From 2d86fbdeb7b0b994440f0844f58ae18ffde90ffb Mon Sep 17 00:00:00 2001 From: Raphael Couturier Date: Thu, 13 Sep 2012 13:55:13 +0200 Subject: [PATCH] quelques modifs --- prng_gpu.tex | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/prng_gpu.tex b/prng_gpu.tex index 38431e5..00b28fe 100644 --- a/prng_gpu.tex +++ b/prng_gpu.tex @@ -93,7 +93,7 @@ On the other side, speed is not the main requirement in cryptography: the great need is to define \emph{secure} generators able to withstand malicious attacks. Roughly speaking, an attacker should not be able in practice to make the distinction between numbers obtained with the secure generator and a true random -sequence. \begin{color}{red} Or, in an equivalent formulation, he or she should not be +sequence. \begin{color}{red} However, in an equivalent formulation, he or she should not be able (in practice) to predict the next bit of the generator, having the knowledge of all the binary digits that have been already released. ``Being able in practice'' refers here to the possibility to achieve this attack in polynomial time, and to the exponential growth @@ -174,15 +174,15 @@ key encryption protocol by using the proposed method. {\bf Main contributions.} In this paper a new PRNG using chaotic iteration is defined. From a theoretical point of view, it is proven that it has fine topological chaotic properties and that it is cryptographically secured (when -the based PRNG is also cryptographically secured). From a practical point of +the initial PRNG is also cryptographically secured). From a practical point of view, experiments point out a very good statistical behavior. Optimized original implementation of this PRNG are also proposed and experimented. Pseudorandom numbers are generated at a rate of 20GSamples/s, which is faster than in~\cite{conf/fpga/ThomasHL09,Marsaglia2003} (and with a better -statistical behavior). Experiments are also provided using BBS as the based +statistical behavior). Experiments are also provided using BBS as the initial random generator. The generation speed is significantly weaker but, as far as we know, it is the first cryptographically secured PRNG proposed on GPU. -Note too that an original qualitative comparison between topological chaotic +Note also that an original qualitative comparison between topological chaotic properties and statistical test is also proposed. } @@ -1840,7 +1840,7 @@ T \leqslant \dfrac{L(N)}{6 N (log_2(N))\varepsilon^{-2}M^2}-2^7 N \varepsilon^{- where $M$ is the length of the output ($M=100$ in our example), and $L(N)$ is equal to $$ -2.8\times 10^{-3} exp \left(1.9229 \times (N ~ln(2)^\frac{1}{3}) \times ln(N~ln 2)^\frac{2}{3}\right) +2.8\times 10^{-3} exp \left(1.9229 \times (N ~ln~ 2)^\frac{1}{3} \times (ln(N~ln~ 2))^\frac{2}{3}\right) $$ is the number of clock cycles to factor a $N-$bit integer. -- 2.39.5