Successful Simple Side Channel Analysis: Vulnerability of an atomic pattern $kP$ algorithm implemented with a constant time crypto library to simple electromagnetic analysis attacks
Alkistis Aikaterini Sigourou, Ievgen Kabin, Peter Langendörfer, Nicolas Sklavos, Zoya Dyka · 2023
Elliptic curve cryptosystem is a widely-used public key cryptosystem that is vulnerable to physical attacks, especially to Side Channel Analysis (SCA) attacks. This paper investigates a version of the atomic patterns$\boldsymbol{kP}$algorithm for elliptic curves over prime finite fields. The atomic patterns for Elliptic Curve (EC) point doublings and additions are well-known countermeasures against simple SCA attacks. We implemented a binary left-to-right$\boldsymbol{kP}$algorithm corresponding to the atomic patterns as proposed by Rondepierre and using the FLECC open-source cryptographic library. The library provides constant-time functions for the implementation of different mathematic operations in prime finite fields, making it suitable for SCA-aware implementations of cryptographic protocols, at a theoretical level. We were able to reveal the scalar k processed during a$\boldsymbol{kP}$execution analyzing the measured electromagnetic trace of the$\boldsymbol{kP}$execution. We determined at least two parts in the measured trace where the distinction between EC point doublings and EC point additions is good observable.