Rigorous Bounds on Cryptanalytic Time/Memory Tradeoffs

In this paper we formalize a general model of cryptanalytic time/memory tradeoffs for the inversion of a random function f : {0, 1, . . . , N - 1} {0, 1, . . . , N - 1}. The model contains all the known tradeoff techniques as special cases. It is based on the new notion of stateful random graphs, whose evolution depends on a hidden state such as the color in the Rainbow scheme or the table number in the classical Hellman scheme. We prove an upper bound on the number of images y = f(x) for which f can be inverted using a tradeoff scheme, and derive from it a lower bound on the number of hidden states. These bounds hold with an overwhelming probability over the random choice of the function f, and their proofs are based on a rigorous combinatorial analysis. With some additional natural assumptions on the behavior of the online phase of the algorithm, we prove a lower bound on its worst-case time complexity T = ( N2 M2 ln N ), where M is the memory complexity. We describe several new var...

• Type: Conference
• Year: 2006
• Where: CRYPTO
• Authors: Elad Barkan, Eli Biham, Adi Shamir
• Keywords: CRYPTO 2006, Cryptology, Hidden States, Lower Bound, Tradeoff