Masked Zero Comparison Without Boolean Mask Conversion
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Solution Overview
Problem
Existing cryptographic algorithms are vulnerable to side-channel attacks and require significant computational resources when performing secure comparisons with zero, especially in the context of quantum computing threats and modular additive masks with prime moduli.
Innovation Solution
A method for secure comparison with zero using a set of n intermediate data partitioned into subsets, where the results of exclusive-or operations on these subsets equal zero only when the input datum is zero, implemented in cryptographic algorithms like Hamming Quasi-Cyclic, FrodoKEM, and Crystals-Kyber, allowing for secure comparisons without converting modular additive masks to Boolean masks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing methods for secure comparison with zero are used, then security against side-channel attacks is improved, but device complexity and computational resource requirements increase significantly
Solution Approach 1:
The patent segments the set of n intermediate data into two subsets, computing XOR results separately for each subset. This segmentation allows the comparison operation to be divided into manageable parts that can be processed with reduced computational complexity while maintaining security properties through the masking scheme.
Solution Approach 2:
The patent changes the parameter of the modulus from being restricted to prime numbers to allowing composite numbers. This parameter change expands the适用范围 of the method to more cryptographic algorithms while reducing computational demands, as composite moduli enable more efficient arithmetic operations in certain contexts.
2Reliability
If existing methods for secure comparison with zero are used, then security against side-channel attacks is improved, but the method is limited to prime modulus q
Solution Approach 1:
The patent changes the parameter of the modulus from being restricted to prime numbers to allowing composite numbers. This parameter change expands the适用范围 of the method to more cryptographic algorithms while reducing computational demands, as composite moduli enable more efficient arithmetic operations in certain contexts.
3Reliability
If quantum computing threats are considered, then cryptographic security requirements are improved, but computational resource demands increase
Solution Approach 1:
The patent performs partial comparison operations by dividing the intermediate data into subsets and computing XOR results for each subset separately. This partial action approach provides sufficient security against quantum attacks while consuming fewer computational resources than a complete comparison would require.
Solution Approach 2:
The patent segments the set of n intermediate data into two subsets, computing XOR results separately for each subset. This segmentation allows the comparison operation to be divided into manageable parts that can be processed with reduced computational complexity while maintaining security properties through the masking scheme.
Data Source
AI summary
A method for carrying out secure comparison with zero of a masked input datum taking the form of a first set of n first shares of a modular additive mask, and comprising the following steps: determining a second set of intermediate data from the first shares, determining a third set of third shares of a Boolean mask of the result of the comparison from the intermediate data, the second set having a partition into a first subset and a second subset such that a result obtained by combination with exclusive-or operations of zero and of the intermediate data of the first subset, is equal to a result obtained by combination with exclusive-or operations of zero and of the intermediate data of the second subset, when and only when the input datum is equal to 0.