HFEv- Signature Scheme Parameter Optimization for Quantum Security
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Solution Overview
Problem
Classical public key cryptographic schemes, such as RSA and DSA, are vulnerable to quantum computer attacks due to Shor's algorithm, necessitating the development of alternative schemes based on hard mathematical problems not affected by quantum computers, and existing multivariate signature schemes like QUARTZ are inefficient due to high-degree polynomials and lack of theoretical parameter selection.
Innovation Solution
The proposal introduces new parameter choices for HFEv-based signature schemes by reducing the degree of the central polynomial and increasing the number of Vinegar variables and Minus equations, resulting in a significantly faster signature generation process while maintaining security, and applies multivariate signature schemes to build white-box encryption schemes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a high degree HFE polynomial is used (as in QUARTZ with degree D=129), then the security of the signature scheme is improved, but the signature generation process becomes very slow
Solution Approach 1:
The patent changes the degree parameter D of the HFE polynomial from high (129 in QUARTZ) to low (e.g., D=5, 7, 11), and simultaneously adjusts other parameters (number of variables n, number of vinegar variables v, number of minus equations a) to maintain security while achieving fast signature generation (e.g., 112-bit security with D=5, n=100, v=40, a=20)
2Productivity
If the degree of the central HFE polynomial is reduced to speed up signature generation, then the signature generation process becomes faster, but the security of the scheme may be weakened
Solution Approach 1:
The patent systematically adjusts multiple parameters together (degree D, number of variables n, vinegar variables v, minus equations a) based on theoretical security analysis, showing that low degree D can achieve both fast signature generation and high security (e.g., 112-bit security level)
Solution Approach 2:
The patent performs preliminary theoretical and experimental analysis of algebraic attack complexity on HFEv- schemes to establish parameter selection guidelines before designing the signature scheme, enabling secure parameter choices with low degree polynomials
3Reliability
If the number of Vinegar variables and Minus equations is increased to compensate for lower polynomial degree, then the security is maintained, but the device complexity increases
Solution Approach 1:
The patent optimizes the balance between vinegar variables v and minus equations a to achieve security with moderate complexity, providing concrete parameter sets that avoid excessive complexity while maintaining high security levels
Data Source
AI summary
We present new designs to choose the parameter sets for more efficient HFEv-based signature schemes. The key method is to reduce the degree of the central HFEv-polynomial while, at the same time, increasing the number of Vinegar variables and Minus equations. The new design speeds up the signature generation process by two orders of magnitude (hundreds of times) compared to QUARTZ. We present also new methods to use multivariate signature schemes to build a white box encryption scheme. This technique is applicable to all existing multivariate signature designs including the HFEV-design and the improvements.