Deconstructing the Welch Equation Using $p$-adic Methods

Abstract

The Welch map x → g 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: g ≡ x (mod pe) where p is a prime and g is a unit modulo p, and looks at other patterns of the equation that could possibly be… (More)

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