Distributional properties of d-FCSR sequences

AbstractIn this paper we study the distribution properties of d-FCSR sequences. These sequences have efficient generators and have several good statistical properties. We show that for d=2 the number of occurrences of an fixed size subsequence differs from the average number of occurrences by at most a small constant times the square root of the average

STATISTICAL PROPERTIES OF PSEUDORANDOM SEQUENCES

Random numbers (in one sense or another) have applications in computer simulation, Monte Carlo integration, cryptography, randomized computation, radar ranging, and other areas. It is impractical to generate random numbers in real life, instead sequences of numbers (or of bits) that appear to be ``random yet repeatable are used in real life applications. These sequences are called pseudorandom sequences. To determine the suitability of pseudorandom sequences for applications, we need to study their properties, in particular, their statistical properties. The simplest property is the minimal period of the sequence. That is, the shortest number of steps until the sequence repeats. One important type of pseudorandom sequences is the sequences generated by feedback with carry shift registers (FCSRs). In this dissertation, we study statistical properties of N-ary FCSR sequences with odd prime connection integer q and least period (q-1)/2. These are called half-ℓ-sequences. More precisely, our work includes: The number of occurrences of one symbol within one period of a half-ℓ-sequence; The number of pairs of symbols with a fixed distance between them within one period of a half-ℓ-sequence; The number of triples of consecutive symbols within one period of a half-ℓ-sequence. In particular we give a bound on the number of occurrences of one symbol within one period of a binary half-ℓ-sequence and also the autocorrelation value in binary case. The results show that the distributions of half-ℓ-sequences are fairly flat. However, these sequences in the binary case also have some undesirable features as high autocorrelation values. We give bounds on the number of occurrences of two symbols with a fixed distance between them in an ℓ-sequence, whose period reaches the maximum and obtain conditions on the connection integer that guarantee the distribution is highly uniform. In another study of a cryptographically important statistical property, we study a generalization of correlation immunity (CI). CI is a measure of resistance to Siegenthaler\u27s divide and conquer attack on nonlinear combiners. In this dissertation, we present results on correlation immune functions with regard to the q-transform, a generalization of the Walsh-Hadamard transform, to measure the proximity of two functions. We give two definitions of q-correlation immune functions and the relationship between them. Certain properties and constructions for q-correlation immune functions are discussed. We examine the connection between correlation immune functions and q-correlation immune functions

ANALYSIS OF SECURITY MEASURES FOR SEQUENCES

Stream ciphers are private key cryptosystems used for security in communication and data transmission systems. Because they are used to encrypt streams of data, it is necessary for stream ciphers to use primitives that are easy to implement and fast to operate. LFSRs and the recently invented FCSRs are two such primitives, which give rise to certain security measures for the cryptographic strength of sequences, which we refer to as complexity measures henceforth following the convention. The linear (resp. N-adic) complexity of a sequence is the length of the shortest LFSR (resp. FCSR) that can generate the sequence. Due to the availability of shift register synthesis algorithms, sequences used for cryptographic purposes should have high values for these complexity measures. It is also essential that the complexity of these sequences does not decrease when a few symbols are changed. The k-error complexity of a sequence is the smallest value of the complexity of a sequence obtained by altering k or fewer symbols in the given sequence. For a sequence to be considered cryptographically ‘strong’ it should have both high complexity and high error complexity values. An important problem regarding sequence complexity measures is to determine good bounds on a specific complexity measure for a given sequence. In this thesis we derive new nontrivial lower bounds on the k-operation complexity of periodic sequences in both the linear and N-adic cases. Here the operations considered are combinations of insertions, deletions, and substitutions. We show that our bounds are tight and also derive several auxiliary results based on them. A second problem on sequence complexity measures useful in the design and analysis of stream ciphers is to determine the number of sequences with a given fixed (error) complexity value. In this thesis we address this problem for the k-error linear complexity of 2n-periodic binary sequences. More specifically: 1. We characterize 2n-periodic binary sequences with fixed 2- or 3-error linear complexity and obtain the counting function for the number of such sequences with fixed k-error linear complexity for k = 2 or 3. 2. We obtain partial results on the number of 2n-periodic binary sequences with fixed k-error linear complexity when k is the minimum number of changes required to lower the linear complexity

