This project is dedicated to the world community as an Open-source Post-quantum blockchain layer 1 project, means anyone can join and contribute based on his/ her passion and skills. SPHINX is a blockchain protocol designed to provide secure and scalable solutions in the post-quantum era.
This repository contains code for the SPHINXHash project, which is a Hashing module for the SPHINX blockchain framework. The SPHINXHash aims to provide a Hash function in the blockchain systems
Today the world well known that Lattice-Based cryptographic algorithms are gaining attention as promising solutions to mitigate security risks posed by quantum computers, SPHINXHash utilizes the 256 digest size from SWIFFTX as main hash function, its involves iteratively applying a compression function to the input data. The compression function in SWIFFTX is based on ideal lattices, which are mathematical structures with desirable properties for cryptographic purposes.
SWIFFTX rely on the HAIFA (HAsh Iterative FrAmework) construction, combined with the use of ideal lattices, allows SWIFFTX to achieve its cryptographic goals, such as collision resistance and preimage resistance.
During the NIST hash function competition in 2008 , SWIFFTX was submitted as a candidate along with other hash functions, as mentioned earlier. While it did not advance to the final round of the competition, SWIFFTX's utilization of ideal lattices and the HAIFA construction contributed to the broader research and understanding of hash function design.
The SWIFFTX compression functions are designed with simplicity and mathematical elegance, which facilitates analysis and optimization. Notably, they possess two unique characteristics:
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Asymptotic Security Proof: It is formally proven that finding a collision in a randomly-selected SWIFFTX compression function is at least as difficult as finding short vectors in cyclic/ideal lattices in the worst-case scenario. This provides a strong foundation for its security guarantees.
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High Parallelizability: SWIFFTX's compression function enables efficient implementations on modern microprocessors, even without relying on multi-core capabilities. This is achieved through an innovative cryptographic utilization of the Fast Fourier Transform (FFT).
The core component of SWIFFTX is the SWIFFT family of compression functions, initially introduced in the 2008 workshop on Fast Software Encryption (Lyubashevsky et al., FSE’08). Careful attention was given to address a major drawback of SWIFFT, which is linearity, while preserving its provable collision resistance.
Specifically, the SWIFFTX compression function maps 2048 input bits to 520 output bits. The chosen mode of operation is HAIFA (Biham and Dunkelman, 2007), resulting in a hash function capable of accommodating inputs of any length up to 264 − 1 bits. The resulting message digests align with the required lengths of SHA-3, including 224, 256, 384, and 512 bits.
It takes a specific input format and produces a sequence of values as output. Here is a description of the SWIFFT function:
Input Format:
The SWIFFT function takes m = 32 (or in one special case, m = 25) 64-bit words, denoted as x1,...,xm, resulting in a total of 2048 (or 1600) bits. These words are indexed by fixed "randomizer" elements a1,0, . . . , am,63 ∈ Z257, which are uniformly random integers modulo 257.
Mathematical Description:
Let rev: {0,...,63} → {0,...,63} be the "bit-reversal" function, which rearranges the bits of a 6-bit binary number. SWIFFT operates as follows:
- Permute the bits
xj,0, . . . , xj,63in each wordxjusing the bit-reversal function to obtainxj,rev(0), . . . , xj,rev(63). - Interpret each (permuted) word
xj,rev(0),...,xj,rev(63) as coefficients of a polynomialpj(α)of degree (at most)63: pj(α) = xj,rev(0) + xj,rev(1) · α + ... + xj,rev(63) · α^63. - Evaluate each polynomial
pj(·)on all the odd powers ofω = 42modulo257: ω, ω^3, ω^5, ..., ω^127. - Multiply each resulting value
pj(ω^2i+1)byaj,iandsumthem over alljto obtainzi' = a1,i · p1(ω^2i+1) + ... + am,i · pm(ω^2i+1).
Evaluating pj(α) on all odd powers of ω can be performed in various ways, with one efficient method involving pre-multiplication of coefficients by ω^i and subsequent evaluation on all powers of ω^2.
The choice of parameters, specifically ω = 42 and modulus 257, was primarily driven by efficiency considerations. Notably, the cryptographic strength of the SWIFFTX function is largely independent of these specific parameter values. In fact, during the post-processing stage of SWIFFTX, an instantiation of SWIFFT with a different modulus is employed.
Since 257 is a prime number, the ring of integers modulo 257 forms a finite field. The multiplicative group of this field is cyclic and consists of exactly 256 elements. It is worth noting that any generator of the multiplicative group has an order of 256. In the context of SWIFFTX, we require an element of order 128, which can be obtained by squaring any generator from the multiplicative group. The value ω = 42 serves as one such element with an order of 128. Additionally, ω = 42 possesses additional properties that facilitate highly optimized implementations.
