Rational Protection against Timing Attacks

Timing attacks can effectively recover keys from cryptosystems. While they can be defeated using constant-time implementations, this defensive approach comes at the price of a performance penalty. One is hence faced with the problem of striking a balance between performance and security against timing attacks. In this paper, we propose a systematic approach for determining the optimal protection against timing attacks, on the example of cryptosystems based on discrete logarithms. Our model includes a resource-bounded timing adversary who strives to maximize the probability of key recovery, and a defender who strives to reduce the cost while maintaining a certain degree of security. We obtain the optimal protection as an equilibrium in a game between the defender and the adversary. At the heart of the equilibrium computation are novel bounds for the probability of key recovery, which are expressed as a function of the applied protection and the attack strategy of a timing adversary. We put our techniques to work in a case study in which we identify optimal protections for libgcrypt's ElGamal implementation. We determine situations in which the optimal choice is to use a defensive, constant-time implementation and a small key, and situations in which the optimal choice is a more aggressively tuned (but leaky) implementation with a longer key.