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

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.