X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/5ccd7174adc0881aa861c67d36462da62a3cb158..2d86fbdeb7b0b994440f0844f58ae18ffde90ffb:/prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 2156752..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
@@ -172,17 +172,17 @@ key encryption protocol by using the proposed method.
 
 \PCH{
 {\bf Main contributions.} In this paper a new PRNG using chaotic iteration
-is defined. From a theoretical point of view, it is proved that it has fine
+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.
-Pseudo-random numbers are generated at a rate of 20GSamples/s which is faster
+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.
 }
 
@@ -1698,7 +1698,7 @@ PRNG too.
 \end{proposition}
 
 \begin{proof}
-The proposition is proved by contraposition. Assume that $X$ is not
+The proposition is proven by contraposition. Assume that $X$ is not
 secure. By Definition, there exists a polynomial time probabilistic
 algorithm $D$, a positive polynomial $p$, such that for all $k_0$ there exists
 $N\geq \frac{k_0}{2}$ satisfying 
@@ -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.