On stream ciphers with provable beyond-the-birthday-bound security against time-memory-data tradeoff attacks

Abstract

Most stream ciphers are vulnerable against generic time-memory-data tradeoff (TMD-TO) attacks, which reduce their effective key length to the birthday bound $n/2$ , where n denotes the inner state length of the underlying keystream generator. This implies the necessity of a comparatively large inner state length for practical stream ciphers (e.g., $n = 288$ and $n = 160$ for the eSTREAM portfolio members Trivium and Grain v1, respectively). In this paper, we propose and analyze the Lizard-construction, a new way to build stream ciphers. We prove a tight $2n/3$ bound on its security against TMD-TO key recovery attacks, where the security lower bound refers to chosen-IV attacks. The security against TMD-TO distinguishing attacks remains at the birthday-bound level $n/2$ . The lower bound refers to a random oracle model which allows to derive formal security results w.r.t. generic TMD-TO attacks. While similar frameworks have already been widely used for analyzing the security of block cipher, MAC, and hash function constructions, to the best of our knowledge this is the first time that such a model is considered in the context of stream ciphers. The security analysis presented in this paper is also of immediate practical relevance as, with the stream cipher Lizard, a first instantiation of our new design principle (which we hence named Lizard-construction) was introduced at FSE 2017. Lizard has an inner state length of only 121 bits and surpasses Grain v1, the most hardware efficient member of the eSTREAM portfolio, in important metrics for lightweight ciphers such as chip area and power consumption.