431 research outputs found
Families of sequences with good family complexity and cross-correlation measure
In this paper we study pseudorandomness of a family of sequences in terms of
two measures, the family complexity (-complexity) and the cross-correlation
measure of order . We consider sequences not only on binary alphabet but
also on -symbols (-ary) alphabet. We first generalize some known methods
on construction of the family of binary pseudorandom sequences. We prove a
bound on the -complexity of a large family of binary sequences of
Legendre-symbols of certain irreducible polynomials. We show that this family
as well as its dual family have both a large family complexity and a small
cross-correlation measure up to a rather large order. Next, we present another
family of binary sequences having high -complexity and low cross-correlation
measure. Then we extend the results to the family of sequences on -symbols
alphabet.Comment: 13 pages. Comments are welcome
On lattice profile of the elliptic curve linear congruential generators
Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (EC-LCG) under this new lattice test and prove that the EC-LCG passes it up to very high dimensions. We also use a result of Brandstätter and Winterhof on the linear complexity profile related to the correlation measure of order k to present lower bounds on the linear complexity profile of some binary sequences derived from the EC-LCG
Some Applications of Coding Theory in Cryptography
viii+80hlm.;24c
The cross-correlation measure for families of binary sequences
Large families of binary sequences of the same length are
considered and a new measure, the cross-correlation measure
of order is introduced to study the connection between
the sequences belonging to the family. It is shown that this new measure is related to certain other important properties of families of binary sequences. Then the size of the cross-correlation measure is studied. Finally, the cross-correlation measures of two important families of pseudorandom binary sequences are estimated
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
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 Sequences from Elliptic Curves
In this article we will generalize some known constructions to produce pseudorandom sequences with the aid of elliptic curves. We will make use of both additive and multiplicative characters on elliptic curves
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