `r2is`: list of r2i polynomials for each i-th CRT basis .
+/// * `r1is`: list of r1i polynomials for each CRT i-th CRT basis.
+/// * `p2is`: list of p2i polynomials for each i-th CRT basis.
+/// * `p1is`: list of p1i polynomials for each i-th CRT basis.
+/// * `ct0is`: list of ct0i (first component of the ciphertext cti) polynomials for each CRT i-th CRT basis.
+/// * `ct1is`: list of ct1i (second component of the ciphertext cti) polynomials for each CRT i-th CRT basis.
+
+#[derive(Deserialize, Clone)]
+pub struct BfvPkEncryptionCircuit {
+    pk0i: Vec<Vec<String>>,
+    pk1i: Vec<Vec<String>>,
+    u: Vec<String>,
+    e0: Vec<String>,
+    e1: Vec<String>,
+    k1: Vec<String>,
+    r2is: Vec<Vec<String>>,
+    r1is: Vec<Vec<String>>,
+    p2is: Vec<Vec<String>>,
+    p1is: Vec<Vec<String>>,
+    ct0is: Vec<Vec<String>>,
+    ct1is: Vec<Vec<String>>,
+}
+
+/// Payload returned by the first phase of the circuit to be reused in the second phase
+pub struct Payload<F: ScalarField> {
+    pk0i_assigned: Vec<PolyAssigned<F>>,
+    pk1i_assigned: Vec<PolyAssigned<F>>,
+    u_assigned: PolyAssigned<F>,
+    e0_assigned: PolyAssigned<F>,
+    e1_assigned: PolyAssigned<F>,
+    k1_assigned: PolyAssigned<F>,
+    r2is_assigned: Vec<PolyAssigned<F>>,
+    r1is_assigned: Vec<PolyAssigned<F>>,
+    p2is_assigned: Vec<PolyAssigned<F>>,
+    p1is_assigned: Vec<PolyAssigned<F>>,
+    ct0is_assigned: Vec<PolyAssigned<F>>,
+    ct1is_assigned: Vec<PolyAssigned<F>>,
+}
+
+impl<F: ScalarField> RlcCircuitInstructions<F> for BfvPkEncryptionCircuit {
+    type FirstPhasePayload = Payload<F>;
+
+    /// #### Phase 0
+
+    /// In this phase, the polynomials for each matrix $S_i$ are assigned to the circuit. Namely:
+    /// * polynomials `u`,'e1, `e0`, `k1`, `pk0i`,`pk1_q1` are assigned to the witness table. This has to be done only once as these polynomial are common to each $S_i$ matrix
+    /// * polynomials `r1i`, `r2i`,`p1i`,`p2i` are assigned to the witness table for each $S_i$ matrix
+    /// * polynomials 'ct0is' and 'ct1is` are assigned to the witness table for each $Ct_i$
+
+    /// Witness values are element of the finite field $\mod{p}$. Negative coefficients $-z$ are assigned as field elements $p - z$.
+
+    /// At the end of phase 0, the witness generated so far is interpolated into a polynomial and committed by the prover. The hash of this commitment is used as challenge and will be used as a source of randomness $\gamma$ in Phase 1. This feature is made available by Halo2 [Challenge API](https://hackmd.io/@axiom/SJw3p-qX3).
+
+    fn virtual_assign_phase0(
+        &self,
+        builder: &mut RlcCircuitBuilder<F>,
+        _: &RangeChip<F>,
+    ) -> Self::FirstPhasePayload {
+        let ctx = builder.base.main(0);
+
+        let mut public_inputs = vec![];
+
+        let pk0i = self
+            .pk0i
+            .iter()
+            .map(|pk0i| Poly::<F>::new(pk0i.clone()))
+            .collect::<Vec<_>>();
+        let pk0i_assigned = pk0i
+            .into_iter()
+            .map(|pk0i| PolyAssigned::new(ctx, pk0i))
+            .collect::<Vec<_>>();
+
+        let pk1i = self
+            .pk1i
+            .iter()
+            .map(|pk1i| Poly::<F>::new(pk1i.clone()))
+            .collect::<Vec<_>>();
+        let pk1i_assigned = pk1i
+            .into_iter()
+            .map(|pk1i| PolyAssigned::new(ctx, pk1i))
+            .collect::<Vec<_>>();
+
+        let u = Poly::<F>::new(self.u.clone());
+        let u_assigned = PolyAssigned::new(ctx, u);
+
+        let e0 = Poly::<F>::new(self.e0.clone());
+        let e0_assigned = PolyAssigned::new(ctx, e0);
+
+        let e1 = Poly::<F>::new(self.e1.clone());
+        let e1_assigned = PolyAssigned::new(ctx, e1);
+
+        let k1 = Poly::<F>::new(self.k1.clone());
+        let k1_assigned = PolyAssigned::new(ctx, k1);
+
+        let r1is_assigned = self
+            .r1is
+            .iter()
+            .map(|r1is| {
+                let r1is = Poly::<F>::new(r1is.clone());
+                PolyAssigned::new(ctx, r1is)
+            })
+            .collect::<Vec<_>>();
+
+        let r2is_assigned = self
+            .r2is
+            .iter()
+            .map(|r2is| {
