Hypersphere Multivariable Signature System Security
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Solution Overview
Problem
Existing multivariate public key signature schemes are insecure due to the lack of a threshold in their quadratic equation design, making them vulnerable to attacks, and they often require complex mathematical operations or result in lengthy public keys, which complicates their practical application.
Innovation Solution
A system and method for multivariate public key signature/verification based on hypersphere, which uses affine transformation inversion, linear equations construction, and Gaussian elimination to generate and verify signatures, eliminating the need for 'Large Field Technology' and hiding the center map with sphere centers, thus enhancing security and reducing public key length.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional multivariate public key signature schemes use quadratic equation design, then signature functionality is provided, but security is compromised due to lack of threshold and vulnerability to attacks
Solution Approach 1:
The patent changes the mathematical parameters from quadratic equations to a system involving sphere centers and distance calculations. By transforming the problem into finding points at specific distances from sphere centers in a multidimensional space, the security threshold is established while maintaining signature functionality. This parameter transformation resolves the contradiction by providing both security and feasibility.
2Ease of operation
If Large Field Technology is used to map public key to large field with isomorphism, then decryption is facilitated, but structure becomes exploitable by attackers
Solution Approach 1:
The patent extracts and removes the vulnerable Large Field Technology component from the system. Instead of mapping to a large field with isomorphism structures that can be exploited, the invention uses direct distance calculations from sphere centers in the original multidimensional space. This extraction eliminates the security vulnerability while preserving the ability to perform decryption through distance verification.
3Productivity
If UOV scheme mixes Oil variables and Vinegar variables in polynomial construction, then signature speed is improved, but public key length becomes very long
Solution Approach 1:
The patent transitions from the polynomial variable mixing approach of UOV to a geometric interpretation in multidimensional space. By representing the signature problem as finding points at specific distances from sphere centers, the invention achieves fast signature generation through simple distance calculations while avoiding the public key length expansion caused by mixing Oil and Vinegar variables in traditional polynomial constructions.
Data Source
AI summary
A hypersphere-based multivariable public key signature/verification system includes signature and verification modules, wherein the signature module comprises a processor, an affine transformation inversion part I, a trap door part and an affine transformation inversion part II. Corresponding operations are sequentially executed on a message, one or more groups of solutions are produced after the processing of the trapdoor part, a group of solutions are randomly selected, then a signature is continuously produced by the various parts, and finally the signature, together with the message, is transmitted to the processor. The verification module comprises a processor and a public key transformation part, wherein the processor transmits a signature to the public key transformation part to execute an operation, and then judges whether the obtained data is equal to a message in a memory or not: if so, the signature is valid, otherwise the signature is invalid.