Practical Investigation on the Distinguishability of Longa's Atomic Patterns

This paper investigates the distinguishability of the atomic patterns for elliptic curve point doubling and addition operations proposed by Longa [1]. We implemented a binary elliptic curve scalar multiplication <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k_{P}$</tex> algorithm with Longa's atomic patterns for the NIST elliptic curve P-256 using the open-source cryptographic library FLECC in C. We measured and analysed an electromagnetic trace of a single <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k_{P}$</tex> execution on a microcontroller (TI Launchpad F28379 board). Due to various technical limitations, significant differences in the execution time and the shapes of the atomic blocks could not be determined. Further investigations of the SCA-resistance can be performed based on this work. Last but not least, we examined and corrected the Longa's atomic patterns corresponding to formulae proposed by Longa.