

\textit{National Institute of Standrs and technologies} or \textbf{NIST} is based on hypothesis testing and includes a 15 batteries of mathematical and physical properties tests for RNG. It was developed to test the randomness of (arbitrary long) binary sequences produced by either HW/SW based cryptographic random or pseudo random bit generators with a fixed input parameters as sequence length of ($10^{3} < N < 10^{7}$) and ($ M < 55 $) of binary sequences (sample size). For each $N$ sequence produced, the NIST determine by prbability computed by $P-value$ (level of test) of all different type of non-randomness exist, where the $P-value$ must be more than a significance level $ \alpha [0.0001, 0.01] $ to classify it as a good RNG and equal to 1 to have perfect randomness. Practically, the NIST test evaluate in first the range of acceptable proportions of binary sequences passing the statistical test, then in second it evaluate the uniformity of the test sequence and computing on the basis of $x^{2}$ test to the $P-value$ obtained.

\textit{TestU01} is now the most complete and difficult batterie of test of RNG. it was developed  by Pierre L'Ecuyer and was implemented in the ANSI C languages with more than 516 tests resumed in 7 big batteries ($ P-value [0.001, 0.999] $). This new Battery of tests covers divers classical tests of the other batteries with new algorithm performance and cryptographic tests. Six predefined batteries of tests are already included, where the last batterie \textbf{FIPS} is the recall for NIST tests. The first three batterie (319 tests) are for sequences of random numbers \textbf{SmallCrush}, \textbf{Crush} and \textbf{BigCrush}, and the three others ( 181 tests) are for bit sequences \textbf{Rabbit}, \textbf{Alphabit} and \textbf{Pseudo-DieHARD} designed to test a finite sequence contained in a random bits.   

The other test batteries are the \textbf{Diehard}, it's include 18 test of Randomness and was developed by George Marsaglia. It was supposed to give a better way of analysis in comparison to original \textbf{FIPS} (16 tests) statistical tests. However and unlike NIST, the $P-value$ have to belong to some fixed chosen interval $[0+ \alpha, 1- \alpha ]$ with a level of signification $\alpha$ of $5 \%$ for example. Where the \textbf{ENT} battery tests was developed to sequences of bytes stored in files and reports the results of those tests as Entropy and $x^{2}$ tests.

The results of this survey presented by the authors, show some different level of what it concerned testing statistic of the RNG implementation from theories to practical results. Where the tests standard evaluate and updated to covert more the characteristic of the RNG starting by the simple to a complex and hard batteries of test. We can analysis the result by two category that it seen more stable and trust tests as the NIST and TESTU01, where the other batteries are even for old tests or they are included in those  two batteries.

The PRNG analysis table show that not all papers has pass the NIST test, where Chaotic PRNG are th most success implementation of FPGA using different meothods. However, all work that use FPGA opetimised resourcec as LUT or acuumulator can pass the test where others not. give a details about this section of tests, where there is some difficult to say it pass it or now specially the coverege of tests. 

 


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\begin{table}[h]
\begin{tabular}{|l|l|l|l|l|l|} \toprule
RNG  & DieHard & FIPS & NIST & TestU01 & AIS   \\ \midrule 
 	 & LF[4,6] & CHO[7]  & LF[$1^{*}$,3,5] & LF[$4^{*}$,$6^{*}$,$7^{*}$,$8^{*}$]  &   \\  %LFSR
PRNG & MT[1,3,8,7] &  & CA[5-9]  & MT[$1^{*}$,$3^{*}$,$8^{*}$,$6^{**}$]  &   \\ 	%MT
	 & CA[2,3,5,8] &  & CHO[1,3,4,6,7,8] &    &    \\ \midrule
TRNG & IRO[7,8]  & PLL[4] & PLL[1,2,5] &  IRO[$7^{**}$]  &  STR[10]  \\ 	%PLL
	 & STR[10] & STR[10,12]  & IRO[6,8] &   &  MTS[13]  \\ 	%IRO
	 &  & MTS[13] & STR[10,12] &    &   \\ 		%STR
	 &   &  & MTS[14,15] &    &   \\ \bottomrule	%MTS
\end{tabular}
\end{table}
