On inversion in $Z {2^n-1}$Report as inadecuate

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1 Fakultät für Mathematik - Institut für Algebra und Geometrie 2 SECRET - Security, Cryptology and Transmissions Inria Paris-Rocquencourt

Abstract : In this paper we determined explicitly the multiplicative inverses of the Dobbertin and Welch APN exponents in Z2n−1, and we described the binary weights of the inverses of the Gold and Kasami exponents. We studied the function Invdn, which for a fixed positive integer d maps integers n⩾1 to the least positive residue of the inverse of d modulo 2n−1, if it exists. In particular, we showed that the function Invd is completely determined by its values for 1⩽n⩽θd, where θd is the order of 2 modulo the largest odd divisor of d.

Keywords : modular inversion APN-AB exponents power functions on finite fi elds algebraic degree binary representation of integers

Author: Gohar Kyureghyan - Valentin Suder -

Source: https://hal.archives-ouvertes.fr/


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