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ON FINDING SOLUTIONS TO EXPONENTIAL CONGRUENCES

  • IGOR E. SHPARLINSKI (a1)

Abstract

We improve some previously known deterministic algorithms for finding integer solutions $x,y$ to the exponential equation of the form $af^{x}+bg^{y}=c$ over finite fields.

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During the preparation of this work, the author was supported in part by the Australian Research Council Grant DP170100786.

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References

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[1] Berndt, B., Evans, R. and Williams, K. S., Gauss and Jacobi Sums, Canadian Mathematical Society Series of Monographs and Advanced Texts, 21 (John Wiley & Sons, New York, 1998).
[2] Crandall, R. and Pomerance, C., Prime Numbers: A Computational Perspective (Springer, Berlin, 2005).
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[4] Sasaki, Y., ‘On zeros of exponential polynomials and quantum algorithms’, Quantum Inf. Processing 9 (2010), 419427.
[5] Shanks, D., Class Number, A Theory of Factorization and Genera, Proceedings of Symposia in Pure Mathematics, 20 (American Mathematical Society, Providence, RI, 1971), 415440.
[6] Storer, T., Cyclotomy and Difference Sets, Lectures in Advanced Mathematics, 2 (Markham Publishing Company, Chicago, IL, 1967).
[7] van Dam, W. and Shparlinski, I. E., Classical and Quantum Algorithms for Exponential Congruences, Lecture Notes in Computer Science, 5106 (Springer, Berlin, 2008), 110.
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ON FINDING SOLUTIONS TO EXPONENTIAL CONGRUENCES

  • IGOR E. SHPARLINSKI (a1)

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