Code-Based Cryptography Using Goppa Codes for Quantum Resistance
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Solution Overview
Problem
Current cryptographic systems, particularly those relying on asymmetric encryption, are vulnerable to quantum computers which can factor large prime numbers efficiently, posing a security threat in the post-quantum computing era, and require large key sizes, making them inefficient for deployment on classical devices like smartphones and IoT devices.
Innovation Solution
A cryptographic system utilizing code-based encryption schemes based on binary irreducible Goppa codes with a support set of rational functions and a weighted Hamming metric, which provides increased security against quantum computers and maintains efficiency in encryption/decryption processes, implemented using a Trusted Platform Module (TPM) or USB secure key for enhanced security.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If asymmetric encryption (RSA, El Gamal) is used to secure data transmission, then security against classical computers is improved, but vulnerability to quantum computer attacks increases and key size becomes large
Solution Approach 1:
The patent changes the fundamental mathematical parameter from factoring large integers (RSA) or discrete logarithms (El Gamal) to decoding linear codes over finite fields (Goppa codes). This parameter change makes the encryption resistant to quantum computer attacks while maintaining security against classical computers, directly resolving the vulnerability issue.
Solution Approach 2:
The patent substitutes the mathematical mechanism from number-theoretic problems (factoring, discrete logs) to coding theory problems (linear code decoding). This substitution replaces the vulnerable cryptographic primitive with a quantum-resistant one based on the hardness of decoding random linear codes, which is believed to be resistant to both classical and quantum attacks.
2Reliability
If large key sizes are used in asymmetric encryption to maintain security, then security strength is improved, but computational efficiency and deployment on resource-constrained devices deteriorates
Solution Approach 1:
The patent changes the cryptographic parameter from large integer keys (2048-4096 bits for RSA) to compact code-based keys. The Goppa code parameters (n, k, t) provide equivalent security with smaller key sizes and faster operations, improving computational efficiency while maintaining security strength.
Solution Approach 2:
The patent substitutes the computationally intensive number-theoretic operations with more efficient linear algebra operations over finite fields. The encoding and decoding operations in code-based cryptography involve matrix multiplications and Gaussian elimination, which are more efficient than modular exponentiation and factorization, especially on resource-constrained devices.
Data Source
AI summary
A system and method for encryption of data. The system and method utilizes a cryptographic function that provides asymmetric encryption/decryption and digital signing capabilities that are hardened against cyber attack from quantum computers.