# Classical and Quantum Algorithms for Exponential Congruences

@inproceedings{Dam2008ClassicalAQ, title={Classical and Quantum Algorithms for Exponential Congruences}, author={W. Dam and I. Shparlinski}, booktitle={TQC}, year={2008} }

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… CONTINUE READING

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