Masked Polynomial Operations for Side-Channel-Resistant Cryptography
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Solution Overview
Problem
Lattice-based cryptographic algorithms are vulnerable to side-channel attacks, and existing masking schemes require unmasking of polynomial coefficients before operations, which compromises security.
Innovation Solution
A method involving lifting polynomial coefficients to a new representation modulo q′, applying randomization through additive and multiplicative masking, and performing operations on randomized polynomials, followed by simple unmasking to retrieve results, ensuring coefficients remain masked during polynomial additions and multiplications.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If polynomial coefficients are masked with random masks to protect against side-channel attacks, then security against side-channel attacks is improved, but polynomial operations cannot be performed without unmasking first
Solution Approach 1:
The patent introduces an intermediary modular arithmetic system where polynomial operations can be performed on masked coefficients. By working in a modular space with carefully chosen moduli, the invention enables additions and multiplications to commute with the masking operation, allowing secure computation without requiring unmasking between operations
Solution Approach 2:
The patent changes the parameter space by introducing modular arithmetic with specific moduli relationships. By transforming the coefficient space to work with modular representations and leveraging number-theoretic properties, the invention allows masked polynomial operations to be performed directly, resolving the contradiction between security and operational capability
2Ease of operation
If polynomial coefficients are unmasked before operations to enable computation, then ease of operation is improved, but security against side-channel attacks deteriorates
Solution Approach 1:
The modular arithmetic system acts as an intermediary that allows polynomial operations to be performed on masked data. The mathematical structure ensures that operations on masked coefficients produce correctly masked results, eliminating the need to unmask and thereby maintaining security while enabling computation
3Reliability
If a masking scheme requires unmasking before each operation, then security is maintained, but computational efficiency deteriorates due to repeated masking and unmasking
Solution Approach 1:
The patent enables continuous polynomial operations on masked coefficients without interruption for unmasking. By designing a masking scheme that is compatible with polynomial arithmetic in the modular domain, the invention maintains the masking throughout the entire computation sequence, thereby improving computational efficiency while preserving security
Solution Approach 2:
The modular arithmetic framework serves as an intermediary that makes masked polynomial operations directly computable. This eliminates the need for repeated masking and unmasking cycles, allowing continuous computation on masked data and significantly improving computational efficiency
Data Source
AI summary
Provided is a method to secure against side channel attacks performing a cryptographic operation of a cryptographic algorithm. It includes selecting a multiplier integer t and determining a second integer q′ by multiplying said first integer q, determining (S2) an invertible random polynomial R[X] in said first polynomial ring Rq, randomizing (S3) the coefficients Ai of said input polynomial A[X] based on said determined second integer q′ and said determined random polynomial R[X], performing (S4) the polynomial operation of the cryptographic operation on said randomized input polynomials A″[X], and unmasking (S5) the result polynomial Res″(X) by applying to its coefficients a modulo said first integer q operation. Other embodiments disclosed.