Cryptographic Vector Randomization for Side-Channel Attack Protection
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Solution Overview
Problem
Cryptographic operations, particularly those using elliptic curve cryptography, are vulnerable to side-channel attacks due to the ability of attackers to correlate processor emissions with specific operations, potentially revealing private keys.
Innovation Solution
Implementing intermediate randomizations, such as random projective scaling and randomized storage of intermediate outputs, to obscure the data flow and make it difficult for attackers to correlate emissions with computational operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If intermediate randomization is applied to protect cryptographic operations, then security against side-channel attacks is improved, but computational complexity increases
Solution Approach 1:
The patent introduces random projective scaling factors as intermediary elements between the original cryptographic data and the processed data. These scaling factors act as mediators that obscure the relationship between input and output data, preventing side-channel attackers from correlating processor emissions with actual cryptographic operations while maintaining the mathematical validity of the computations.
Solution Approach 2:
The patent transforms the cryptographic data by changing its representation parameters through random projective scaling. Instead of operating directly on the original data points, the system operates on scaled versions where the scaling parameters are randomly selected, thereby changing the observable characteristics of the data without altering the underlying cryptographic relationships.
2Difficulty of detecting and measuring
If random projective scaling is used to obscure data flow, then correlation of processor emissions with operations becomes difficult, but additional computational operations are required
Solution Approach 1:
The patent applies random projective scaling selectively at critical points in the cryptographic algorithm rather than uniformly throughout all operations. This partial application provides sufficient obfuscation to prevent correlation attacks while minimizing the additional computational overhead by avoiding redundant scaling operations in every step of the algorithm.
Data Source
AI summary
Aspects of the present disclosure involve a method and a system to support execution of the method to perform a cryptographic operation involving a first vector and a second vector, by projectively scaling the first vector, performing a first operation involving the scaled first vector and the second vector to obtain a third vector, generating a random number, storing the third vector in a first location, responsive to the random number having a first value, or in a second location, responsive to the random number having a second value, and performing a second operation involving a first input and a second input, wherein, based on the random number having the first value or the second value, the first input is the third vector stored in the first location or the second location and the second input is a fourth vector stored in the second location or the first location.