Feedback Registers Based on Ramified Extensions of the 2-Adic Numbers

Andrew Klapper, 779A Anderson Hall, Dept. of Computer Science, University of Kentucky, Lexington, KY, 40506-0046, klapper at

Mark Goresky, Institute for Advanced Study

Abstract A new class of feedback register, based on ramified extensions of the 2-adic numbers, is described. An algebraic framework for the analysis of these registers and the sequences they output is given. This framework parallels that of linear feedback shift registers and feedback with carry shift registers. As one consequence of this, a method for cracking summation ciphers is given. These registers give rise to new measures of cryptologic security.

Index Terms -- Binary sequences, shift registers, combiners with memory, cryptanalysis, ramified extensions of 2-adic numbers.