Single Linear Feedback Shift Register Research Articles

Breaking Modified Bruer Generator by Solving the System of Linear Equations of the Generated Sequence

Linear Feedback Shift Register (LFSR) systems are used widely in stream cipher systems field. Golomb used the recurrence relation to find the next state values of single LFSR depending on initial values, s.t. he can be considered the first who can construct a linear equations system of a single LFSR. Attacking of key generator means attempt to find the initial values of the combined LFSR's.In this paper, a Golomb's method introduced to construct a linear equations system of a single LFSR. This method developed to construct a linear equations system of key generator (a LFSR system) where the effect of combining function of LFSR is obvious. Finally, before solving the linear equations system, the uniqueness of the solution must be tested, then solving the linear equations system using one of the classical methods like Gauss Elimination. Find the solution of linear equations system means find the initial values of the generator. One of the known generators; Modified Bruer generator, treated as a practical example of this work.

Generalization of the Self-Shrinking Generator in the Galois Field

The proposed by Meier and Staffelbach Self-Shrinking Generator (SSG) which has efficient hardware implementation only with a single Linear Feedback Shift Register is suitable for low-cost and fast stream cipher applications. In this paper we generalize the idea of the SSG for arbitrary Galois Field . The proposed variant of the SSG is called the -ary Generalized Self-Shrinking Generator (pGSSG). We suggest a method for transformation of a non-binary self-shrunken pGSSG sequence into balanced binary sequence. We prove that the keystreams of the pGSSG have large period and good statistical properties. The analysis of the experimental results shows that the pGSSG sequences have good randomness properties. We examine the complexity of exhaustive search and entropy attacks of the pGSSG. We show that the pGSSG is more secure than SSG and Modified SSG against these attacks. We prove that the complexity of the used pGSSG attacks increases with increasing the prime . Previously mentioned properties give the reason to say that the pGSSG satisfy the basic security requirements for a stream chipper and can be useful as a part of modern stream ciphers.

A New Built-in TPG Based on Berlekamp–Massey Algorithm

In this work, a new method to design a mixed-mode Test Pattern Generator (TPG) based only on a simple and single Linear Feedback Shift Register (LFSR) is described. Such an LFSR is synthesized by Berlekamp---Massey algorithm (BMA) and is capable of generating pre-computed deterministic test patterns which detect the hard-to-detect faults of the circuit. Moreover, the LFSR generates residual patterns which are sufficient to detect the remaining easy-to-detect faults. In this way, the BMA-designed LFSR is a mixed-mode TPG which achieves total fault coverage with short testing length and low hardware overhead compared with previous schemes according to the experimental results.

Generalized inversion attack on nonlinear filter generators

A nonlinear filter generator is a basic keystream generator for stream cipher applications consisting of a single linear feedback shift register whose output is filtered by a nonlinear combining function. A binary nonlinear filter generator is viewed as a finite input memory automaton with one binary input and one binary output. The generalized inversion attack on a binary nonlinear filter generator is developed and analyzed by the theory of critical branching processes. Its objective is to recover the unknown input sequence from a given segment of the output sequence, provided that the filter function is known. Unlike the inversion attack, which requires that the filter function be linear in the first or the last input variable, this attack can be applied for any filter function. Both theory and systematic experiments show that its time complexity remains dose to 2/sup M/, which is the time complexity of the inversion attack, where M denotes the input memory size in bits.

A VLSI-efficient technique for generating multiple uncorrelated noise sources and its application to stochastic neural networks

A method for generating multiple arbitrarily shifted pseudorandom bit streams from a single linear feedback shift register (LFSR) is presented. Each bit stream is obtained by tapping the outputs of selected LFSR cells and feeding these tapped cell outputs through a set of exclusive-OR gates. This enables many neurons to share a single LFSR, resulting in an acceptably small overhead for VLSI implementation. >