Paper 2005/207

Some Thoughts on Time-Memory-Data Tradeoffs

Alex Biryukov

Abstract

In this paper we show that Time-Memory tradeoff by Hellman may be extended to Time-Memory-Key tradeoff thus allowing attacks much faster than exhaustive search for ciphers for which typically it is stated that no such attack exists. For example, as a result AES with 128-bit key has only 85-bit security if $2^{43}$ encryptions of an arbitrary fixed text under different keys are available to the attacker. Such attacks are generic and are more practical than some recent high complexity chosen related-key attacks on round-reduced versions of AES. They constitute a practical threat for any cipher with 80-bit or shorter keys and are marginally practical for 128-bit key ciphers. We also show that UNIX password scheme even with carefully generated passwords is vulnerable to practical tradeoff attacks. Finally we also demonstrate a combination of rainbow tables with the time-memory-data tradeoff which results in a new tradeoff curve.

Note: It seems that we will have to give up the convenient world in which we assumed a k-bit security for a good k-bit key cipher.