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Deconstructing The Welch Equation Using P-Adic Methods, Abigail Mann, Adelyn Yeoh
Deconstructing The Welch Equation Using P-Adic Methods, Abigail Mann, Adelyn Yeoh
Rose-Hulman Undergraduate Research Publications
The Welch map x -> gx-1+c is similar to the discrete exponential map x -> gx, which is used in many cryptographic applications including the ElGamal signature scheme. This paper analyzes the number of solutions to the Welch equation: gx-1+c = x (mod pe) where p is a prime, and looks at other patterns of the equation that could possibly exploited in a similar cryptographic system. Since the equation is modulo pe, where p is a prime number, p-adic methods of analysis are used in counting the number of solutions modulo p …