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. 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.