A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum computation and quantum information
Quantum computation and quantum information
Quantum Cryptanalysis of Hash and Claw-Free Functions
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Quantum Algorithms for Element Distinctness
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
Quantum Speed-Up of Markov Chain Based Algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Quantum Algorithms for Element Distinctness
SIAM Journal on Computing
Quantum verification of matrix products
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Quantum Query Complexity of Some Graph Problems
SIAM Journal on Computing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum Walk Algorithm for Element Distinctness
SIAM Journal on Computing
Quantum Algorithms for the Triangle Problem
SIAM Journal on Computing
Quantum algorithms for subset finding
Quantum Information & Computation
Promised and distributed quantum search
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
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The claw finding problem has been studied in terms of query complexity as one of the problems closely connected to cryptography. Given two functions, f and g, with domain sizes 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 problem has been considered in both quantum and classical settings in terms of query complexity. This paper describes an optimal algorithm that uses quantum walk to solve this problem. Our algorithm can be slightly modified to solve the more general problem of finding a tuple consisting of elements in the two function domains that has a prespecified property. It can also be generalized to find a claw of k functions for any constant integer k1, where the domain sizes of the functions may be different.