The need of software-flexible stream ciphers has led to several alternative proposals in the last few years. One of them is a new Pseudo Random Number Generator (PRNG), named N-adic Summation-Shrinking (NSumSG), which architecture is described in this paper. It uses N-1 parallel working slave summation generators and one N-adic summation generator, controlling the nonlinearity in the generator....

In this paper we argue that hand-writing a program generator generator has a number of advantages compared to generating a program generator generator by self-application of a partial evaluator. We show the basic principles of how to construct a program generator generator by presenting a program generator generator for a skeletal language, and we argue that it is not more difficult to use the ...

it is shown that there are exactly seventy-eight 3-generator 2-groups of order $2^{11}$ with trivial schur multiplier. we then give 3-generator, 3-relation presentations for forty-eight of them proving that these groups have deficiency zero.

De, Trevisan and Tulsiani [CRYPTO 2010] show that every distribution over n-bit strings which has constant statistical distance to uniform (e.g., the output of a pseudorandom generator mapping n− 1 to n bit strings), can be distinguished from the uniform distribution with advantage by a circuit of size O(2 2). We generalize this result, showing that a distribution which has less than k bits of ...

Today we will study some conditions under which a very powerful pseudorandom generator can be shown to exist, and also some consequences of the existence of such a pseudorandom generator. We will start by assuming the existence of a permutation p : {0, 1}n → {0, 1}n which is computable in poly(n) time and which, for some constant δ > 0, is (2δn, 2−δn)-one way. (This is an extremely strong assum...

Q: Why are we using circuit lower bounds here, as opposed to a claim such as E ̸⊆ P for example? A: The proof of the Nisan-Wigderson pseudorandom generator relies on nonuniformity, by showing that distinguishing a pseudorandom generator implies a circuit for solving a hard problem – this reduction involves hardwiring advice into a circuit in order to solve the hard problem. A contradiction requi...

We postulate that a distribution is pseudorandom if it cannot be told apart from the uniform distribution by any eecient procedure. This yields a robust deenition of pseudorandom generators as eecient deterministic programs stretching short random seeds into longer pseudorandom sequences. Thus, pseudorandom generators can be used to reduce the randomness-complexity in any eecient procedure. Pse...

AC 0 circuits of size n log n augmented with log n MODm gates, for every odd integer m and any sufficiently small . As a consequence, for every odd integer m, we obtain a pseudorandom generator, based on the MOD2 function, for circuits of size S containing log S MODm gates. Our results are based on recent bounds of exponential sums that were previously introduced for proving lower bounds for MA...