Weak Keys and Cryptanalysis of a Cold War Block Cipher

T-310 is a cipher that was used for encryption of governmental communications in East Germany during the final years of the Cold War. Due to its complexity and the encryption process,there was no published attack for a period of more than 40 years until 2018 by Nicolas T. Courtois et al. in [10]. In this thesis we study the so called 'long term keys' that were used in the cipher, in order to expose weaknesses which will assist the design of various attacks on T-310

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. 1 Arithmetic Correlations and Walsh Transforms

Abstract—In this paper the authors continue a program to find arithmetic, or “with-carry, ” analogs of polynomial based phenomena that appear in the design and analysis of cryptosystems and other branches of digital computation and communications. They construct arithmetic analogs of the Walsh-Hadamard transform and correlation functions of Boolean functions. These play central roles in the cryptographic analysis of block ciphers and stream ciphers. After making basic definitions and constructing various algebraic tools they: (1) show how to realize arithmetic correlations as cardinalities of intersections of hypersurfaces; (2) show that the arithmetic Walsh spectrum characterizes a Boolean function; (3) study the average behavior of arithmetic Walsh transforms; (4) find the arithmetic Walsh transforms of linear and affine functions. Index Terms—Walsh-Hadamard transform, correlation functions, p-adic numbers