EC Scalar Multiplication: Successful Simple Address-Bit SCA Attack against Atomic Patterns

Abstract

In this work we discuss the resistance of our hardware accelerator for Elliptic Curve Cryptography against simple side-channel analysis (SCA) attacks. We implemented an elliptic curve point multiplication $kP$ corresponding to the atomicity principle that is a well-known countermeasure against simple SCA attacks. We evaluated the resistance of our design by analysing a single simulated power trace of a $kP$ execution. 552 out of 32700 extracted key candidates were identical to the scalar $k$ used in the $kP$ execution, i.e. we were able to reveal the scalar $k$ completely. The reason of the success of our attack is the key-dependent addressing of blocks/registers in the implemented $kP$ algorithm. This means that applying of atomic patterns as effective countermeasures against simple SCA has to be revised, at least for hardware implementations.