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

Authors:

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