+                let r2is = Poly::<F>::new(r2is.clone());
+                PolyAssigned::new(ctx, r2is)
+            })
+            .collect::<Vec<_>>();
+
+        let p1is_assigned = self
+            .p1is
+            .iter()
+            .map(|p1is| {
+                let p1is = Poly::<F>::new(p1is.clone());
+                PolyAssigned::new(ctx, p1is)
+            })
+            .collect::<Vec<_>>();
+
+        let p2is_assigned = self
+            .p2is
+            .iter()
+            .map(|p2is| {
+                let p2is = Poly::<F>::new(p2is.clone());
+                PolyAssigned::new(ctx, p2is)
+            })
+            .collect::<Vec<_>>();
+
+        let ct0is_assigned = self
+            .ct0is
+            .iter()
+            .map(|ct0is| {
+                let ct0is = Poly::<F>::new(ct0is.clone());
+                PolyAssigned::new(ctx, ct0is)
+            })
+            .collect::<Vec<_>>();
+
+        let ct1is_assigned = self
+            .ct1is
+            .iter()
+            .map(|ct1is| {
+                let ct1is = Poly::<F>::new(ct1is.clone());
+                PolyAssigned::new(ctx, ct1is)
+            })
+            .collect::<Vec<_>>();
+
+        for pk0 in pk0i_assigned.iter() {
+            public_inputs.push(pk0.assigned_coefficients[0]);
+        }
+        for pk1 in pk1i_assigned.iter() {
+            public_inputs.push(pk1.assigned_coefficients[0]);
+        }
+        for ct0 in ct0is_assigned.iter() {
+            public_inputs.push(ct0.assigned_coefficients[0]);
+        }
+        for ct1 in ct1is_assigned.iter() {
+            public_inputs.push(ct1.assigned_coefficients[0]);
+        }
+
+        builder.base.assigned_instances[0] = public_inputs;
+
+        Payload {
+            pk0i_assigned,
+            pk1i_assigned,
+            u_assigned,
+            e0_assigned,
+            e1_assigned,
+            k1_assigned,
+            r2is_assigned,
+            r1is_assigned,
+            p2is_assigned,
+            p1is_assigned,
+            ct0is_assigned,
+            ct1is_assigned,
+        }
+    }
+
+    /// #### Phase 1
+
+    /// In this phase, the following two core constraints are enforced:
+
+    /// - The coefficients of $S_i$ are in the expected range.
+    /// - $P_i(\gamma) \times S_i(\gamma) =Ct_{0,i}(\gamma)$
+
+    /// ##### Range Check
+
+    /// The coefficients of the private polynomials from each $i$-th matrix $S_i$ are checked to be in the correct range
+    /// * Range check polynomials `u`, `e0`,`e1`,`k1`. This has to be done only once as these polynomial are common to each $S_i$ matrix
+    /// * Range check polynomials `r1i`, `r2i` for each $S_i$ matrix
+    /// * Range check polynomials `p1i`, `p2i` for each $S_i$ matrix
+    /// * Range check polynomials `pk0`, `pk1` for each $U_i$ matrix
+
+    /// Since negative coefficients `-z` are assigned as `p - z` to the circuit, this might result in very large coefficients. Performing the range check on such large coefficients requires large lookup tables. To avoid this, the coefficients (both negative and positive) are shifted by a constant to make them positive and then perform the range check.
+
+    /// ##### Evaluation at $\gamma$ Constraint
+
+    /// * Constrain the evaluation of the polynomials `u`, `e0`, `e1`, `k1` at $\gamma$. This has to be done only once as these polynomial are common to each $S_i$ matrix
+    /// * Constrain the evaluation of the polynomials `r1i`, `r2i` at $\gamma$ for each $S_i$ matrix
+    /// * Constrain the evaluation of the polynomials `p1i`, `p2i` at $\gamma$ for each $S_i$ matrix
+
+    /// ##### Correct Encryption Constraint
+
+    /// It is needed to prove that $P_i(\gamma) \times S_i(\gamma) =Ct_{0,i}(\gamma)$. This can be rewritten as `ct0i = ct0i_hat + r1i * qi + r2i * cyclo`, where `ct0i_hat = pk0i * u + e0 + k1 * k0i`.
+
+    /// This constrained is enforced by proving that `LHS(gamma) = RHS(gamma)`. According to the Schwartz-Zippel lemma, if this relation between polynomial when evaluated at a random point holds true, then then the polynomials are identical with high probability. Note that `qi` and `k0i` (for each $U_i$ matrix) are constants to the circuit encoded during key generation.
