Correction de coquilles dans le texte de pch

[prng_gpu.git] / prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 7629e10fa7f50075e8cfed1877352ce68cc46f2f..678217540467750ffd9322330118fe8e6593fa47 100644 (file)
--- 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
 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,
 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 $D$. 
 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 $D$.