modif dans le bbs

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 4feac7cc64b8730163298a05ba2edca48d894eeb..de8f46488c1cd1b4843a1f759bbea5433f41cb71 100644 (file)
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -1092,13 +1092,12 @@ As a  comparison,   Listing~\ref{algo:seqCIPRNG}  leads   to the  generation of
 
 
 
 
 
 

-In Figure~\ref{fig:time_bbs_gpu}  we highlight the performances  of the optimized
-BBS-based  PRNG on GPU. On the  Tesla C1060 we
-obtain approximately 700MSample/s and on the GTX 280 about 670MSample/s, which is
-obviously slower than the xorlike-based PRNG on GPU. However, we will show in the 
-next sections that 
-this new PRNG has a strong level of security, which is necessary paid by a speed
-reduction. 
+In Figure~\ref{fig:time_bbs_gpu} we highlight  the performances of the optimized
+BBS-based PRNG on GPU.  On  the Tesla C1060 we obtain approximately 700MSample/s
+and  on the  GTX 280  about  670MSample/s, which  is obviously  slower than  the
+xorlike-based PRNG on GPU. However, we  will show in the next sections that this
+new PRNG  has a strong  level of  security, which is  necessary paid by  a speed
+reduction.

 
 \begin{figure}[htbp]
 \begin{center}
 
 \begin{figure}[htbp]
 \begin{center}


@@ -1339,20 +1338,24 @@ on the variable  $t$ and stores the result in  $t$, and $BBS1(bbs1)\&15$ selects
 the last  four bits  of the  result of $BBS1$.   Thus an  operation of  the form
 $t<<=4; t|=BBS1(bbs1)\&15\;$  realizes in $t$ a  left shift of 4  bits, and then
 puts the 4 last bits of $BBS1(bbs1)$  in the four last positions of $t$.  Let us
 the last  four bits  of the  result of $BBS1$.   Thus an  operation of  the form
 $t<<=4; t|=BBS1(bbs1)\&15\;$  realizes in $t$ a  left shift of 4  bits, and then
 puts the 4 last bits of $BBS1(bbs1)$  in the four last positions of $t$.  Let us

-remark that to initialize $t$ is not a necessity as we fill it 4 bits by 4 bits,
-until having obtained 32-bits.  The two last new shifts are realized in order to
-enlarge  the  small periods  of  the  BBS used  here,  to  introduce  a kind  of
+remark that the initialization $t$ is not a  necessity as we fill it 4 bits by 4
+bits, until  having obtained 32-bits.  The  two last new shifts  are realized in
+order to enlarge the small periods of  the BBS used here, to introduce a kind of

 variability.  In these operations, we make twice a left shift of $t$ of \emph{at
   most}  3 bits,  represented by  \texttt{shift} in  the algorithm,  and  we put
 \emph{exactly} the \texttt{shift}  last bits from a BBS  into the \texttt{shift}
 variability.  In these operations, we make twice a left shift of $t$ of \emph{at
   most}  3 bits,  represented by  \texttt{shift} in  the algorithm,  and  we put
 \emph{exactly} the \texttt{shift}  last bits from a BBS  into the \texttt{shift}

-last bits of $t$.
+last bits of $t$. For this, an array named \texttt{array\_shift}, containing the
+correspondance between the  shift and the number obtained  with \texttt{shift} 1
+to make the \texttt{and} operation is used. For example, with a left shift of 0,
+we  make an  and operation  with 0,  with  a left  shift of  3, we  make an  and
+operation with 7 (represented by 111 in binary mode).

 
 

-It should  be noticed that this generator has another time the form $x^{n+1} = x^n \oplus S^n$,
+It should  be noticed that this generator has once more the form $x^{n+1} = x^n \oplus S^n$,

 where $S^n$ is referred in this algorithm as $t$: each iteration of this
 PRNG ends with $x = x \wedge t$. This $S^n$ is only constituted
 by secure bits produced by the BBS generator, and thus, due to
 Proposition~\ref{cryptopreuve}, the resulted PRNG is cryptographically
 where $S^n$ is referred in this algorithm as $t$: each iteration of this
 PRNG ends with $x = x \wedge t$. This $S^n$ is only constituted
 by secure bits produced by the BBS generator, and thus, due to
 Proposition~\ref{cryptopreuve}, the resulted PRNG is cryptographically

-secure
+secure.