X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/1ad3649fd6e60ffa7c238cf99b577c7cce7d7b26..3abda4f59d76446238e6b891bc14e1ac7b44c34a:/supplementary.tex

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