Folding-BSD Algorithm for Binary Sequence Decomposition

Abstract

The Internet of Things (IoT) revolution leads to a range of critical services which rely on IoT devices. Nevertheless, they often lack proper security, becoming the gateway to attack the whole system. IoT security protocols often rely on stream ciphers, where pseudo-random number generators (PRNGs) are an essential part of them. In this article, a family of ciphers with strong characteristics that make them difficult to be analyzed by standard methods is described. In addition, we will discuss an innovative technique of sequence decomposition and present a novel algorithm to evaluate the strength of binary sequences, a key part of the IoT security stack. The density of the binomial sequences in the decomposition has been studied experimentally to compare the performance of the presented algorithm with previous works.

A Hadamard Matrix-Based Algorithm to Evaluate the Strength of Binary Sequences

“…We define the binomial matrix H 2 t as the binary Hadamard matrix [12] of size 2 t × 2 t constructed as follows: 1) For t = 0,…”

Review of the Lineal Complexity Calculation through Binomial Decomposition-Based Algorithms

“…Such an algorithm takes full advantage of the binomial sequence symmetry. A preliminary version of this algorithm by the same authors was introduced in [16,34]. First of all, we study the symmetry properties of the binomial sequences.…”

“…In addition, we present the half-interval search algorithm. Despite it being based on our previous design of the folding algorithm [16], in this work we complete the available knowledge on such an algorithm providing a mathematical proof of its behaviour and correctness. The matrix binomial decomposition algorithm is another novelty of this article, which is based on a recent representation of the generalized self-shrunken sequences [17].…”

An Efficient Algorithm to Compute the Linear Complexity of Binary Sequences

“…The technique herein presented uses Hadamard matrices [25] and the B-representation of sequences proposed in [26,27]. Our algorithm was much more efficient than the other ones proposed in the literature [26,[28][29][30], and the required amount of sequence to perform this computation was also more realistic.…”

“…The folding algorithm [30] is another technique to compute the LC of sequences with a period of a power of two, T = 2 t . It is based on successive foldings of the own sequence to locate the maximum binomial sequence and calculate LC.…”