A homomorphism of the de Bruijn graph that maps a graph of order n onto one of order n -1 and its applications to the design of nonsingular feedback shift registers are discussed. The properties preserved under this mapping suggest a new design technique whose main advantage is due to the fact that the problem of designing a desired n-stage shift register may be reduced to a problem of order n ...

Feedback with carry shift registers (FCSRs) are arithmetic analogs of linear feedback shift registers (LFSRs). In this paper we survey some of the basic properties of FCSRs. For comparison, we first review some basic facts about LFSRs. We then define FCSRs and discuss their relation to the N -adic numbers. This leads to the analysis of periodicity of FCSR sequences, their exponential representa...

We give the results of a computer search for maximally equidistributed combined linear feedback shift register (or Tausworthe) random number generators, whose components are trinomials of degrees slightly less than 32 or 64. These generators are fast and have good statistical properties.

In this paper, a lemma in algebraic coding theory is established, which is frequently appeared in the encoding and decoding for algebraic codes such as Reed–Solomon codes and algebraic geometry codes. This lemma states that two vector spaces, one corresponds to information symbols and the other is indexed by the support of Gröbner basis, are canonically isomorphic, and moreover, the isomorphism...

Feedback shift registers are basic building blocks for many cryptographic primitives. Due to the insecurities of Linear Feedback Shift Register (LFSR) based systems, the use of Nonlinear Feedback Shift Registers (NFSRs) became more popular. In this work, we study the feedback functions of NFSRs with period 2n. First, we provide two new necessary conditions for feedback functions to be maximum l...

A data encryption technology which ensures secrecy of the data while being transferred over a long distance. It can provide about 80-85% data security as decoding of data involves inverting the feedback function or generating the binary sequence which will help in retrieving the data after some recombination operation.

Many proposals of pseudorandom sequence generators and stream ciphers employ linear feedback shift registers with dynamic feedback (DLFSR) as the main module to increase the period and linear span of the involved msequences. In this paper, we present a theoretical model that allows the design of longer sequences with higher linear span than in previous DLFSR schemes. The model determines the co...

Three different types of high-speed transistor shift registers are discussed. The high speed (3 to 5 microseconds per shift pulse) is made possible by the use of oneand two-transistor nonsaturating bistable circuits. The design of these circuits and their limitations when used .is shift register stages is discussed CAMBRIDGE MASSACHUSETTS

In this work we present a new structure for multiplication in finite fields. This structure is based on a digit-level LFSR (Linear Feedback Shift Register) multiplier in which the area of digit-multipliers are reduced using the Karatsuba method. We compare our results with the other works of the literature for F397 . We also propose new formulas for multiplication in F36·97 . These new formulas...

Built-In Self-Test (BIST), as the name suggests is a technique in which the circuit is capable of testing itself. This paper presents two techniques: Linear Feedback Shift Register (LFSR) and Cellular Automata (CA), used for test pattern generation and test response analysis in a typical BIST circuit. Both LFSR and CA are analyzed based on their construction and characteristics. A comparison of...