From 3abda4f59d76446238e6b891bc14e1ac7b44c34a Mon Sep 17 00:00:00 2001 From: couturie Date: Fri, 21 Sep 2012 19:58:14 +0200 Subject: [PATCH] modif ref entre 2 documents --- supplementary.tex | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/supplementary.tex b/supplementary.tex index 1fead57..1ad62e6 100644 --- a/supplementary.tex +++ b/supplementary.tex @@ -27,7 +27,7 @@ \usepackage{subfigure} \usepackage{xr-hyper} \usepackage{hyperref} -\externaldocument{prng_gpu} +\externaldocument[M-]{prng_gpu} %\usepackage{hyperref} @@ -342,7 +342,7 @@ theory of chaos and tests embedded into the NIST battery. %Such relations need t \begin{itemize} - \item \textbf{Regularity}. As stated in Section~\ref{subsec:Devaney} of the main document, a chaotic dynamical system must + \item \textbf{Regularity}. As stated in Section~\ref{M-subsec:Devaney} of the main document, a chaotic dynamical system must have an element of regularity. Depending on the chosen definition of chaos, this element can be the existence of a dense orbit, the density of periodic points, etc. The key idea is that a dynamical system with no periodicity is not as chaotic as a system having periodic orbits: in the first situation, we can predict something and gain a @@ -391,7 +391,7 @@ not only sought in general to obtain chaos, but they are also required for rando \end{itemize} -We have proven in our previous works~\cite{guyeux12:bc} that chaotic iterations satisfying Theorem~\ref{Th:Caractérisation des IC chaotiques} of the main document are, among other +We have proven in our previous works~\cite{guyeux12:bc} that chaotic iterations satisfying Theorem~\ref{M-Th:Caractérisation des IC chaotiques} of the main document are, among other things, strongly transitive, topologically mixing, chaotic as defined by Li and Yorke, and that they have a topological entropy and an exponent of Lyapunov both equal to $ln(\mathsf{N})$, where $\mathsf{N}$ is the size of the iterated vector. @@ -634,7 +634,7 @@ raise ambiguity. \section{Practical Security Evaluation} \label{sec:Practicak evaluation} -Pseudorandom generators based on Eq.~\eqref{equation Oplus} of the main document are thus cryptographically secure when +Pseudorandom generators based on Eq.~\eqref{M-equation Oplus} of the main document are thus cryptographically secure when they are XORed with an already cryptographically secure PRNG. But, as stated previously, such a property does not mean that, whatever the @@ -685,7 +685,7 @@ A pseudorandom generator is $(T,\varepsilon)-$secure if there exists no $(T,\var -Suppose now that the PRNG of Eq.~\eqref{equation Oplus} of the main document will work during +Suppose now that the PRNG of Eq.~\eqref{M-equation Oplus} of the main document will work during $M=100$ time units, and that during this period, an attacker can realize $10^{12}$ clock cycles. We thus wonder whether, during the PRNG's @@ -695,7 +695,7 @@ greater than $\varepsilon = 0.2$. We consider that $N$ has 900 bits. Predicting the next generated bit knowing all the -previously released ones by Eq.~\eqref{equation Oplus} of the main document is obviously equivalent to predicting the +previously released ones by Eq.~\eqref{M-equation Oplus} of the main document is obviously equivalent to predicting the next bit in the BBS generator, which is cryptographically secure. More precisely, it is $(T,\varepsilon)-$secure: no -- 2.39.5