Quantum Safe Cryptography Using Rank Deficient Matrices
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Solution Overview
Problem
Current public key encryption systems are vulnerable to quantum computer attacks using Shor's algorithm and are not secure for future quantum computing capabilities.
Innovation Solution
A quantum-safe cryptography and advanced encryption and key exchange method utilizing simple linear algebra, rank deficient matrices, and bilinear equations to create a secure symmetric key exchange system that is resistant to quantum computer attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If public key encryption is used to securely exchange symmetric keys, then key exchange security is improved, but the system becomes vulnerable to quantum computer attacks using Shor's algorithm
Solution Approach 1:
The patent changes the mathematical parameters from discrete logarithm problems (vulnerable to Shor's algorithm) to rank-deficient matrix problems over finite fields. By transforming the underlying mathematical structure from number-theoretic parameters to linear algebra parameters, the system achieves quantum resistance while maintaining key exchange functionality.
Solution Approach 2:
The patent substitutes the traditional public key cryptography mechanism (based on integer factorization or discrete logarithms) with a completely different mathematical mechanism based on rank-deficient matrices and bilinear equations. This substitution replaces the vulnerable cryptographic primitive with one that is resistant to quantum attacks.
2Reliability
If traditional public key encryption is used for key exchange, then security is provided, but the encryption speed is slow
Solution Approach 1:
The patent segments the cryptographic system into two distinct parts: a fast symmetric encryption layer for bulk data encryption and a rank-deficient matrix-based key exchange layer for secure key distribution. This segmentation allows each layer to be optimized independently, with the symmetric encryption providing high speed and the key exchange providing quantum-resistant security.
Solution Approach 2:
The patent introduces rank-deficient matrices as an intermediary mathematical structure that enables efficient key exchange. The matrices serve as a mediator between the communicating parties, allowing them to establish shared secrets through fast matrix operations rather than through slow traditional public key algorithms.
3Object-affected harmful factors
If quantum safe cryptography using rank deficient matrices and bilinear equations is implemented, then quantum resistance is achieved, but system complexity increases
Solution Approach 1:
The patent uses disposable, randomly generated rank-deficient matrices for each key exchange session. These matrices are simple mathematical structures that can be easily generated and discarded, providing quantum-resistant security without requiring complex, long-term cryptographic infrastructure. The simplicity of the matrix structure keeps implementation complexity manageable.
Data Source
AI summary
An advanced encryption and key exchange (AEKE) algorithm for quantum safe cryptography is disclosed. The AEKE algorithm does not use hard mathematical problems that are easily solvable on a quantum computer with Shor's algorithm. Instead, new encryption algorithm uses simple linear algebra, rank deficient matrix and bilinear equation, which will be easy to understand, fast, efficient and practical but virtually impossible to crack.