From c8b95c6c1d99f1ab0375abf07c90613c94d4e261 Mon Sep 17 00:00:00 2001 From: couturie Date: Fri, 16 Dec 2011 20:31:14 +0100 Subject: [PATCH] spell check --- prng_gpu.tex | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/prng_gpu.tex b/prng_gpu.tex index 7d94e0c..6c6c980 100644 --- a/prng_gpu.tex +++ b/prng_gpu.tex @@ -135,7 +135,7 @@ allows us to generate almost 20 billion of pseudorandom numbers per second. Furthermore, we show that the proposed post-treatment preserves the cryptographical security of the inputted PRNG, when this last has such a property. -Last, but not least, we propose a rewritting of the Blum-Goldwasser asymmetric +Last, but not least, we propose a rewriting of the Blum-Goldwasser asymmetric key encryption protocol by using the proposed method. The remainder of this paper is organized as follows. In Section~\ref{section:related @@ -536,7 +536,7 @@ x^0 \in \llbracket 0, 2^\mathsf{N}-1 \rrbracket, S \in \llbracket 0, 2^\mathsf{N \label{equation Oplus} \end{equation} where $\oplus$ is for the bitwise exclusive or between two integers. -This rewritting can be understood as follows. The $n-$th term $S^n$ of the +This rewriting can be understood as follows. The $n-$th term $S^n$ of the sequence $S$, which is an integer of $\mathsf{N}$ binary digits, presents 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 @@ -950,7 +950,7 @@ NumThreads: number of threads\;} Algorithm~\ref{algo:gpu_kernel} presents a naive implementation of the proposed PRNG on GPU. Due to the available memory in the GPU and the number of threads -used simultenaously, the number of random numbers that a thread can generate +used simultaneously, the number of random numbers that a thread can generate inside a kernel is limited (\emph{i.e.}, the variable \texttt{n} in algorithm~\ref{algo:gpu_kernel}). For instance, if $100,000$ threads are used and if $n=100$\footnote{in fact, we need to add the initial seed (a 32-bits number)}, @@ -1255,7 +1255,7 @@ lesser than $2^{16}$. So in practice we can choose prime numbers around indistinguishable bits is lesser than or equals to $log_2(log_2(M))$). In other words, to generate a 32-bits number, we need to use 8 times the BBS algorithm with possibly different combinations of $M$. This -approach is not sufficient to be able to pass all the TestU01, +approach is not sufficient to be able to pass all the tests of TestU01, as small values of $M$ for the BBS lead to small periods. So, in order to add randomness we have proceeded with the followings modifications. @@ -1344,7 +1344,7 @@ 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 $t$. For this, an array named \texttt{array\_shift}, containing the -correspondance between the shift and the number obtained with \texttt{shift} 1 +correspondence 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). -- 2.39.5