On the security of some elliptic curve standards in the presence of random fault analysis attacks

Fault attacks are a type of physical attacks where an attacker injects faults to influence the cryptosystems. The attacker can exploit erroneous results, obtained after injecting the faults, to deduce secret keys. Various fault models are proposed, but random fault model remains the most realistic in the practice. In this paper, we show mathematically that current elliptic curve standards (e.g., NIST, Brainpool, ANSSI, and OSCCA) are vulnerable to random fault attacks, and an attacker has a high probability to succeed such attacks. In addition, we give a mathematical description of a parallelized random fault attack, including an implementation using PARI/GP system.