Modified Mclaren-marsaglia Pseudo-random Number Generator and Stochastic Key Agreement

A discussion of problems in cryptographic applications, with a brief survey of pseudo-random number generators (PRNG) used as synchronous stream ciphers, leads to a discussion of the McClaren-Marsaglia shuffling PRNG, and some means of altering its structure to both provide a more secure PRNG and to provide effective means by which to inject aperiodicity into a modified form of McClaren-Marsaglia. A discussion of two closely related protocols using this modified form of McClaren-Marsaglia as means by which correspondents may agree upon a set of random bits in a manner suitable for use in cryptographic applications is then presented, with implementation in the C programming language of the second protocol. Analysis of the protocols concludes that a reasonable expectation of confidentiality and cryptographic strength in the agreed bit-sequence is obtained.Computer Science Departmen

Space programs summary no. 37-26, volume IV FOR the period February 1, 1964 to March 31, 1964. Supporting research and advanced development

Research project summaries in propulsion, guidance and control, trajectory optimization, physics and chemistry, communications, and related space science

Ozone in the Troposphere and Stratosphere, part 1

This is the first part of a 2-part Conference Publication. This document contains papers presented at the 1992 Quadrennial Ozone Symposium held at the Charlottesville, Virginia, from June 4-13, 1992. The papers cover topics in both Tropospheric and Stratospheric research. These topics include ozone trends and climatology, ground based, aircraft, balloon, rocket and satellite measurements, Arctic and Antarctic research, global and regional modeling, and volcanic effects

Proceedings of the 6th International Symposium on the Mediterranean Pig. October 11 – 13, 2007. Messina - Capo d’Orlando (ME), Italy

These proceedings publish 79 communications that were distributed in six sessions and in one conference at the 6th Symposium on the Mediterranean Pig, both as main lectures, oral and poster presentation. The major arguments treated are the improvement and the management of the genetic resources, the sanitary approaches in the outdoor systems, the feeding and the rearing techniques, the quality of meat and meat products, the traceability for typical products and their socio-economical dynamics. Particular attention is given to the pig's local breeds and to their meat products, highlighting the importance to preserve the biodiversity as well as the typicality of some unique pork products. The monitoring of pig parasitic diseases is examined as well as the non conventional rearing systems used for typical pig breeds and their effects on the pork quality. It is highlighted also the importance of the products traceability and the need to better understand the purchasing dynamics of typical pork products

Proceedings of the 6th International Symposium on the Mediterranean Pig. October 11 – 13, 2007. Messina - Capo d’Orlando (ME), Italy

These proceedings publish 79 communications that were distributed in six sessions and in one conference at the 6th Symposium on the Mediterranean Pig, both as main lectures, oral and poster presentation. The major arguments treated are the improvement and the management of the genetic resources, the sanitary approaches in the outdoor systems, the feeding and the rearing techniques, the quality of meat and meat products, the traceability for typical products and their socio-economical dynamics. Particular attention is given to the pig's local breeds and to their meat products, highlighting the importance to preserve the biodiversity as well as the typicality of some unique pork products. The monitoring of pig parasitic diseases is examined as well as the non conventional rearing systems used for typical pig breeds and their effects on the pork quality. It is highlighted also the importance of the products traceability and the need to better understand the purchasing dynamics of typical pork products

Periodicity and distribution properties of combined FCSR sequences

www.cs.uky.edu/~klapper Abstract. This is a study of some of the elementary statistical properties of the bitwise exclusive or of two maximum period feedback with carry shift register sequences. We obtain conditions under which the resulting sequences has the maximum possible period, and we obtain bounds on the variation in the distribution of blocks of a fixed length. This may lead to improved design of stream ciphers using FCSRs