Horizontal SCA Attacks on Binary kP Algorithms using Chevallier-Mames Atomic Blocks
Gerald Isheanesu Matungamire, Alkistis Aikaterini Sigourou, Gerrit Schrock, Zoya Dyka, Peter Langendoerfer + 1 more
TLDR
Binary kP algorithms using Chevallier-Mames atomic blocks are vulnerable to single-trace side-channel attacks, even with randomization.
Key contributions
- Demonstrated single-trace SCA vulnerabilities in binary kP algorithms with Chevallier-Mames atomic blocks.
- Confirmed these vulnerabilities for both right-to-left and left-to-right kP implementations.
- Showed left-to-right kP remains vulnerable even with projective coordinate randomization.
Why it matters
Elliptic Curve cryptosystems rely on scalar multiplication (kP), a frequent target for side-channel attacks. This work reveals that a common protection, Chevallier-Mames atomic blocks, is insufficient against single-trace SCA. This finding is crucial for developing truly secure cryptographic implementations.
Original Abstract
Scalar multiplication kP is the operation most frequently targeted in Elliptic Curve (EC) cryptosystems. To protect against single-trace Side-Channel Analysis (SCA) attacks, the atomicity principle and various atomic block patterns have been proposed in the past. In this work we use our software and hardware implementations to demonstrate that binary right-to left and left-to-right kP algorithms, when implemented with Chevallier-Mames atomic block patterns, are still vulnerable to single-trace SCA attacks. The vulnerability remains true for the left-to-right kP algorithm with projective coordinate randomization.
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