Counting Solutions to Non-Algebraic Equations Modulo Prime Powers
Date
2021-07-02
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Abstract
In the digital age, cryptology, always important during conflicts, is becoming more and more significant as cybersecurity influences world affairs. We are interested in studying the mathematical properties of certain functions that are employed to create digital signatures, in particular via the ElGamal Digital Signature Scheme. Using techniques from Holden, Richardson and Robinson [3], we examine the properties of these non-algebraic functions and, more specifically, we count the number of fixed points of these functions modulo any positive power of a prime p. We show explicitly how the singular points of the function (i.e. the points where the derivative is zero modulo p) complicate the solution.
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Number Theory, cryptology