+    /// * Constrain that `ct0i(gamma) = ai(gamma) * s(gamma) + e(gamma) + k1(gamma) * k0i + r1i(gamma) * qi + r2i(gamma) * cyclo(gamma)` for each $i$-th CRT basis
+    ///
+
+    fn virtual_assign_phase1(
+        builder: &mut RlcCircuitBuilder<F>,
+        range: &RangeChip<F>,
+        rlc: &RlcChip<F>,
+        payload: Self::FirstPhasePayload,
+    ) {
+        let Payload {
+            pk0i_assigned,
+            pk1i_assigned,
+            u_assigned,
+            e0_assigned,
+            e1_assigned,
+            k1_assigned,
+            r2is_assigned,
+            r1is_assigned,
+            p2is_assigned,
+            p1is_assigned,
+            ct0is_assigned,
+            ct1is_assigned,
+        } = payload;
+
+        // ASSIGNMENT
+
+        let (ctx_gate, ctx_rlc) = builder.rlc_ctx_pair();
+        let gate = range.gate();
+
+        let mut qi_constants = vec![];
+        let mut k0i_constants = vec![];
+
+        for z in 0..ct0is_assigned.len() {
+            let qi_constant = Constant(F::from_str_vartime(QIS[z]).unwrap());
+            qi_constants.push(qi_constant);
+
+            let k0i_constant = Constant(F::from_str_vartime(K0IS[z]).unwrap());
+            k0i_constants.push(k0i_constant);
+        }
+
+        // cyclo poly is equal to x^N + 1
+        let bits_used = (usize::BITS as usize) - (N.leading_zeros() as usize);
+        rlc.load_rlc_cache((ctx_gate, ctx_rlc), gate, bits_used);
+        let cyclo_at_gamma_assigned = rlc.rlc_pow_fixed(ctx_gate, gate, N);
+        let cyclo_at_gamma_assigned =
+            gate.add(ctx_gate, cyclo_at_gamma_assigned, Constant(F::from(1)));
+
+        u_assigned.range_check(ctx_gate, range, U_BOUND);
+        e0_assigned.range_check(ctx_gate, range, E_BOUND);
+        e1_assigned.range_check(ctx_gate, range, E_BOUND);
+        k1_assigned.range_check(ctx_gate, range, K1_BOUND);
+
+        let _ = pk0i_assigned
+            .iter()
+            .enumerate()
+            .map(|(i, pk_assigned)| pk_assigned.range_check(ctx_gate, range, PK_BOUND[i]));
+
+        let _ = pk1i_assigned
+            .iter()
+            .enumerate()
+            .map(|(i, pk_assigned)| pk_assigned.range_check(ctx_gate, range, PK_BOUND[i]));
+
+        for z in 0..ct0is_assigned.len() {
+            r2is_assigned[z].range_check(ctx_gate, range, R2_BOUNDS[z]);
+            r1is_assigned[z].range_check(ctx_gate, range, R1_BOUNDS[z]);
+            p2is_assigned[z].range_check(ctx_gate, range, P2_BOUNDS[z]);
+            p1is_assigned[z].range_check(ctx_gate, range, P1_BOUNDS[z]);
+        }
+
+        let u_at_gamma = u_assigned.enforce_eval_at_gamma(ctx_rlc, rlc);
+        let e0_at_gamma = e0_assigned.enforce_eval_at_gamma(ctx_rlc, rlc);
+        let e1_at_gamma = e1_assigned.enforce_eval_at_gamma(ctx_rlc, rlc);
+        let k1_at_gamma = k1_assigned.enforce_eval_at_gamma(ctx_rlc, rlc);
+        let pk0i_at_gamma = pk0i_assigned
+            .iter()
+            .map(|pk_assigned| pk_assigned.enforce_eval_at_gamma(ctx_rlc, rlc))
+            .collect::<Vec<_>>();
+        let pk1i_at_gamma = pk1i_assigned
+            .iter()
+            .map(|pk_assigned| pk_assigned.enforce_eval_at_gamma(ctx_rlc, rlc))
+            .collect::<Vec<_>>();
+        let gate = range.gate();
+
+        // For each `i` Prove that LHS(gamma) = RHS(gamma)
+        // pk0_u = pk0i(gamma) * u(gamma) + e0(gamma)
+        // LHS = ct0i(gamma)
+        // RHS = pk0_u  + k1(gamma) * k0i + r1i(gamma) * qi + r2i(gamma) * cyclo(gamma)
+
+        for z in 0..ct0is_assigned.len() {
+            let pk0_u = gate.mul_add(ctx_gate, pk0i_at_gamma[z], u_at_gamma, e0_at_gamma);
+            let r1i_at_gamma = r1is_assigned[z].enforce_eval_at_gamma(ctx_rlc, rlc);
+            let r2i_at_gamma = r2is_assigned[z].enforce_eval_at_gamma(ctx_rlc, rlc);
+
+            // CORRECT ENCRYPTION CONSTRAINT
+
+            // rhs = pk0_u + k1(gamma) * k0i
+            let rhs = gate.mul_add(ctx_gate, k1_at_gamma, k0i_constants[z], pk0_u);
+
+            // rhs = rhs + r1i(gamma) * qi
+            let rhs = gate.mul_add(ctx_gate, r1i_at_gamma, qi_constants[z], rhs);
+
+            // rhs = rhs + r2i(gamma) * cyclo(gamma)
+            let rhs = gate.mul_add(ctx_gate, r2i_at_gamma, cyclo_at_gamma_assigned, rhs);
+            let lhs = ct0is_assigned[z].enforce_eval_at_gamma(ctx_rlc, rlc);
+
+            // LHS(gamma) = RHS(gamma)
+            let res = gate.is_equal(ctx_gate, lhs, rhs);
+            gate.assert_is_const(ctx_gate, &res, &F::from(1));
+        }
+
+        for z in 0..ct1is_assigned.len() {
+            let pk1_u = gate.mul_add(ctx_gate, pk1i_at_gamma[z], u_at_gamma, e1_at_gamma);
+
+            let p1i_at_gamma = p1is_assigned[z].enforce_eval_at_gamma(ctx_rlc, rlc);
