A Comparison of Time-Memory Trade-Off Attacks on Stream Ciphers

Abstract

Introduced by Hellman, Time-Memory Trade-Off (TMTO) attacks offer a generic technique to reverse one-way functions, where one can trade off time and memory costs and which are especially effective against stream ciphers. Hellman's original idea has seen many different improvements, notably the Distinguished Points attack and the Rainbow Table attack. The trade-off curves of these approaches have been compared in literature, but never leading to a satisfying conclusion. A new TMTO attack was devised for the A5/1 cipher used in GSM, which combines both distinguished points and rainbow tables, which we refer to as the Kraken attack. 1 . This paper compares these four approaches by looking at concrete costs of these attacks instead of comparing their trade-off curves. We found that when multiple samples are available the Distinguished Points attack has the lowest costs. The Kraken attack is an alternative to save more disk space at the expense of attack time.

Analysis of the Non-perfect Table Fuzzy Rainbow Tradeoff

“…The multi-target version of the fuzzy rainbow tradeoff is described as having been used during the presentation [21,22] of a fully implemented attack on GSM phones, but no theoretical analysis was given there. The work [26] provides an entry-level analysis of the same algorithm, but incorrect assumptions were made concerning the parameters. Neither work mentions that the algorithm being dealt with appeared previously in [6,8].…”

Information Theory Based Evaluation of the RC4 Stream Cipher Outputs

“…The proposed method is divided into two phases, following an idea similar to a time memory trade off (TMTO) attack [ 27 ]. The first is the precomputation phase, often called the offline phase, where the probabilities and entropy in each time of T are estimated over each output value .…”

Analysis of the Perfect Table Fuzzy Rainbow Tradeoff

“…The fuzzy rainbow tradeoff [4,5] is a more recent algorithm that combines the distinguished point and rainbow methods. The algorithm has already been used in the multitarget setting as an integral component of a fully functional attack [6,7] on GSM phones, and an elementary analysis of the fuzzy rainbow tradeoff appeared in [8]. The latter work cites a work related to [6] and refers to the attack by the name Kraken, but none of these works cite the original publication [4,5], indicating these to be an independent line of work.…”

“…The latter work cites a work related to [6] and refers to the attack by the name Kraken, but none of these works cite the original publication [4,5], indicating these to be an independent line of work. In fact, the analyses of [8] fall short of even the preliminary discussions given by [4,5]. For now, the execution complexities of the fuzzy rainbow tradeoff are not known accurately enough for the purpose of comparing the performances of different tradeoff algorithms.…”