From 4635b3f66f097ccf0ad342948e2a29906bdbb32a Mon Sep 17 00:00:00 2001 From: guyeux Date: Wed, 7 Dec 2011 11:22:18 +0100 Subject: [PATCH] Correction de coquilles dans le texte de pch --- prng_gpu.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/prng_gpu.tex b/prng_gpu.tex index 7629e10..6782175 100644 --- a/prng_gpu.tex +++ b/prng_gpu.tex @@ -1118,15 +1118,15 @@ 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 $w$ of length $N$, $G(w)$ (the output of $G$ on the input $w$) has size -$\ell_G(N)$ with $\ell_G(N)>N$. +seed $k$ of length $k$, $G(k)$ (the output of $G$ on the input $k$) has size +$\ell_G(k)$ with $\ell_G(k)>k$. 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, -$$| \mathrm{Pr}[D(G(U_k))=1]-Pr[D(U_{\ell_G(k)})=1]|< \frac{1}{p(N)},$$ +$$| \mathrm{Pr}[D(G(U_k))=1]-Pr[D(U_{\ell_G(k)})=1]|< \frac{1}{p(k)},$$ 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 internal coin tosses of $D$. -- 2.39.5