+            let p2i_at_gamma = p2is_assigned[z].enforce_eval_at_gamma(ctx_rlc, rlc);
+
+            //rhs = pk1_u + p2i * cyclo(gamma)
+            let rhs = gate.mul_add(ctx_gate, p2i_at_gamma, cyclo_at_gamma_assigned, pk1_u);
+
+            //rhs = rhs + p1s * qi
+            let rhs = gate.mul_add(ctx_gate, p1i_at_gamma, qi_constants[z], rhs);
+
+            let lhs = ct1is_assigned[z].enforce_eval_at_gamma(ctx_rlc, rlc);
+
+            let res = gate.is_equal(ctx_gate, lhs, rhs);
+            gate.assert_is_const(ctx_gate, &res, &F::from(1));
+        }
+    }
+
+    fn instances(&self) -> Vec<Vec<F>> {
+        let mut instance = vec![];
+        for pk0 in self.pk0i.iter() {
+            let pk0_poly = Poly::<F>::new(pk0.clone());
+            instance.push(pk0_poly.coefficients[0]);
+        }
+        for pk1 in self.pk1i.iter() {
+            let pk1_poly = Poly::<F>::new(pk1.clone());
+            instance.push(pk1_poly.coefficients[0]);
+        }
+        for ct0i in self.ct0is.iter() {
+            let ct0i_poly = Poly::<F>::new(ct0i.clone());
+            instance.push(ct0i_poly.coefficients[0]);
+        }
+        for ct1i in self.ct1is.iter() {
+            let ct1i_poly = Poly::<F>::new(ct1i.clone());
+            instance.push(ct1i_poly.coefficients[0]);
+        }
+        vec![instance]
+    }
+}
+#[cfg(test)]
+mod test {
+    use std::{fs::File, io::Read};
+
+    use axiom_eth::{
+        halo2_proofs::{
+            dev::{FailureLocation, MockProver, VerifyFailure},
+            plonk::{keygen_pk, keygen_vk, Any, SecondPhase},
+        },
+        halo2curves::bn256::Fr,
+        rlc::{
+            circuit::{builder::RlcCircuitBuilder, instructions::RlcCircuitInstructions},
+            utils::executor::RlcExecutor,
+        },
+    };
+    use halo2_base::{
+        gates::circuit::CircuitBuilderStage,
+        utils::{
+            fs::gen_srs,
+            testing::{check_proof_with_instances, gen_proof_with_instances},
+        },
+    };
+
+    use crate::constants::pk_enc_constants::pk_enc_constants_1024_15x60_65537::R1_BOUNDS;
+
+    use super::{test_params, BfvPkEncryptionCircuit};
+
+    #[test]
+    fn test_pk_enc_valid() {
+        let file_path_zeros = "src/data/pk_enc_data/pk_enc_1024_15x60_65537_zeroes.json";
+        let mut file = File::open(file_path_zeros).unwrap();
+        let mut data = String::new();
+        file.read_to_string(&mut data).unwrap();
+        let empty_pk_enc_circuit = serde_json::from_str::<BfvPkEncryptionCircuit>(&data).unwrap();
+
+        // 2. Generate (unsafe) trusted setup parameters
+        // Here we are setting a small k for optimization purposes
+        let k = 14;
+        let kzg_params = gen_srs(k as u32);
+
+        // 3. Build the circuit for key generation,
+        let mut key_gen_builder =
+            RlcCircuitBuilder::<Fr>::from_stage(CircuitBuilderStage::Keygen, 0).use_k(k);
+        key_gen_builder.base.set_lookup_bits(k - 1); // lookup bits set to `k-1` as suggested [here](https://docs.axiom.xyz/protocol/zero-knowledge-proofs/getting-started-with-halo2#technical-detail-how-to-choose-lookup_bits)
+        key_gen_builder.base.set_instance_columns(1);
+        let rlc_circuit = RlcExecutor::new(key_gen_builder, empty_pk_enc_circuit.clone());
+
+        // The parameters are auto configured by halo2 lib to fit all the columns into the `k`-sized table
+        let rlc_circuit_params = rlc_circuit.0.calculate_params(Some(9));
+
+        // 4. Generate the verification key and the proving key
+        let vk = keygen_vk(&kzg_params, &rlc_circuit).unwrap();
+        let pk = keygen_pk(&kzg_params, vk, &rlc_circuit).unwrap();
+        let break_points = rlc_circuit.0.builder.borrow().break_points();
+        drop(rlc_circuit);
+
+        // 5. Generate the proof, here we pass the actual inputs
+        let mut proof_gen_builder: RlcCircuitBuilder<Fr> =
+            RlcCircuitBuilder::from_stage(CircuitBuilderStage::Mock, 0)
+                .use_params(rlc_circuit_params);
+        proof_gen_builder.base.set_lookup_bits(k - 1);
+        proof_gen_builder.base.set_instance_columns(1);
+
+        let file_path = "src/data/pk_enc_data/pk_enc_1024_15x60_65537.json";
+        let mut file = File::open(file_path).unwrap();
+        let mut data = String::new();
+        file.read_to_string(&mut data).unwrap();
+        let pk_enc_circuit = serde_json::from_str::<BfvPkEncryptionCircuit>(&data).unwrap();
+
+        let rlc_circuit = RlcExecutor::new(proof_gen_builder, pk_enc_circuit.clone());
+
+        rlc_circuit
+            .0
+            .builder
+            .borrow_mut()
+            .set_break_points(break_points);
+        let instances = pk_enc_circuit.instances();
