Authenticated key exchange under bad randomness, revisited

A bad randomness may cause catastrophic results in security; thus, it is of importance to make cryptographic systems secure against bad randomness. In this paper, we focus on a practical situation where an adversary is able to force participants in an authenticated key exchange (AKE) system to reuse the random values and the functions of these values, called related randomness attack (RRA). Following the existing randomness resetting security model of AKE and the RRA security model of public-key encryption, we present a model of RRA security for authenticated key exchange, as well as the necessary restrictions on the related randomness functions used to obtain the security definition. Then we show how a related randomness attack adversary breaks the security of some existing AKE protocols, and propose some constructions of RRA-secure authenticated key exchange in the random oracle model and standard model, respectively.