A new fault coverage test pattern generator using a linear feedback shift register (LFSR) called FC-LFSR can perform fault analysis and reduce the power of a circuit during test by generating three intermediate patterns between the random patterns by reducing the hardware utilization. The goal of having intermediate patterns is to reduce the transitional activities of Primary Inputs (PI) which ...

In this paper, feedback with carry shift registers (FCSRs) are analyzed with main focus on the general case of FCSRs with arbitrary connection integer and on maximum-period FCSRs. Moreover, a keystream generator that employs the structure of the linear feedback shift register (LFSR)-based Geffegenerator is studied in connection with FCSRs as a special nonlinear combining generator. The consider...

LFSR (Linear Feedback Shift Register) is commonly employed in various cryptography applications to generate pseudo-random numbers. The overall number of random state produced by the LFSR is determined by the feedback polynomial. LFSR is a shift register in which some of their outputs are taken in exclusive-OR format that forms the feedback path. So it capable to generate maximum of 2-1 random s...

A d-feedback-with-carry shift register (d-FCSR) is a finite state machine, similar to a linear feedback shift register, in which a small amount of memory and a delay (by d-clock cycles) is used in the feedback algorithm (see [4, 5]). The output sequences of these simple devices may be described using arithmetic in a ramified extension field of the rational numbers. In this paper we show how man...

Let a be an l-sequence generated by a feedback-with-carry shift register with connection integer q = pe, where p is an odd prime and e 1. Goresky and Klapper conjectured that when pe = 2 f5; 9; 11; 13g, all decimations of a are cyclically distinct. When e = 1 and p > 13, they showed that the set of distinct decimations is large and, in some cases, all deciamtions are distinct. In this article, ...

For any integer N > 1, we construct feedback with carry shift registers over Z/(N) (N -FCSRs). The case when N is a prime, was investigated by Klapper and Goresky [1, 2]. We present the basic properties of N -FCSRs. We solve the register synthesis problem: given a small number of symbols of a sequence over Z/(N) synthesize the smallest N -FCSR that outputs the sequence.

We consider the problem of enumerating the number of irreducible transformation shift registers. We give an asymptotic formula for the number of irreducible transformation shift registers in some special cases. Moreover, we derive a short proof for the exact number of irreducible transformation shift registers of order two using a recent generalization of a theorem of Carlitz.

A method is presented for finding the amplitude distribution of the sum of the contents of more than n stages of a feedback shift register connected with feedback over n stages. The analysis illustrates the causes of the skew distributions observed in practice. Some theoretical results are presented.