+        let proof = gen_proof_with_instances(&kzg_params, &pk, rlc_circuit, &[&instances[0]]);
+
+        // 6. Verify the proof
+        check_proof_with_instances(&kzg_params, pk.get_vk(), &proof, &[&instances[0]], true);
+    }
+
+    #[test]
+    pub fn test_pk_enc_full_prover() {
+        // 1. Define the inputs of the circuit.
+        // Since we are going to use this circuit instance for key gen, we can use an input file in which all the coefficients are set to 0
+        let file_path_zeros = "src/data/pk_enc_data/pk_enc_1024_15x60_65537_zeroes.json";
+        let mut file = File::open(file_path_zeros).unwrap();
+        let mut data = String::new();
+        file.read_to_string(&mut data).unwrap();
+        let empty_pk_enc_circuit = serde_json::from_str::<BfvPkEncryptionCircuit>(&data).unwrap();
+
+        // 2. Generate (unsafe) trusted setup parameters
+        // Here we are setting a small k for optimization purposes
+        let k = 14;
+        let kzg_params = gen_srs(k as u32);
+
+        // 3. Build the circuit for key generation,
+        let mut key_gen_builder =
+            RlcCircuitBuilder::from_stage(CircuitBuilderStage::Keygen, 0).use_k(k);
+        key_gen_builder.base.set_lookup_bits(k - 1); // lookup bits set to `k-1` as suggested [here](https://docs.axiom.xyz/protocol/zero-knowledge-proofs/getting-started-with-halo2#technical-detail-how-to-choose-lookup_bits)
+        key_gen_builder.base.set_instance_columns(1);
+        let rlc_circuit = RlcExecutor::new(key_gen_builder, empty_pk_enc_circuit.clone());
+
+        // The parameters are auto configured by halo2 lib to fit all the columns into the `k`-sized table
+        let rlc_circuit_params = rlc_circuit.0.calculate_params(Some(9));
+
+        // 4. Generate the verification key and the proving key
+        let vk = keygen_vk(&kzg_params, &rlc_circuit).unwrap();
+        let pk = keygen_pk(&kzg_params, vk, &rlc_circuit).unwrap();
+        let break_points = rlc_circuit.0.builder.borrow().break_points();
+        drop(rlc_circuit);
+
+        // 5. Generate the proof, here we pass the actual inputs
+        let mut proof_gen_builder: RlcCircuitBuilder<Fr> =
+            RlcCircuitBuilder::from_stage(CircuitBuilderStage::Prover, 0)
+                .use_params(rlc_circuit_params);
+        proof_gen_builder.base.set_lookup_bits(k - 1);
+        proof_gen_builder.base.set_instance_columns(1);
+
+        let file_path = "src/data/pk_enc_data/pk_enc_1024_15x60_65537.json";
+        let mut file = File::open(file_path).unwrap();
+        let mut data = String::new();
+        file.read_to_string(&mut data).unwrap();
+        let pk_enc_circuit = serde_json::from_str::<BfvPkEncryptionCircuit>(&data).unwrap();
+        let instances = pk_enc_circuit.instances();
+
+        let rlc_circuit = RlcExecutor::new(proof_gen_builder, pk_enc_circuit.clone());
+
+        rlc_circuit
+            .0
+            .builder
+            .borrow_mut()
+            .set_break_points(break_points);
+        let proof = gen_proof_with_instances(&kzg_params, &pk, rlc_circuit, &[&instances[0]]);
+
+        // 6. Verify the proof
+        check_proof_with_instances(&kzg_params, pk.get_vk(), &proof, &[&instances[0]], true);
+    }
+
+    #[test]
+    pub fn test_pk_enc_invalid_range() {
+        // 1. Define the inputs of the circuit
+        let file_path = "src/data/pk_enc_data/pk_enc_1024_15x60_65537.json";
+        let mut file = File::open(file_path).unwrap();
+        let mut data = String::new();
+        file.read_to_string(&mut data).unwrap();
+        let mut pk_enc_circuit = serde_json::from_str::<BfvPkEncryptionCircuit>(&data).unwrap();
+        let instances = pk_enc_circuit.instances();
+
+        // 2. Invalidate the circuit by setting the value of a coefficient of the polynomial `r1is[0]` to be out of range
+        let out_of_range_coeff = R1_BOUNDS[0] + 1;
+        pk_enc_circuit.r1is[0][0] = out_of_range_coeff.to_string();
+
+        // 3. Build the circuit for MockProver
+        let rlc_circuit_params = test_params();
+        let mut mock_builder: RlcCircuitBuilder<Fr> =
+            RlcCircuitBuilder::from_stage(CircuitBuilderStage::Mock, 0)
+                .use_params(rlc_circuit_params.clone());
+        mock_builder.base.set_lookup_bits(8); // Set the lookup bits to 8
+        mock_builder.base.set_instance_columns(1);
+
+        let rlc_circuit = RlcExecutor::new(mock_builder, pk_enc_circuit);
+
+        // 4. Run the mock prover
+        let invalid_mock_prover = MockProver::run(
+            rlc_circuit_params.base.k.try_into().unwrap(),
+            &rlc_circuit,
+            instances,
+        )
+        .unwrap();
+
+        // 5. Assert that the circuit is not satisfied
