Isogeny-Based Cryptosystem Randomization Against Side-Channel Attacks
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Solution Overview
Problem
Isogeny-based cryptosystems are vulnerable to side-channel attacks, which exploit unintended information leakage, and there is a need to enhance their security while maintaining competitive performance, power, and area efficiency, especially in the context of post-quantum cryptography.
Innovation Solution
The method introduces randomness into isogeny-based cryptosystems by utilizing random inputs and entropy pools to change intermediate elliptic curve points and scalars, and to select isogeny formulas, thereby randomizing the computational hierarchy with minimal overhead, using techniques such as random projective coordinate representations, isomorphisms, and scalar randomization in point multiplication operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If randomness is added to isogeny-based cryptosystems to protect against side-channel attacks, then security is improved, but computational overhead increases
Solution Approach 1:
The patent applies parameter changes by modifying the representation of elliptic curve points from standard affine coordinates to random projective coordinates. This transformation introduces randomness into the computational parameters without fundamentally changing the cryptographic algorithm, thereby enhancing security against side-channel attacks while maintaining computational efficiency.
Solution Approach 2:
The patent uses random projective coordinate representations as an intermediary layer between the cryptographic operations and the physical implementation. This intermediary transformation obscures the direct relationship between input operations and physical side-channels (power consumption, timing), making it difficult for attackers to extract information without significantly increasing computational complexity.
2Reliability
If random projective coordinate representations are used to randomize intermediate computations, then resistance to side-channel attacks is improved, but computational operations become more complex
Solution Approach 1:
The patent changes the parameter representation of elliptic curve points from affine coordinates (x, y) to random projective coordinates (X, Y, Z) where x = X/Z and y = Y/Z. This parameter transformation allows the same mathematical operations to be performed with randomized values, improving side-channel resistance while the projective coordinate system itself maintains computational efficiency for elliptic curve operations.
Data Source
AI summary
A computer processing system having an isogeny-based cryptosystem for randomizing computational hierarchy to protect against side-channel analysis in isogeny-based cryptosystems.