400 research outputs found
Cryptanalysis of a Generalized Subset-Sum Pseudorandom Generator
We present attacks on a generalized subset-sum pseudorandom generator, which was proposed by von zur Gathen and Shparlinski in 2004. Our attacks rely on a sub-quadratic algorithm for solving a vectorial variant of the 3SUM problem, which is of independent interest. The attacks presented have complexities well below the brute-force attack, making the generators vulnerable. We provide a thorough analysis of the attacks and their complexities and demonstrate their practicality through implementations and experiments
Pseudorandom Vectors Generation Using Elliptic Curves And Applications
In this paper we present, using the arithmetic of elliptic curves over finite
fields, an algorithm for the efficient generation of sequence of uniform
pseudorandom vectors in high dimension with long period, that simulates sample
sequence of a sequence of independent identically distributed random variables,
with values in the hypercube with uniform distribution. As an
application, we obtain, in the discrete time simulation, an efficient algorithm
to simulate, uniformly distributed sample path sequence of a sequence of
independent standard Wiener processes. This could be employed for use, in the
full history recursive multi-level Picard approximation method, for numerically
solving the class of semilinear parabolic partial differential equations of the
Kolmogorov type
Some Applications of Coding Theory in Cryptography
viii+80hlm.;24c
Finite Fields: Theory and Applications
Finite fields are the focal point of many interesting geometric, algorithmic and combinatorial problems. The workshop was devoted to progress on these questions, with an eye also on the important applications of finite field techniques in cryptography, error correcting codes, and random number generation
Artin's primitive root conjecture -a survey -
This is an expanded version of a write-up of a talk given in the fall of 2000
in Oberwolfach. A large part of it is intended to be understandable by
non-number theorists with a mathematical background. The talk covered some of
the history, results and ideas connected with Artin's celebrated primitive root
conjecture dating from 1927. In the update several new results established
after 2000 are also discussed.Comment: 87 pages, 512 references, to appear in Integer
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