Dynamic MDS Matrices for Substantial Cryptographic Strength

Ciphers get their strength from the mathematical functions of confusion and diffusion, also known as substitution and permutation. These were the basics of classical cryptography and they are still the basic part of modern ciphers. In block ciphers diffusion is achieved by the use of Maximum Distance Separable (MDS) matrices. In this paper we present some methods for constructing dynamic (and random) MDS matrices.Comment: Short paper at WISA'10, 201

Matrix Power S-box Analysis

* Work supported by the Lithuanian State Science and Studies Foundation.Construction of symmetric cipher S-box based on matrix power function and dependant on key is analyzed. The matrix consisting of plain data bit strings is combined with three round key matrices using arithmetical addition and exponent operations. The matrix power means the matrix powered by other matrix. This operation is linked with two sound one-way functions: the discrete logarithm problem and decomposition problem. The latter is used in the infinite non-commutative group based public key cryptosystems. The mathematical description of proposed S-box in its nature possesses a good “confusion and diffusion” properties and contains variables “of a complex type” as was formulated by Shannon. Core properties of matrix power operation are formulated and proven. Some preliminary cryptographic characteristics of constructed S-box are calculated

Revisiting LFSMs

Linear Finite State Machines (LFSMs) are particular primitives widely used in information theory, coding theory and cryptography. Among those linear automata, a particular case of study is Linear Feedback Shift Registers (LFSRs) used in many cryptographic applications such as design of stream ciphers or pseudo-random generation. LFSRs could be seen as particular LFSMs without inputs. In this paper, we first recall the description of LFSMs using traditional matrices representation. Then, we introduce a new matrices representation with polynomial fractional coefficients. This new representation leads to sparse representations and implementations. As direct applications, we focus our work on the Windmill LFSRs case, used for example in the E0 stream cipher and on other general applications that use this new representation. In a second part, a new design criterion called diffusion delay for LFSRs is introduced and well compared with existing related notions. This criterion represents the diffusion capacity of an LFSR. Thus, using the matrices representation, we present a new algorithm to randomly pick LFSRs with good properties (including the new one) and sparse descriptions dedicated to hardware and software designs. We present some examples of LFSRs generated using our algorithm to show the relevance of our approach.Comment: Submitted to IEEE-I