An improved claw finding algorithm using quantum walk

Abstract

The claw finding problem has been studied in terms of query complexity as one of the problems closely connected to cryptography. For given two functions, f and g, as an oracle which have domains of size N and M (N ≤ M), respectively, and the same range, the goal of the problem is to find x and y such that f(x) = g(y). This paper describes a quantum-walk-based algorithm that solves this problem; it improves the previous upper bounds. Our algorithm can be generalized to find a claw of k functions for any constant integer k > 1, where the domains of the functions may have different size. © Springer-Verlag Berlin Heidelberg 2007.