Gmp optional

README.md

@@ -27,6 +27,8 @@ pip install -e .
 ```
 *Note that the `-e` flag will instruct pip to install the package as "editable". That is, when changes are made to any part of the package during development, those changes will immediately be available system-wide on the activated python environment.*
 
+For best performance, [install gmpy2](https://gmpy2.readthedocs.io/en/latest/intro.html#installation).
+
 All requirements for this package should be added to `setup.py`.
 
 ## Public and Private Keys

damgard_jurik/crypto.py

@@ -11,11 +11,9 @@
 from secrets import randbelow
 from typing import Any, List, Tuple
 
-from gmpy2 import mpz
-
 from damgard_jurik.prime_gen import gen_safe_prime_pair
 from damgard_jurik.shamir import share_secret
-from damgard_jurik.utils import int_to_mpz, crm, inv_mod, pow_mod
+from damgard_jurik.utils import int_to_mpz, crm, inv_mod, pow_mod, mpzCast
 
 
 class EncryptedNumber:
@@ -169,7 +167,7 @@ def encrypt(self, m: int) -> EncryptedNumber:
         :return: An EncryptedNumber containing the encryption of `m`.
         """
         # Choose random r in Z_n^*
-        r = mpz(randbelow(self.n - 1)) + 1
+        r = mpzCast(randbelow(self.n - 1)) + 1
         c = pow(self.n + 1, m, self.n_s_1) * pow(r, self.n_s, self.n_s_1) % self.n_s_1
 
         return EncryptedNumber(value=c, public_key=self)
@@ -271,17 +269,17 @@ def n_pow(p: int) -> int:
     @lru_cache(int(s))
     @int_to_mpz
     def fact(k: int) -> int:
-        return mpz(factorial(k))
+        return mpzCast(factorial(k))
 
-    i = mpz(0)
+    i = mpzCast(0)
     for j in range(1, s + 1):
-        j = mpz(j)
+        j = mpzCast(j)
 
         t_1 = L(a % n_pow(j + 1))
         t_2 = i
 
         for k in range(2, j + 1):
-            k = mpz(k)
+            k = mpzCast(k)
 
             i = i - 1
             t_2 = t_2 * i % n_pow(j)
@@ -337,7 +335,7 @@ def lam(i: int) -> int:
             return l
 
         # Decrypt
-        c_prime = mpz(1)
+        c_prime = mpzCast(1)
         for c_i, i in zip(c_list, self.i_list):
             c_prime = (c_prime * pow_mod(c_i, (2 * lam(i)), self.public_key.n_s_1)) % self.public_key.n_s_1
 

damgard_jurik/prime_gen.py

@@ -9,10 +9,25 @@
 from secrets import randbits
 from typing import Tuple
 
-from gmpy2 import bit_set, is_prime, next_prime
-
-
-def gen_prime(n_bits: int) -> int:
+try:
+    try:
+        from gmpy2 import bit_set, is_prime, next_prime
+    except ImportError:
+        from gmpy import bit_set, is_prime, next_prime
+except ImportError:
+    GMP_AVAILABLE = False
+else:
+    GMP_AVAILABLE = True
+
+if (not GMP_AVAILABLE):
+    try:
+        from Cryptodome.Util.number import isPrime as is_prime
+        from Cryptodome.Util.number import getPrime as crypto_prime
+    except ImportError:
+        from Crypto.Util.number import isPrime as is_prime
+        from Crypto.Util.number import getPrime as crypto_prime
+
+def gmp_prime(n_bits: int) -> int:
     """Returns a prime number with `n_bits` bits.
 
     :param n_bits: The number of bits the prime number should contain.
@@ -24,6 +39,12 @@ def gen_prime(n_bits: int) -> int:
 
     return p
 
+if (GMP_AVAILABLE):
+    gen_prime = gmp_prime
+else:
+    def gen_prime (n_bits: int) -> int:
+        return crypto_prime(n_bits)
+
 
 def gen_safe_prime(n_bits: int) -> int:
     """Returns a safe prime p with `n_bits` bits.
@@ -39,8 +60,12 @@ def gen_safe_prime(n_bits: int) -> int:
         if is_prime(q):
             p = 2 * q + 1
 
-            if is_prime(p):
-                return p
+            if (GMP_AVAILABLE):
+                if is_prime(p):
+                    return p
+            else:
+                if is_prime(p, 15):
+                    return p
 
 
 def gen_safe_prime_pair(n_bits: int) -> Tuple[int, int]:

damgard_jurik/shamir.py

@@ -9,9 +9,7 @@
 from secrets import randbelow
 from typing import List, Tuple
 
-from gmpy2 import mpz
-
-from damgard_jurik.utils import int_to_mpz, inv_mod
+from damgard_jurik.utils import int_to_mpz, inv_mod, mpzCast
 
 
 class Polynomial:
@@ -24,7 +22,7 @@ def __init__(self, coeffs: List[int], modulus: int):
         :param coeffs: The coefficients of x^0, x^1, x^2, ...
