138,437 research outputs found
Close to Uniform Prime Number Generation With Fewer Random Bits
In this paper, we analyze several variants of a simple method for generating
prime numbers with fewer random bits. To generate a prime less than ,
the basic idea is to fix a constant , pick a
uniformly random coprime to , and choose of the form ,
where only is updated if the primality test fails. We prove that variants
of this approach provide prime generation algorithms requiring few random bits
and whose output distribution is close to uniform, under less and less
expensive assumptions: first a relatively strong conjecture by H.L. Montgomery,
made precise by Friedlander and Granville; then the Extended Riemann
Hypothesis; and finally fully unconditionally using the
Barban-Davenport-Halberstam theorem. We argue that this approach has a number
of desirable properties compared to previous algorithms.Comment: Full version of ICALP 2014 paper. Alternate version of IACR ePrint
Report 2011/48
Stopping time signatures for some algorithms in cryptography
We consider the normalized distribution of the overall running times of some
cryptographic algorithms, and what information they reveal about the
algorithms. Recent work of Deift, Menon, Olver, Pfrang, and Trogdon has shown
that certain numerical algorithms applied to large random matrices exhibit a
characteristic distribution of running times, which depends only on the
algorithm but are independent of the choice of probability distributions for
the matrices. Different algorithms often exhibit different running time
distributions, and so the histograms for these running time distributions
provide a time-signature for the algorithms, making it possible, in many cases,
to distinguish one algorithm from another. In this paper we extend this
analysis to cryptographic algorithms, and present examples of such algorithms
with time-signatures that are indistinguishable, and others with
time-signatures that are clearly distinct.Comment: 20 page
A Comparative Study of Some Pseudorandom Number Generators
We present results of an extensive test program of a group of pseudorandom
number generators which are commonly used in the applications of physics, in
particular in Monte Carlo simulations. The generators include public domain
programs, manufacturer installed routines and a random number sequence produced
from physical noise. We start by traditional statistical tests, followed by
detailed bit level and visual tests. The computational speed of various
algorithms is also scrutinized. Our results allow direct comparisons between
the properties of different generators, as well as an assessment of the
efficiency of the various test methods. This information provides the best
available criterion to choose the best possible generator for a given problem.
However, in light of recent problems reported with some of these generators, we
also discuss the importance of developing more refined physical tests to find
possible correlations not revealed by the present test methods.Comment: University of Helsinki preprint HU-TFT-93-22 (minor changes in Tables
2 and 7, and in the text, correspondingly
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