Digital Signatures Using Error Polynomials for Quantum Resistance
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Solution Overview
Problem
Existing digital signature schemes may become insecure with the advent of higher capacity computing, such as quantum computing, and are often inefficient in practice, lacking robustness against forgery attempts.
Innovation Solution
The use of digital signatures that incorporate error polynomials for generating verification keys, where coefficients are limited and computed using randomization techniques, providing a signing key to produce message signatures and a verification key to authenticate messages, leveraging the hardness of the learning with errors problem to secure the verification process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing digital signature schemes are used, then implementation is straightforward, but security becomes vulnerable to quantum computing and higher capacity computing
Solution Approach 1:
The patent changes the mathematical parameters and structure of digital signature schemes by incorporating error polynomials and lattice-based cryptography. This transforms traditional signature schemes into quantum-resistant variants by fundamentally altering the underlying mathematical problems from discrete logarithm-based to lattice-based hardness assumptions, thereby improving security against quantum computing while maintaining functional versatility
Solution Approach 2:
The patent combines multiple cryptographic elements (error polynomials, lattice structures, and traditional signature components) into a composite cryptographic system. This hybrid approach integrates the hardness of lattice problems with polynomial error terms to create a multi-layered security structure that resists both classical and quantum attacks while preserving digital signature functionality
2Reliability
If traditional digital signature schemes are used, then computational efficiency is acceptable, but robustness against forgery attempts is insufficient
Solution Approach 1:
The patent performs preliminary actions by pre-generating verification keys with embedded error polynomials and lattice structures before actual signing operations. This advance preparation ensures that the cryptographic structure is already optimized for forgery resistance, allowing verification processes to rely on pre-established hardness assumptions rather than computing them in real-time, thus balancing robustness with manageable complexity
3Power
If quantum computing becomes feasible, then computing power increases, but existing digital signature schemes become insecure
Solution Approach 1:
The patent converts the potential harm of quantum computing into a benefit by designing signature schemes based on lattice problems that are believed to be hard for both classical and quantum computers. Instead of trying to prevent quantum computing, the invention embraces it by selecting mathematical problems whose hardness is preserved even against quantum algorithms, effectively turning the quantum threat into an opportunity for more robust cryptography
Data Source
AI summary
Representations of polynomials a, s, t, e—1 and e—2 can be provided. Values of coefficients of the polynomials can be limited, and can be computed using randomization techniques. A verification key can be generated to include representations of polynomials a, b, and c. Computation of b can include computing a product using a and s, and adding e—1. Computation of c can include computing a product using a and t, and adding e—2. A signing key can represent s and t. The signing key can be used to produce a message signature that can represent a sum of t and a product of s and m, with m being derived from a message to be signed. The verification key can be used to verify the signature by checking coefficient sizes of a polynomial represented by the signature, and of a checking polynomial derived from the verification key and the signature.