Diophantine Digital Signatures for Quantum-Resistant Authentication
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Solution Overview
Problem
Existing digital signature schemes are vulnerable to quantum computing, lacking robustness against parallel and sequential computations, and require protection against brute force algorithms for private key calculation.
Innovation Solution
A digital signature scheme based on Diophantine systems of equations, utilizing polynomial equations with integer coefficients and uniform distribution of random variables, providing resistance against standard and quantum computing through the non-existence of a general algorithm for solving such equations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing digital signature schemes are used, then ease of operation is maintained, but security against quantum computing is compromised
Solution Approach 1:
The patent changes the mathematical parameters from standard asymmetric cryptography to Diophantine equations with multiple variables. This transformation increases security against quantum computing by leveraging the computational difficulty of solving systems of Diophantine equations, while maintaining operational functionality through structured equation systems with known solutions for legitimate users.
Solution Approach 2:
The digital signature scheme combines multiple Diophantine equations with different variables and coefficients into a composite system. This composite structure creates layered security where solving the signature requires addressing multiple interconnected equations simultaneously, providing quantum resistance while maintaining signature verification capability.
2Reliability
If standard asymmetric cryptography is used, then ease of manufacture is maintained, but vulnerability to brute force algorithms increases
Solution Approach 1:
The patent segments the private key into multiple variables within the Diophantine equation system rather than using a single key value. This segmentation increases resistance to brute force attacks because an attacker must solve for multiple interrelated variables simultaneously, exponentially increasing the computational effort required compared to traditional single-key systems.
Solution Approach 2:
The patent transitions from one-dimensional key spaces in standard cryptography to multi-dimensional solution spaces in Diophantine equations. By introducing multiple variables and equations, the security landscape expands to higher dimensions, making traditional brute force and parallel computation approaches ineffective while maintaining implementability through structured mathematical frameworks.
3Reliability
If quantum computing resistance is implemented, then security is improved, but computational overhead increases
Solution Approach 1:
The patent performs preliminary setup by establishing the Diophantine equation system and pre-computing certain parameters during key generation. This preliminary action allows the legitimate user to have pre-prepared components that facilitate faster signature generation, reducing the computational overhead during actual signing operations while maintaining quantum resistance.
Solution Approach 2:
The patent uses copying by having the legitimate user work with known solutions and pre-established relationships in the Diophantine system. Instead of performing complex computations from scratch during signature generation, the system leverages pre-computed values and known mathematical relationships, significantly improving signature generation speed while maintaining security.
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.