Generalized Self-shrinking Generator Research Articles

Randomness study of the concatenation of generalized sequences

Abstract Keystream sequences should look as random as possible, i.e. should present no logical pattern to be exploited in cryptographic attacks. The generalized self-shrinking generator, a sequence generator based on irregular decimation, produces a family of sequences with good cryptographic properties. In this work, we display a detailed analysis on the randomness of the sequences resulting from the concatenation of elements of this family. We apply the most important batteries of statistical and graphical tests providing powerful results and a new method to construct sequences with good cryptographic properties.

Representations of Generalized Self-Shrunken Sequences

Output sequences of the cryptographic pseudo-random number generator, known as the generalized self-shrinking generator, are obtained self-decimating Pseudo-Noise (PN)-sequences with shifted versions of themselves. In this paper, we present three different representations of this family of sequences. Two of them, the p and G-representations, are based on the parameters p and G corresponding to shifts and binary vectors, respectively, used to compute the shifted versions of the original PN-sequence. In addition, such sequences can be also computed as the binary sum of diagonals of the Sierpinski’s triangle. This is called the B-representation. Characteristics and generalities of the three representations are analyzed in detail. Under such representations, we determine some properties of these cryptographic sequences. Furthermore, these sequences form a family that has a group structure with the bit-wise XOR operation.

Randomness Analysis for the Generalized Self-Shrinking Sequences

In cryptography, the property of randomness in pseudo-random generators is very important to avoid any pattern in output sequences, to provide security against attacks, privacy and anonymity. In this article, the randomness of the family of sequences obtained from the generalized self-shrinking generator is analyzed. Moreover, the characteristics, generalities and relationship between the t-modified self-shrinking generator and the generalized self-shrinking generator are presented. We find that the t-modified self-shrunken sequences can be generated from a generalized self-shrinking generator. Then, an in-depth analysis of randomness focused on the generalized sequences by means of complete and powerful batteries of statistical tests and graphical tools is done, providing a useful vision of the behaviour of these sequences and proving that they are suitable to be used in cryptography.

RANDOMNESS TESTING OF SEQUENCES PRODUCED BY P-ARY GENERALIZED SELF-SHRINKING GENERATOR USING APPROXIMATE ENTROPY

In this paper a supervene testing for sequences generated by p-ary Generalized Self-Shrinking Generator (pGSSG) is made. Thanks to the Approximate Entropy (ApEn) approach certain randomness properties are proved to be possessed by them. In order to test the applicability of the generator the pGSSG sequence minimum length in excess of which it can be considered that the sequence behaves as truly random is detected.

Software Stream Cipher based on pGSSG Generator

Secrecy of a software stream cipher based on p-ary Generalized Self-Shrinking Generator (pGSSG) is examined in this paper. Background information for the generator’s algorithm is provided. The software architecture and key management for the cipher initialization are explained. Galois Field GF(257 32 ) and feedback polynomials are chosen for initialization of the generator. In order to examine the secrecy mathematical model of the software system is made. It is proved that the cipher is not perfect but the empirical tests result in less than 0,0125% deviation of the encrypted files’ entropy from the perfect secrecy. At last the proposed cipher is compared to four eSTREAM finalists by key length and period.

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.

Analysis of the generalized self-shrinking generator

This work shows that the output sequences of a well-known cryptographic generator, the so-called generalized self-shrinking generator, are particular solutions of homogeneous linear difference equations with binary coefficients. In particular, all those generated sequences are just linear combinations of primary sequences weighted by binary values. Furthermore, the complete class of solutions of these difference equations includes other balanced sequences with the same period and even greater linear complexity than that of the generalized self-shrinking sequences. Cryptographic parameters of all above mentioned sequences are here analyzed in terms of linear equation solutions. In addition, this work describes an efficient algorithm to synthesize the component primary sequences as well as to compute the linear complexity and period of any generalized self-shrinking sequence.

Chaotic modelling of the generalized self-shrinking generator

In this paper, a method of obtaining cryptographic sequences based on discrete time chaotic dynamical systems is presented. The importance of the proposal is due to that such cryptographic sequences are also output sequences of a nonlinear keystream generator known as generalized self-shrinking generator, which is still considered secure for symmetric cryptography. It is remarkable that the linearity of the proposed chaotic model based on additive one-dimensional cellular automata might be used to launch a cryptanalysis against such nonlinear generators.

Generalized Self-Shrinking Generator

In this correspondence, we present a simple bit-stream generator. It is a specialization of shrinking generator and a generalization of self-shrinking generator. We call it "generalized self-shrinking generator." The family of such generated sequences has a group structure. The correlation between the sequences is quite good and the sequences themselves are balanced. For each k, 0<k<n, no more than 1/2/sup n-k/ of the sequences have least periods less than 2/sup k/. No more than 1/4 of the sequences have least periods less than 2/sup n-1/. There are two sequences with least periods of 2. There is no sequence with a least period p such that 2<p<n/2.