From cae68b58b70de455ef66b7312c8625f25e83a37f Mon Sep 17 00:00:00 2001
From: Christophe Guyeux <christophe.guyeux@univ-fcomte.fr>
Date: Wed, 17 Jun 2015 11:04:29 +0200
Subject: [PATCH] Fin de mon boulot.

---
 computePeriod.py | 14 ++++++++++++++
 mabase.bib       | 17 ++++++++++++++++-
 prng_gpu.tex     |  5 +++++
 3 files changed, 35 insertions(+), 1 deletion(-)
 create mode 100644 computePeriod.py

diff --git a/computePeriod.py b/computePeriod.py
new file mode 100644
index 0000000..3e3a881
--- /dev/null
+++ b/computePeriod.py
@@ -0,0 +1,14 @@
+from operator import xor
+from itertools import product
+from sys import argv
+N=eval(argv[-2])
+n=eval(argv[-1])
+
+for s in product(range(2**N), repeat=n):
+    S=s*20
+    for x in range(4):
+        print str(s)+",",
+        for k in range(25):
+            print x,
+            x = xor(x,S[k])
+        print
diff --git a/mabase.bib b/mabase.bib
index 32a2081..b1d62d4 100644
--- a/mabase.bib
+++ b/mabase.bib
@@ -4404,4 +4404,19 @@ booktitle =	"Proceedings of the {ACM}/{SIGDA} 17th International
   year = 	 {2007},
 }
 
-
+@inproceedings{Sidorenko:2005:CSB:2179218.2179250,
+ author = {Sidorenko, Andrey and Schoenmakers, Berry},
+ title = {Concrete Security of the Blum-blum-shub Pseudorandom Generator},
+ booktitle = {Proceedings of the 10th International Conference on Cryptography and Coding},
+ series = {IMA'05},
+ year = {2005},
+ isbn = {3-540-30276-X, 978-3-540-30276-6},
+ location = {Cirencester, UK},
+ pages = {355--375},
+ numpages = {21},
+ url = {http://dx.doi.org/10.1007/11586821_24},
+ doi = {10.1007/11586821_24},
+ acmid = {2179250},
+ publisher = {Springer-Verlag},
+ address = {Berlin, Heidelberg},
+} 
diff --git a/prng_gpu.tex b/prng_gpu.tex
index db219a1..8d4f21b 100644
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -724,6 +724,11 @@ the list of cells to update in the state $x^n$ of the system (represented
 as an integer having $\mathsf{N}$ bits too). More precisely, the $k-$th 
 component of this state (a binary digit) changes if and only if the $k-$th 
 digit in the binary decomposition of $S^n$ is 1.
+\begin{color}{red} 
+Obviously, when $S$ is periodic of period $p$, then $x$ is periodic too of
+period either $p$ or $2p$, depending of the fact that, after $p$ iterations,
+the state of the system may or not be the same than before these iterations.
+\end{color}
 
 The single basic component presented in Eq.~\ref{equation Oplus} is of 
 ordinary use as a good elementary brick in various PRNGs. It corresponds
-- 
2.39.5