Polynomial Matrix Digital Signatures for Quantum-Resistant Authentication
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Solution Overview
Problem
Existing digital signature schemes like RSA and ECDSA are vulnerable to quantum computers, and existing quantum-secure schemes like Crystals Dilithium and SPHINCS are computationally complex and generate large signatures.
Innovation Solution
A method and system using polynomial matrices for generating and verifying digital signatures, employing linear and quadratic polynomials over finite fields to create secure, lightweight digital signatures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If quantum-secure digital signature schemes like Crystals Dilithium and SPHINCS are used, then quantum resistance is improved, but computational complexity and signature size increase
Solution Approach 1:
The patent changes the mathematical parameters by using multivariate quadratic equations over finite fields with specific dimensions (m=2, n=64) to achieve quantum security without the computational overhead of existing quantum-secure schemes. This parameter optimization reduces signature size and computation time while maintaining quantum resistance.
Solution Approach 2:
The patent combines multiple mathematical components (linear polynomial matrix, non-singular matrix, quadratic polynomials, and hash functions) into a composite signature scheme that achieves both security and efficiency. The signature consists of multiple components (s1, s2, t1, t2) that work together to provide quantum resistance without excessive complexity.
2Ease of manufacture
If existing digital signature schemes like RSA and ECDSA are used, then ease of implementation is improved, but quantum vulnerability increases
Solution Approach 1:
The patent replaces the mathematical foundations of RSA (integer factorization) and ECDSA (discrete logarithms) with a different mathematical approach based on multivariate quadratic equations over finite fields. This substitution creates a signature scheme that is resistant to quantum attacks while maintaining practical implementability through standard cryptographic operations.
3Reliability
If larger security parameters are used, then security level is improved, but signature size and computation time increase
Solution Approach 1:
The patent uses a balanced approach with m=2 quadratic polynomials and n=64 variables, which provides sufficient security without excessive complexity. This partial action approach achieves the required security level with minimal signature components, avoiding the need for overly large parameters that would increase signature size and computation time.
Data Source
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AI summary
This disclosure relates generally to cryptography and more particularly to a method and system for generating and verifying digital signature using polynomial matrices. Already available techniques for generating digital signature are easy to solve on a quantum computer. The disclosed method for digital signature generation is based on multivariate quadratic systems over finite fields and generates digital signatures with small size and computations are very lightweight which may be performed in all hardware platforms. The disclosed method uses matrix consisting of linear multivariate polynomial to define a private key and further uses the square of the private key matrix to define a public key polynomials. Further, the method uses matrices consisting of constants chosen randomly from finite field and uses a random matrix for digital signature generation. The digital signatures created are very small in size approximately in 100 bytes.