+        // In particular, it should fail the range check enforced in the second phase for the first coefficient of r1is[0] and the equality check in the second phase for the 0-th basis
+        assert_eq!(
+            invalid_mock_prover.verify(),
+            Err(vec![
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 115709 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 115719 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914202 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914222 }
+                },
+            ])
+        );
+    }
+
+    #[test]
+    pub fn test_pk_enc_invalid_polys() {
+        // 1. Define the inputs of the circuit
+        let file_path = "src/data/pk_enc_data/pk_enc_1024_15x60_65537.json";
+        let mut file = File::open(file_path).unwrap();
+        let mut data = String::new();
+        file.read_to_string(&mut data).unwrap();
+        let mut pk_enc_circuit = serde_json::from_str::<BfvPkEncryptionCircuit>(&data).unwrap();
+
+        // 2. Invalidate the circuit by setting a different `s` polynomial
+        let invalid_u = vec!["1".to_string(); 1024];
+        pk_enc_circuit.u = invalid_u;
+
+        // 3. Build the circuit for MockProver
+        let rlc_circuit_params = test_params();
+        let mut mock_builder: RlcCircuitBuilder<Fr> =
+            RlcCircuitBuilder::from_stage(CircuitBuilderStage::Mock, 0)
+                .use_params(rlc_circuit_params.clone());
+        mock_builder.base.set_lookup_bits(8); // Set the lookup bits to 8
+
+        let instances = pk_enc_circuit.instances();
+        let rlc_circuit = RlcExecutor::new(mock_builder, pk_enc_circuit);
+
+        // 4. Run the mock prover
+        let invalid_mock_prover = MockProver::run(
+            rlc_circuit_params.base.k.try_into().unwrap(),
+            &rlc_circuit,
+            instances,
+        )
+        .unwrap();
+
+        // 5. Assert that the circuit is not satisfied
+        // In particular, it should fail the equality check (LHS=RHS) in the second phase for each i-th CRT basis
+        assert_eq!(
+            invalid_mock_prover.verify(),
+            Err(vec![
+                VerifyFailure::Permutation {
+                    column: (Any::Fixed, 1).into(),
+                    location: FailureLocation::InRegion {
+                        region: (2, "base+rlc phase 1").into(),
+                        offset: 1
+                    }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914202 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914222 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914230 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914250 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914258 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914278 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914286 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914306 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914314 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914334 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914342 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914362 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914370 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914390 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914398 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914418 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914426 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914446 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914454 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914474 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914482 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914502 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914510 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914530 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914538 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914558 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914566 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914586 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914594 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914610 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914618 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914634 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914642 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914658 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914666 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914682 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914690 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914706 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914714 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914730 