Inverting the pseudo exponentiation

Abstract

At Eurocrypt’89 W. J. Jaburek suggested an algorithm, which he called pseudo exponentiation, for use in generalized El-Gamal type public key cryptoaysteius. This pseudo exponentiation uses a modified form of binary addition in the place of multiplication in an ordinary exponentiation. In this paper we show that the pseudo exponentiation on the set GF(2)k of bitstrings of length k has a considerable amount of math- ematical structure. Using this structure we present an algorithm for inverting pseudo exponentiation that has a running time polynomial in k.