214 research outputs found
Note on Marsaglia's Xorshift Random Number Generators
Marsaglia (2003) has described a class of Xorshift random number generators (RNGs) with periods 2^n - 1 for n = 32, 64, etc. We show that the sequences generated by these RNGs are identical to the sequences generated by certain linear feedback shift register (LFSR) generators using "exclusive or" (xor) operations on n-bit words, with a recurrence defined by a primitive polynomial of degree n.
Randomness Quality of CI Chaotic Generators: Applications to Internet Security
Due to the rapid development of the Internet in recent years, the need to
find new tools to reinforce trust and security through the Internet has became
a major concern. The discovery of new pseudo-random number generators with a
strong level of security is thus becoming a hot topic, because numerous
cryptosystems and data hiding schemes are directly dependent on the quality of
these generators. At the conference Internet`09, we have described a generator
based on chaotic iterations, which behaves chaotically as defined by Devaney.
In this paper, the proposal is to improve the speed and the security of this
generator, to make its use more relevant in the Internet security context. To
do so, a comparative study between various generators is carried out and
statistical results are given. Finally, an application in the information
hiding framework is presented, to give an illustrative example of the use of
such a generator in the Internet security field.Comment: 6 pages,6 figures, In INTERNET'2010. The 2nd Int. Conf. on Evolving
Internet, Valencia, Spain, pages 125-130, September 2010. IEEE Computer
Society Press Note: Best Paper awar
An experimental exploration of Marsaglia's xorshift generators, scrambled
Marsaglia proposed recently xorshift generators as a class of very fast,
good-quality pseudorandom number generators. Subsequent analysis by Panneton
and L'Ecuyer has lowered the expectations raised by Marsaglia's paper, showing
several weaknesses of such generators, verified experimentally using the
TestU01 suite. Nonetheless, many of the weaknesses of xorshift generators fade
away if their result is scrambled by a non-linear operation (as originally
suggested by Marsaglia). In this paper we explore the space of possible
generators obtained by multiplying the result of a xorshift generator by a
suitable constant. We sample generators at 100 equispaced points of their state
space and obtain detailed statistics that lead us to choices of parameters that
improve on the current ones. We then explore for the first time the space of
high-dimensional xorshift generators, following another suggestion in
Marsaglia's paper, finding choices of parameters providing periods of length
and . The resulting generators are of extremely
high quality, faster than current similar alternatives, and generate
long-period sequences passing strong statistical tests using only eight logical
operations, one addition and one multiplication by a constant
Improving random number generators by chaotic iterations. Application in data hiding
In this paper, a new pseudo-random number generator (PRNG) based on chaotic
iterations is proposed. This method also combines the digits of two XORshifts
PRNGs. The statistical properties of this new generator are improved: the
generated sequences can pass all the DieHARD statistical test suite. In
addition, this generator behaves chaotically, as defined by Devaney. This makes
our generator suitable for cryptographic applications. An illustration in the
field of data hiding is presented and the robustness of the obtained data
hiding algorithm against attacks is evaluated.Comment: 6 pages, 8 figures, In ICCASM 2010, Int. Conf. on Computer
Application and System Modeling, Taiyuan, China, pages ***--***, October 201
A Pseudo Random Numbers Generator Based on Chaotic Iterations. Application to Watermarking
In this paper, a new chaotic pseudo-random number generator (PRNG) is
proposed. It combines the well-known ISAAC and XORshift generators with chaotic
iterations. This PRNG possesses important properties of topological chaos and
can successfully pass NIST and TestU01 batteries of tests. This makes our
generator suitable for information security applications like cryptography. As
an illustrative example, an application in the field of watermarking is
presented.Comment: 11 pages, 7 figures, In WISM 2010, Int. Conf. on Web Information
Systems and Mining, volume 6318 of LNCS, Sanya, China, pages 202--211,
October 201
Note on Marsaglia's Xorshift Random Number Generators
Marsaglia (2003) has described a class of Xorshift random number generators (RNGs) with periods 2n - 1 for n = 32, 64, etc. We show that the sequences generated by these RNGs are identical to the sequences generated by certain linear feedback shift register (LFSR) generators using "exclusive or" (xor) operations on n-bit words, with a recurrence defined by a primitive polynomial of degree n
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