A New Type of Timing Attack: Application to GPS

We investigate side-channel attacks where the attacker only needs the Hamming weights of several secret exponents to guess a longterm secret. Such weights can often be recovered by SPA, EMA, or simply timing attack. We apply this principle to propose a timing attack on the GPS identification scheme. We consider implementations of GPS where the running time of the exponentiation (commitment phase) leaks the exponent’s Hamming weight, which is typical of a square and multiply algorithm for example. We show that only 800 time measures allow the attacker to find the private key in a few seconds on a PC with a success probability of 80%. Besides its efficiency, two other interesting points in our attack are its resistance to some classical countermeasures against timing attacks, and the fact that it works whether the Chinese Remainder Technique is used or not.