Multivariate Polynomial Digital Signature Quantum Resistance
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Solution Overview
Problem
Current digital signature schemes and public-key authentication schemes rely on problems like prime factorization and discrete logarithm, which can be easily solved by quantum computers, compromising their security. There is a need for schemes based on different problems, such as multivariate polynomial problems, to ensure high security.
Innovation Solution
An information processing apparatus and method using a multi-order multivariate polynomial set and vector, where the polynomial set and vector are public keys, and a secret key is used to generate messages and responses for verification, ensuring security through the difficulty of solving multi-order multivariate simultaneous equations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If digital signature schemes based on prime factorization or discrete logarithm problems are used, then current security standards are met, but security is compromised when quantum computers are utilized
Solution Approach 1:
The patent changes the mathematical foundation from classical problems (prime factorization, discrete logarithm) to multivariate polynomial problems. Specifically, it uses a system of multivariate quadratic equations over finite fields, where the security relies on the difficulty of solving these equations without knowledge of the secret key structure, a problem that remains hard even for quantum computers.
2Reliability
If new digital signature schemes based on multivariate polynomial problems are implemented, then resistance to quantum computer attacks is achieved, but computational complexity increases
Solution Approach 1:
The patent segments the multivariate polynomial system into specific structured components: public matrices A and B, secret matrices S and T, and a structured polynomial system. This segmentation allows the complex problem to be divided into manageable parts where the public key consists of easily computable matrices while the security relies on the hidden structure of the secret matrices and their relationship through the polynomial equations.
3Reliability
If multi-order multivariate simultaneous equations are used for security, then quantum resistance is achieved, but solving difficulty increases even for classical computers
Solution Approach 1:
The patent creates an asymmetric structure where the public key (matrices A and B) appears simple and easy to work with, while the secret key (matrices S and T with their specific structural relationships) provides the hardness. The asymmetry lies in the fact that while A and B are publicly available, deriving the secret structure from them requires solving the hard multivariate polynomial problem, creating a one-way function suitable for digital signatures.
Data Source
AI summary
Provided is an information processing apparatus including a message generating unit that generates a message based on a multi-order multivariate polynomial set F=(f1, . . . , fm) defined on a ring K and a vector s that is an element of a set Kn, a message providing unit that provides the message to a verifier holding the multi-order multivariate polynomial set F and a vector y=(y1, . . . , ym)=(f1(s), . . . , fm(s)), and a response providing unit that provides the verifier with response information corresponding to a verification pattern selected by the verifier from among k (where k≧3) verification patterns. The vector s is a secret key. The multi-order multivariate polynomial set F and the vector y are public keys. The message is information obtained by performing an operation prepared for a verification pattern corresponding to the response information in advance using the public keys and the response information.