The output of the SWIFFT function is comprised of elements in Z257, we need a function that converts them into binary quantities for further use. We perform a simple change of base from 257 to 256 by taking groups of 8 elements z0′ ,...,z7′ ∈ Z257 and producing 8 elements z0,...,z7 in Z256 and a bit `b ∈ {0,1}.
In the SWIFFTX compression function, the ConvertToBytes procedure combines bits from 8 groups to form one byte. Consequently, ConvertToBytes is an injective function that maps 64 elements of Z257 into 65 bytes.
The linearity of the SWIFFT functions in the inner and outer layers of SWIFFTX is disrupted by two factors: the base change performed by ConvertToBytes and an S-Box operation. The S-Box is a simple permutation that maps one byte to another byte, ensuring it is a permutation and lacking any trapdoors. Notably, the S-Box is constructed using the digits of 'e' in a specific manner.
The SWIFFTX compression function takes a 2048-bit input and applies three SWIFFT functions with distinct randomizers. The FFT operation needs to be performed only once for each set of input blocks. The resulting intermediate values are computed as follows:
for i in range(7):
zi·257 = zi·256 + b·256
Here, 'b' represents the bit from each group of 8. The computed values are then used in subsequent computations.
The output of the three SWIFFT functions is fed into the ConvertToBytes function, resulting in a total of 195 bytes (3 × 65). Each byte is then processed through the S-box, completing the linearity disruption in SWIFFTX.
The arrangement of these 195 bytes, 5 bytes corresponding to S-box(0) are appended, resulting in a total of 200 bytes or 1600 bits.
This 1600-bit output serves as the input for the subsequent SWIFFT. The output of this SWIFFT is then passed through the ConvertToBytes function, resulting in 520 bits. These bits can either be fed into the next compression function or directed to the FinalTransform function (described below).
The output of SWIFFTX, while almost regularly distributed over the domain Z64, needs to be uniformly distributed over Z512 for the entire hash function. However, when converted to 65 bytes using the ConvertToBytes function, the resulting 520 bits exhibit statistical bias. To address this, after processing the final block of the input, it is necessary to convert these 520 skewed bits into 512 uniformly-distributed bits. Our objective is to preserve the security proof while achieving this transformation, which is achieved by performing an operation equivalent to evaluating an additional SWIFFT function with a 520-bit input.
To accomplish this, 520 bits to 576 bits by padding them with zero bits. Next, we break these bits into 9 groups of 64 bits, treating each group as a polynomial 'xi' of degree at most 63. We leverage the 576 randomizer elements that were previously created and create 9 polynomials 'pi'. Then, we compute the expression x0p0 + x1p1 + ... + x8p8 over the ring Z256[α]/(α64 + 1). The result is a polynomial of degree 63 whose coefficients are elements modulo 256, representing bytes. This process ensures the generation of the required 512 bits for the final transformed output.
Find the document here SWIFFTX
The code in the repository is a part of the SPHINX blockchain algorithm, which is currently in development and not fully integrated or extensively tested for functionality. The purpose of this repository is to provide a framework and algorithm for the main hash function scheme in the SPHINX blockchain project.
As the project progresses, further updates and enhancements will be made to ensure the code's stability and reliability. We encourage contributors to participate in improving and refining the SPHINXHash algorithm by submitting pull requests and providing valuable insights.
We appreciate your understanding and look forward to collaborative efforts in shaping the future of the SPHINX blockchain project.
To get started with the SPHINX blockchain project, follow the instructions below:
- Clone the repository:
git clone https://github.com/ChyKusuma/SPHINXHash.git - Install the necessary dependencies (List the dependencies or provide a link to the installation guide).
- Explore the codebase to understand the project structure and components.
- Run the project or make modifications as needed.
We welcome contributions from the developer community to enhance the SPHINX blockchain project. If you are interested in contributing, please follow the guidelines below:
- Fork the repository on GitHub.
- Create a new branch for your feature or bug fix:
git checkout -b feature/your-feature-nameorgit checkout -b bugfix/your-bug-fix. - Make your modifications and ensure the code remains clean and readable.
- Write tests to cover the changes you've made, if applicable.
- Commit your changes:
git commit -m "Description of your changes". - Push the branch to your forked repository:
git push origin your-branch-name. - Open a pull request against the main repository, describing your changes and the problem it solves.
- Insert your information (i.e name, email) in the authors space.
Specify the license under which the project is distributed (MIT License).
If you have any questions, suggestions, or feedback regarding the SPHINX blockchain project, feel free to reach out to us at [email protected].