In testing certain systems, checking for burst errors is important. This is due to the fact that errors are confined to a certain number of bits. If signature analysis is used to test a circuit then the testing capabilities depend on the polynomial that defines the linear feedback shift register (LFSR) used in the test. In this paper we show that the LFSR that is suitable for checking for burst...

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, ...

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...

This paper presents a method for constructing n-stage Galois NLFSRs with period 2n − 1 from n-stage maximum length LFSRs. We introduce nonlinearity into state cycles by adding a nonlinear Boolean function to the feedback polynomial of the LFSR. Each assignment of variables for which this function evaluates to 1 acts as a crossing point for the LFSR state cycle. By adding a copy of the same func...

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.

A stream cipher is a symmetric cipher which operates with a time-varying transformation on individual plaintext digits. By contrast, block ciphers operate with a fixed transformation on large blocks of plaintext digits. More precisely, in a stream cipher a sequence of plaintext digits, m0m1 . . ., is encrypted into a sequence of ciphertext digits c0c1 . . . as follows: a pseudorandom sequence s...

Feedback Shift Register (FSR) sequences have been successfully implemented in many communication systems for their randomness properties and ease of implementation. These include ranging and navigation systems, spread spectrum communication systems, CDMA mobile communication systems, and crypto systems such as streamciphers. This article gives a brief overview of FSR sequences, both linear and ...

In this paper, scan and ring schemes of the pseudo-ring memory self-testing are investigated. Both schemes are based on emulation of the linear or nonlinear feedback shift register by memory itself. Peculiarities of the pseudo-ring schemes implementation for multi-port and embedded memories, and for register file are described. It is shown that only small additional logic is required and allows...

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...