Masking Matrix Key Generation for Side-Channel Protection
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Solution Overview
Problem
Existing cryptographic technologies are vulnerable to side-channel attacks, particularly during key generation, as operations like GCD computation can leak secret information through physical emissions.
Innovation Solution
The implementation of matrix-based masking techniques, where input numbers are masked using elements of a masking matrix with random elements, to perform GCD and modular inversion operations, thereby protecting against side-channel attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional key generation operations are performed without masking, then computational efficiency is maintained, but the system becomes vulnerable to side-channel attacks that can leak secret information through physical emissions
Solution Approach 1:
The patent introduces masking matrices as intermediary elements that mediate between the secret cryptographic inputs and the computational operations. These matrices transform the secret values into masked representations that can be processed without directly exposing the secrets, thereby preventing side-channel leakage while maintaining the ability to perform necessary cryptographic computations
Solution Approach 2:
The patent changes the parameter representation by transforming secret values into masked forms using randomly generated masking matrices. This parameter transformation allows the system to work with equivalent mathematical representations that do not directly reveal the secret information through physical emissions, thus improving security against side-channel attacks
2Reliability
If masking techniques are applied to protect against side-channel attacks, then security is improved, but the computational overhead and operation time increase
Solution Approach 1:
The patent applies preliminary masking to the cryptographic inputs before the key generation operations commence. By pre-transforming the secret values into masked representations using randomly generated matrices, the system prepares the data in advance to resist side-channel attacks during the actual computational phase, avoiding the need for repeated masking operations throughout the computation
Solution Approach 2:
The patent segments the key generation process into distinct phases: masking preparation, masked computation, and result extraction. This segmentation allows the system to perform computationally intensive masking operations in advance and separately, enabling parallel processing and optimizing the timing of different operations to minimize overall execution time
3Reliability
If random masking matrices are used to mask input numbers, then protection against side-channel attacks is enhanced, but the mathematical operations become more complex
Solution Approach 1:
The patent changes the mathematical parameters by transforming secret values into masked forms using randomly generated matrices. This parameter transformation allows the system to work with equivalent mathematical representations that do not directly reveal the secret information through physical emissions, thus improving security against side-channel attacks
Data Source
AI summary
Disclosed are systems and techniques for enhanced protection of cryptographic key generation in cryptographic applications. In particular, described is a method and a system that performs the method of obtaining input numbers associated with a cryptographic application, generating masking matrix based on at least one random value, obtaining masked numbers using a matrix product of the MM and the input numbers, determining a greatest common divisor (GCD) of the masked numbers, identifying a GCD of the input numbers, and using the identified GCD to generate a cryptographic key.