in Computer Science 4117
نویسندگان
چکیده
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 a new notion of stateful random graphs. The evolution of a path in the stateful random graph 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, and derive from it a lower bound on the number of hidden states. These bounds hold for an overwhelming majority of the functions 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 scheme, we prove a lower bound on its worst-case time complexity T = Ω( N 2 M2 lnN ), where M is the memory complexity. Finally, we describe new rainbowbased time/memory/data tradeoffs, and a new method for improving the time complexity of the online phase (by a small factor) by performing a deeper analysis during preprocessing.
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تاریخ انتشار 2008