Same Values Analysis Attack on Weierstrass Binary Elliptic Curves

Public key Crystosystems based on Elliptic Curves are increasingly recommended, due to their small key size. However, they are vulnerable to a type of attack called Side Channel Attack (SCA). A Side Channel Attack on Elliptic Curve Cryptography (ECC) is an attack which exploits information like power consumption, current consumption and tries to obtain the secret key. Among Side Channel Attacks on ECC, we have the Same Values Analysis (SVA) which exploits the same intermediate values when adding or doubling points and use internal collision to recover the secret key. In this paper we study SVA on elliptic curves defined over binary fields. We study same-values points on Standards for Efficient Cryptography Group (SECG) recommended curves and the National Institute of Standard Technology (NIST) recommended curves with the computer algebra software Sagemath.