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914738 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914754 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914762 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914778 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914786 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914802 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914810 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914826 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914834 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914850 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914858 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914874 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914882 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914898 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914906 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914922 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914930 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914946 }
+                },
+                VerifyFailure::Permutation {
+                    column: (Any::advice_in(SecondPhase), 1).into(),
+                    location: FailureLocation::OutsideRegion { row: 2914954 }
+                }
+            ])
+        );
+    }
+
+    #[test]
+    #[cfg(feature = "bench")]
+    pub fn bench_pk_enc_full_prover() {
+        let file_path = "src/data/pk_enc_data/pk_enc_1024_15x60_65537.json";
+
+        pub struct Config {
+            kzg_params: ParamsKZG<Bn256>,
+            k: usize,
+        }
+
+        // Generate unsafe parameters for different values of k
+        let mut configs = vec![];
+        for k in 12..=18 {
+            let kzg_params = gen_srs(k as u32);
+            let config = Config { kzg_params, k };
+            configs.push(config);
+        }
+
+        // Prepare a table to display results
+        let mut table = Table::new();
+        table.add_row(row![
+            "K",
+            "VK Generation Time",
+            "PK Generation Time",
+            "Proof Generation Time",
+            "Proof Verification Time"
+        ]);
+
+        for config in &configs {
+            println!("Running bench for k={}", config.k);
+            // 1. Define the inputs of the circuit.
+            // Since we are going to use this circuit instance for key gen, we can use an input file in which all the coefficients are set to 0
+            let file_path_zeros = "src/data/pk_enc_data/pk_enc_1024_15x60_65537_zeroes.json";
+            let mut file = File::open(file_path_zeroes).unwrap();
+            let mut data = String::new();
+            file.read_to_string(&mut data).unwrap();
+            let empty_pk_enc_circuit =
+                serde_json::from_str::<BfvPkEncryptionCircuit>(&data).unwrap();
+
+            // 2. Build the circuit for key generation,
+            let mut key_gen_builder =
+                RlcCircuitBuilder::from_stage(CircuitBuilderStage::Keygen, 0).use_k(config.k);
+            key_gen_builder.base.set_lookup_bits(config.k - 1); // lookup bits set to `k-1` as suggested [here](https://docs.axiom.xyz/protocol/zero-knowledge-proofs/getting-started-with-halo2#technical-detail-how-to-choose-lookup_bits)
+
+            let rlc_circuit = RlcExecutor::new(key_gen_builder, empty_pk_enc_circuit.clone());
+
+            // The parameters are auto configured by halo2 lib to fit all the columns into the `k`-sized table
+            let rlc_circuit_params = rlc_circuit.0.calculate_params(Some(9));
+
+            // 3. Generate the verification key and the proving key
+            let timer = std::time::Instant::now();
+            let vk = keygen_vk(&config.kzg_params, &rlc_circuit).unwrap();
+            let vk_gen_time = timer.elapsed();
+            let timer = std::time::Instant::now();
+            let pk = keygen_pk(&config.kzg_params, vk, &rlc_circuit).unwrap();
+            let pk_gen_time = timer.elapsed();
+            let break_points = rlc_circuit.0.builder.borrow().break_points();
+            drop(rlc_circuit);
+
+            // 4. Generate the proof, here we pass the actual inputs
+            let mut proof_gen_builder: RlcCircuitBuilder<Fr> =
+                RlcCircuitBuilder::from_stage(CircuitBuilderStage::Prover, 0)
+                    .use_params(rlc_circuit_params);
+            proof_gen_builder.base.set_lookup_bits(config.k - 1);
+
+            let file_path = "src/data/pk_enc_data/pk_enc_1024_15x60_65537.json";
+            let mut file = File::open(file_path).unwrap();
+            let mut data = String::new();
+            file.read_to_string(&mut data).unwrap();
