Polynomial Coefficient Lifting for Fault-Resistant Post-Quantum Crypto
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Solution Overview
Problem
Emerging quantum computing poses a threat to classical cryptographic schemes like RSA and ECC, making lattice-based cryptographic algorithms vulnerable to quantum attacks, and these algorithms are prone to side-channel and fault attacks due to their complexity, necessitating efficient countermeasures for resource-constrained devices.
Innovation Solution
A method involving transforming polynomial coefficients from a smaller integer ring to a larger ring using a lifting and randomization mechanism, followed by verification to detect faults and mask coefficients, ensuring security against side-channel and fault attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If lattice-based cryptographic algorithms are used to resist quantum attacks, then security against quantum computing threats is improved, but the algorithms become more complex with longer execution times and higher memory usage
Solution Approach 1:
The patent segments the polynomial coefficients into multiple parts by introducing a splitting integer, dividing the coefficient space into smaller manageable components that can be processed separately through modular arithmetic operations
Solution Approach 2:
The patent changes the parameter space by introducing a splitting integer parameter that transforms the coefficient representation from a single large integer to multiple smaller integers modulo the splitting integer, enabling more efficient processing while maintaining security
2Reliability
If polynomial operations are performed with larger integer rings to protect against side-channel attacks, then security against implementation attacks is improved, but computational resources and storage requirements increase
Solution Approach 1:
The patent changes the integer ring parameter by introducing a splitting integer that creates a modular arithmetic system with smaller prime modulus, reducing the computational burden while maintaining security through the modular structure
Solution Approach 2:
The patent segments the large integer ring operations into multiple smaller modular operations by introducing the splitting integer, allowing parallel processing and reducing the computational resources required for each individual operation
3Reliability
If masking of polynomial coefficients is implemented to prevent side-channel attacks, then security is improved, but the number of intermediate variables and potential leakage points increase
Solution Approach 1:
The patent makes the masking mechanism universal by using the splitting integer to simultaneously achieve multiple objectives: protecting against side-channel attacks, enabling fault detection, and maintaining computational efficiency through a single integrated approach
Data Source
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AI summary
The method is executed by a computing device (300). It includes a cryptographic operation including at least one polynomial operation (130; 230) on at least one polynomial (A, B) with coefficients in an integer ring ( ℤq) that represents the integers modulo q, q being an integer, said method comprising : A) transforming (120; 220) the polynomial coefficients from said integer ring ℤq( ℤpqt) into a larger integer ring (), at least by lifting (123) the coefficients with a lifting integer (rp; rA_p, rB_p) from another integer ring ( ℤp) that represents the integers modulo p, p being an integer, so that the transformed coefficients modulo p are equal to said lifting integer (rp; rA_p, rB_p), B) performing (130; 230) the at least one polynomial operation with the transformed coefficients to obtain an intermediate result that is verifiable based on said lifting integer (rp; rA_p, rB_p), and C) reducing coefficients of said intermediate result modulo q to provide a result of the cryptographic operation.