From: couturie <couturie@carcariass.(none)>
Date: Sat, 17 Dec 2011 19:33:32 +0000 (+0100)
Subject: modif
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/commitdiff_plain/979f9e26b08888c2d5d492f72a2b4b4fc21b1185

modif
---

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 6c6c980..48705d0 100644
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -1128,17 +1128,17 @@ In this section the concatenation of two strings $u$ and $v$ is classically
 denoted by $uv$.
 In a cryptographic context, a pseudorandom generator is a deterministic
 algorithm $G$ transforming strings  into strings and such that, for any
-seed $k$ of length $k$, $G(k)$ (the output of $G$ on the input $k$) has size
-$\ell_G(k)$ with $\ell_G(k)>k$.
+seed $s$ of length $m$, $G(s)$ (the output of $G$ on the input $s$) has size
+$\ell_G(m)$ with $\ell_G(m)>m$.
 The notion of {\it secure} PRNGs can now be defined as follows. 
 
 \begin{definition}
 A cryptographic PRNG $G$ is secure if for any probabilistic polynomial time
 algorithm $D$, for any positive polynomial $p$, and for all sufficiently
-large $k$'s,
-$$| \mathrm{Pr}[D(G(U_k))=1]-Pr[D(U_{\ell_G(k)})=1]|< \frac{1}{p(k)},$$
+large $m$'s,
+$$| \mathrm{Pr}[D(G(U_m))=1]-Pr[D(U_{\ell_G(m)})=1]|< \frac{1}{p(m)},$$
 where $U_r$ is the uniform distribution over $\{0,1\}^r$ and the
-probabilities are taken over $U_N$, $U_{\ell_G(N)}$ as well as over the
+probabilities are taken over $U_m$, $U_{\ell_G(m)}$ as well as over the
 internal coin tosses of $D$. 
 \end{definition}
 
@@ -1147,7 +1147,7 @@ distinguish a perfect uniform random generator from $G$ with a non
 negligible probability. The interested reader is referred
 to~\cite[chapter~3]{Goldreich} for more information. Note that it is
 quite easily possible to change the function $\ell$ into any polynomial
-function $\ell^\prime$ satisfying $\ell^\prime(N)>N)$~\cite[Chapter 3.3]{Goldreich}.
+function $\ell^\prime$ satisfying $\ell^\prime(m)>m)$~\cite[Chapter 3.3]{Goldreich}.
 
 The generation schema developed in (\ref{equation Oplus}) is based on a
 pseudorandom generator. Let $H$ be a cryptographic PRNG. We may assume,
@@ -1452,4 +1452,4 @@ in a simulation context or in a cryptographic one.
 
 \bibliographystyle{plain} 
 \bibliography{mabase}
-\end{document}
+\end{document}
\ No newline at end of file