Square Masking in Binary Fields for Side-Channel Protection
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Solution Overview
Problem
Existing cryptographic algorithms are vulnerable to side-channel attacks, which exploit physical quantities like electricity consumption and electromagnetic radiation to infer secret keys, and current masking techniques, such as Boolean and multiplicative masking, fail to provide an optimal balance between security and performance, especially against high-order attacks.
Innovation Solution
A method using square masking in binary finite fields, where operations are performed on masked representations generated by exponentiating secret variables with a random power of two, combined with conversions to other masking types like Boolean, multiplicative, or affine masking as needed, to protect against side-channel attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If masking techniques are applied to protect against side-channel attacks, then security against attacks is improved, but computational complexity increases
Solution Approach 1:
The patent applies segmentation by dividing the secret variable into multiple shares (at least two shares) and performing operations on these shares rather than on the secret variable directly. This segmentation approach masks the secret variable against side-channel attacks while the linearity of operations on shares maintains computational efficiency, resolving the contradiction between security improvement and complexity increase.
2Reliability
If higher-order masking is used to resist higher-order attacks, then security against high-order attacks is improved, but performance degradation increases
Solution Approach 1:
The patent changes the parameter of masking order by using at least first-order masking (with at least two shares) to protect against first-order attacks, and optionally higher-order masking to resist higher-order attacks. The linearity of operations on masked values ensures that the performance degradation is minimized compared to non-linear masking approaches, thus resolving the contradiction between security improvement and performance maintenance.
3Object-affected harmful factors
If secret variables are masked and operations are modified, then vulnerability to side-channel attacks is reduced, but algorithm operation complexity increases
Solution Approach 1:
The patent introduces masked values as intermediaries between the secret variables and the output. Operations are performed on these intermediary masked values rather than directly on secret variables. The linearity of operations on masked values allows the use of simple operations (addition, multiplication, exponentiation) that maintain algorithmic simplicity while effectively protecting against side-channel attacks through the intermediary masking layer.
Data Source
AI summary
The present invention relates to a method for protecting an electronic device against side-channel attacks. The electronic device is configured to execute a cryptographic algorithm comprising operations in a binary finite field GF(2n), n being a positive integer. The algorithm uses at least one secret variable s to be protected. The method includes:determining a random variable k,computing a masked representation M(s, k) of the secret variable s using a masking function M including an exponentiation by 2{circumflex over ( )}k,for each operation involving a sensitive variable v corresponding to the secret variable s or to an intermediate result obtained from the secret variable s, executing the operation from a masked representation M(v, k′) of the sensitive variable v,determining an output variable r from a final result obtained in the form of a masked representation M(r, k″).