Classical and Quantum Algorithms for Exponential Congruences

Igor E Shparlinski,Wim Van Dam

doi:10.1007/978-3-540-89304-2_1

Classical and Quantum Algorithms for Exponential Congruences

Igor E Shparlinski, Wim Van Dam

Open Access

https://doi.org/10.1007/978-3-540-89304-2_1

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Publication Date: Jan 1, 2008

Citations: 33

Affiliation: Macquarie University, University of California, Santa Barbara

#Classical Algorithms #Quantum Algorithms + Show 8 more

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Abstract

We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af x + bg y = c over finite fields . A quantum algorithm with time complexity q 3/8 (logq) O(1) is presented. While still superpolynomial in logq, this quantum algorithm is significantly faster than the best known classical algorithm, which has time complexity q 9/8 (logq) O(1). Thus it gives an example of a natural problem where quantum algorithms provide about a cubic speed-up over classical ones.

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