         :param modulus: The modulus of the field the polynomial is in.
         """
-        self.coeffs = [mpz(c_i) for c_i in coeffs]
+        self.coeffs = [mpzCast(c_i) for c_i in coeffs]
         self.modulus = modulus
 
     @int_to_mpz
@@ -34,10 +32,10 @@ def __call__(self, x: int) -> int:
         :param x: The input to the polynomial.
         :return: The integer f(x) where f is this polynomial.
         """
-        f_x = mpz(0)
+        f_x = mpzCast(0)
 
         for i, c_i in enumerate(self.coeffs):
-            f_x = (f_x + c_i * pow(x, mpz(i), self.modulus) % self.modulus) % self.modulus
+            f_x = (f_x + c_i * pow(x, mpzCast(i), self.modulus) % self.modulus) % self.modulus
 
         return f_x
 
@@ -70,7 +68,7 @@ def share_secret(secret: int,
     f = Polynomial(coeffs, modulus)
 
     # Use the polynomial to share the secret
-    X = [mpz(x) for x in range(1, n_shares + 1)]
+    X = [mpzCast(x) for x in range(1, n_shares + 1)]
     shares = [(x, f(x)) for x in X]
 
     return shares
@@ -88,12 +86,12 @@ def reconstruct(shares: List[Tuple[int, int]],
     :return: The secret.
     """
     # Convert to mpz
-    shares = [(mpz(x), mpz(f_x)) for x, f_x in shares]
+    shares = [(mpzCast(x), mpzCast(f_x)) for x, f_x in shares]
 
     # Reconstruct secret
-    secret = mpz(0)
+    secret = mpzCast(0)
     for i, (x_i, f_x_i) in enumerate(shares):
-        product = mpz(1)
+        product = mpzCast(1)
 
         for j, (x_j, _) in enumerate(shares):
             if i != j:

damgard_jurik/utils.py

@@ -10,29 +10,45 @@
 from math import gcd
 from typing import Callable, List, Tuple
 
-from gmpy2 import mpz
 
+try:
+    try:
+        from gmpy2 import mpz
+    except ImportError:
+        from gmpy import mpz
+except ImportError:
+    GMP_AVAILABLE = False
+else:
+    GMP_AVAILABLE = True
+
+def mpzCast(num: int) -> int:
+    if (GMP_AVAILABLE):
+        return mpz(num)
+    else:
+        return num
 
 def int_to_mpz(func: Callable) -> Callable:
     """A decorator which converts all int arguments to mpz.
 
     :param func: The function to decorate.
     :return: The function `func` but with all int arguments converted to mpz.
     """
-    @wraps(func)
-    def func_wrapper(*args, **kwargs):
-        return func(*[mpz(arg) if isinstance(arg, int) else arg for arg in args],
-                    **{key: mpz(value) if isinstance(value, int) else value for key, value in kwargs.items()})
-    return func_wrapper
-
+    if (GMP_AVAILABLE):
+        @wraps(func)
+        def func_wrapper(*args, **kwargs):
+            return func(*[mpz(arg) if isinstance(arg, int) else arg for arg in args],
+                        **{key: mpz(value) if isinstance(value, int) else value for key, value in kwargs.items()})
+        return func_wrapper
+    else:
+        return func
 
 def prod(nums: List[int]) -> int:
     """Returns the product of the numbers in the list.
 
     :param nums: A list of integers.
     :return: The product of the numbers in `nums`.
     """
-    product = mpz(1)
+    product = mpzCast(1)
 
     for num in nums:
         product *= num
@@ -66,7 +82,7 @@ def extended_euclidean(a: int, b: int) -> Tuple[int, int]:
     :param b: The integer b in the above equation.
     :return: A tuple of integers x and y such that ax + by = gcd(a, b).
     """
-    x0, x1, y0, y1 = mpz(0), mpz(1), mpz(1), mpz(0)
+    x0, x1, y0, y1 = mpzCast(0), mpzCast(1), mpzCast(1), mpzCast(0)
 
     while a != 0:
         q, b, a = b // a, a, b % a
@@ -104,8 +120,8 @@ def crm(a_list: List[int], n_list: List[int]) -> int:
     :param n_list: A list of integers b_i in the above equation.
     :return: The unique integer x such that x = a_i (mod n_i) for all i.
     """
-    a_list = [mpz(a_i) for a_i in a_list]
-    n_list = [mpz(n_i) for n_i in n_list]
+    a_list = [mpzCast(a_i) for a_i in a_list]
+    n_list = [mpzCast(n_i) for n_i in n_list]
 
     N = prod(n_list)
     y_list = [N // n_i for n_i in n_list]

setup.py

@@ -24,7 +24,7 @@
     url='https://github.com/cryptovoting/damgard-jurik',
     packages=setuptools.find_packages(),
     install_requires=[
-        'gmpy2'
+        'pycryptodomex'
     ],
     classifiers=[
         'Programming Language :: Python :: 3',