Diophantine Digital Signatures for Quantum-Resistant Authentication
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Solution Overview
Problem
Existing digital signature schemes are vulnerable to quantum computing, lacking effective protection against parallel and sequential computations, and require improvements to ensure security against both standard and quantum computing threats.
Innovation Solution
A digital signature scheme based on Diophantine systems of equations, utilizing polynomial equations with integer coefficients and a finite number of unknowns, employs a hash function and public-private key pairs to create a signature that is computationally infeasible to break, even with quantum computers, by leveraging the unsolvability of Hilbert's tenth problem.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing digital signature schemes are used, then the authentication process is simple and efficient, but the security is vulnerable to quantum computing attacks
Solution Approach 1:
The patent changes the fundamental mathematical parameters from standard cryptographic problems (factoring, discrete logarithm) to Diophantine equations with specific constraints. By modifying the mathematical domain and parameters used in digital signatures, the system achieves quantum resistance while maintaining operational functionality.
Solution Approach 2:
The patent replaces the traditional cryptographic mechanism (based on algebraic structures like groups and fields) with a number-theoretic mechanism based on Diophantine equations. This substitution creates a fundamentally different computational problem that is resistant to quantum algorithms while preserving the digital signature functionality.
2Reliability
If Diophantine systems are used for digital signatures, then resistance against quantum computing is achieved, but the computational complexity increases
Solution Approach 1:
The patent performs preliminary setup by pre-computing and storing certain Diophantine equation parameters and solutions. This preliminary action reduces the computational burden during actual signing and verification operations, thereby reducing computation time while maintaining quantum resistance.
Solution Approach 2:
The patent segments the Diophantine equation solving process into manageable parts, using pre-computed values and structured approaches to solve the equations efficiently. By breaking down the complex computational task into smaller, pre-prepared components, the system reduces real-time computation requirements.
Data Source
AI summary
Digital signatures using the Diophantine system of equations are implemented. A digital signature is an authentication mechanism that enables the creator of a message to attach a code that acts as a signature. A digital signature scheme typically includes three algorithms: a key generation algorithm, a signing algorithm, and a signature verifying algorithm. The key generation algorithm selects a private key uniformly at random from a set of possible private keys. The key generation algorithm outputs the private key and a corresponding public key. The signing algorithm produces a signature given a message and a private key. The signature verifying algorithm either accepts or rejects a message's claim to authenticity based at least in part on the message, the public key, and the signature.