+            let pk_enc_circuit = serde_json::from_str::<BfvPkEncryptionCircuit>(&data).unwrap();
+
+            let rlc_circuit = RlcExecutor::new(proof_gen_builder, pk_enc_circuit.clone());
+
+            rlc_circuit
+                .0
+                .builder
+                .borrow_mut()
+                .set_break_points(break_points);
+            let timer = std::time::Instant::now();
+            let proof = gen_proof_with_instances(&config.kzg_params, &pk, rlc_circuit);
+            let proof_gen_time = timer.elapsed();
+
+            // 5. Verify the proof
+            let timer = std::time::Instant::now();
+            check_proof_with_instances(&config.kzg_params, pk.get_vk(), &proof, true);
+            let proof_verification_time = timer.elapsed();
+
+            table.add_row(row![
+                config.k,
+                format!("{:?}", vk_gen_time),
+                format!("{:?}", pk_gen_time),
+                format!("{:?}", proof_gen_time),
+                format!("{:?}", proof_verification_time)
+            ]);
+        }
+        println!("bfv params: {:?}", file_path);
+        table.printstd();
+    }
+}
diff --git a/src/sk_encryption_circuit.rs b/src/sk_encryption_circuit.rs
index 0f612f3..d239219 100644
--- a/src/sk_encryption_circuit.rs
+++ b/src/sk_encryption_circuit.rs
@@ -1,4 +1,4 @@
-use crate::constants::sk_enc_constants_4096_2x55_65537::{
+use crate::constants::sk_enc_constants::sk_enc_constants_4096_2x55_65537::{
     E_BOUND, K0IS, K1_BOUND, N, QIS, R1_BOUNDS, R2_BOUNDS, S_BOUND,
 };
 use crate::poly::{Poly, PolyAssigned};
@@ -246,7 +246,6 @@ impl<F: ScalarField> RlcCircuitInstructions<F> for BfvSkEncryptionCircuit {
             gate.assert_is_const(ctx_gate, &res, &F::from(1));
         }
     }
-
     fn instances(&self) -> Vec<Vec<F>> {
         let mut instance = vec![];
         for ai in self.ais.iter() {
@@ -266,7 +265,7 @@ mod test {
 
     use super::test_params;
     use crate::{
-        constants::sk_enc_constants_4096_2x55_65537::R1_BOUNDS,
+        constants::sk_enc_constants::sk_enc_constants_4096_2x55_65537::R1_BOUNDS,
         sk_encryption_circuit::BfvSkEncryptionCircuit,
     };
     use axiom_eth::rlc::{
@@ -297,7 +296,7 @@ mod test {
     #[test]
     pub fn test_sk_enc_valid() {
         // 1. Define the inputs of the circuit
-        let file_path = "src/data/sk_enc_4096_2x55_65537.json";
+        let file_path = "src/data/sk_enc_data/sk_enc_4096_2x55_65537.json";
         let mut file = File::open(file_path).unwrap();
         let mut data = String::new();
         file.read_to_string(&mut data).unwrap();
@@ -328,7 +327,7 @@ mod test {
     pub fn test_sk_enc_full_prover() {
         // 1. Define the inputs of the circuit.
         // Since we are going to use this circuit instance for key gen, we can use an input file in which all the coefficients are set to 0
-        let file_path_zeroes = "src/data/sk_enc_4096_2x55_65537_zeroes.json";
+        let file_path_zeroes = "src/data/sk_enc_data/sk_enc_4096_2x55_65537_zeroes.json";
         let mut file = File::open(file_path_zeroes).unwrap();
         let mut data = String::new();
         file.read_to_string(&mut data).unwrap();
@@ -361,7 +360,7 @@ mod test {
             RlcCircuitBuilder::from_stage(CircuitBuilderStage::Prover, 0)
                 .use_params(rlc_circuit_params);
 
-        let file_path = "src/data/sk_enc_4096_2x55_65537.json";
+        let file_path = "src/data/sk_enc_data/sk_enc_4096_2x55_65537.json";
         let mut file = File::open(file_path).unwrap();
         let mut data = String::new();
         file.read_to_string(&mut data).unwrap();
@@ -385,7 +384,7 @@ mod test {
     #[test]
     pub fn test_sk_enc_invalid_range() {
         // 1. Define the inputs of the circuit
-        let file_path = "src/data/sk_enc_4096_2x55_65537.json";
+        let file_path = "src/data/sk_enc_data/sk_enc_4096_2x55_65537.json";
         let mut file = File::open(file_path).unwrap();
         let mut data = String::new();
         file.read_to_string(&mut data).unwrap();
@@ -442,7 +441,7 @@ mod test {
     #[test]
     pub fn test_sk_enc_invalid_polys() {
         // 1. Define the inputs of the circuit
-        let file_path = "src/data/sk_enc_4096_2x55_65537.json";
+        let file_path = "src/data/sk_enc_data/sk_enc_4096_2x55_65537.json";
         let mut file = File::open(file_path).unwrap();
         let mut data = String::new();
         file.read_to_string(&mut data).unwrap();
@@ -501,7 +500,7 @@ mod test {
     #[test]
     #[cfg(feature = "bench")]
     pub fn bench_sk_enc_full_prover() {
-        let file_path = "src/data/sk_enc_4096_2x55_65537";
+        let file_path = "src/data/sk_enc_data/sk_enc_4096_2x55_65537";
 
         pub struct Config {
             kzg_params: ParamsKZG<Bn256>,