modif ref entre 2 documents

[prng_gpu.git] / supplementary.tex

diff --git a/supplementary.tex b/supplementary.tex
index 1fead570b7c22f9357e5a67e464dd48d4d9f6e3f..1ad62e6ef1b6755471ff1341260a9b2079582c7b 100644 (file)
--- a/supplementary.tex
+++ b/supplementary.tex
@@ -27,7 +27,7 @@
 \usepackage{subfigure}
 \usepackage{xr-hyper}
 \usepackage{hyperref}
 \usepackage{subfigure}
 \usepackage{xr-hyper}
 \usepackage{hyperref}

-\externaldocument{prng_gpu}
+\externaldocument[M-]{prng_gpu}

 %\usepackage{hyperref}
 
 
 %\usepackage{hyperref}
 
 


@@ -342,7 +342,7 @@ theory of chaos and tests embedded into the NIST battery. %Such relations need t
 
 
 \begin{itemize}
 
 
 \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
 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}
 
 
 \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.
 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}
 
 \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
 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 
 $M=100$ 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
 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 
 next bit in the BBS generator, which
 is cryptographically secure. More precisely, it
 is $(T,\varepsilon)-$secure: no