9 research outputs found
On the Distribution of the Power Generator over a Residue Ring for Parts of the Period
Get PDFThis paper studies the distribution of the power generator of pseudorandom numbers over a residue ring for parts of the period. These results compliment some recently obtained distribution bounds of the power generator modulo an arbitrary number for the entire period. Also, the arbitrary modulus case may have some cryptography related applications and could be of interest in other settings which require quality pseudorandom numbers.This paper studies the distribution of the power generator of pseudorandom numbers over a residue ring for parts of the period. These results compliment some recently obtained distribution bounds of the power generator modulo an arbitrary number for the entire period. Also, the arbitrary modulus case may have some cryptography related applications and could be of interest in other settings which require quality pseudorandom numbers
On the linear complexity and linear complexity profile of sequences in finite fields
Get PDFPseudo random sequences, that are used for stream ciphers, are required to havetheproperties of unpredictability and randomness. An important tool for measuringthese features is the linear complexity profile of the sequence in use.In this thesis we present a survey of some recent results obtained on linearcomplexity and linear complexity profile of pseudo random sequences. The relationbetween the polynomial degree and the linear complexity of a function over a finite field is given, bounds for linear complexity of the "power generator" and "the selfshrinking generator" are presented and a new method of construction of sequences of high linear complexity profile is illustrated
Recent advances in the theory of nonlinear pseudorandom number generators
Get PDFThe classical linear congruential method for generating uniform pseudorandom numbers has some deficiencies that can render them useless for some simulation problems. This fact motivated the design and the analysis of nonlinear congruential methods for the generation of pseudorandom numbers. In this thesis, we aim to review the recent developments in the study of nonlinear congruential pseudorandom generators. Our exposition concentrates on inversive generators. We also describe the so-called power generator and the quadratic exponential generator which are particularly interesting for cryptographic applications. We give results on the period length and theoretical analysis of these generators. The emphasis is on the lattice structure, discrepancy and linear complexity of the generated sequences
