CryptRndTest (version 1.2.2)

book.stack: Book Stack Test

Description

Performs Book Stack test of Ryabko and Monarev (2005) to evaluate the randomness of an RNG. The Chi-Square test is applied as the goodness-of-fit test.

Usage

book.stack(x, B, k=2, alpha=0.05, bit=FALSE)

Arguments

x

a vector or matrix that includes random data. See details for further information.

B

the length of words (B-bit) that the chippered file will be divided.

k

the number of subsets that the alphabet will be divided. It should be chosen to ensure $|x|/k$ will be an integer.

alpha

a predetermined value of significance level with the default value of 0.05.

bit

if x contains a sequence of bits, bit is set TRUE. Otherwise, a sequence of integers is entered and bit is set FALSE.

Value

statistic

calculated value of the test statistic.

p.value

p-value of the Chi-Square test.

BS.result

returns 0 if H0 is rejected and 1 otherwise.

Details

If x contains a sequence of bits, then x should be a matrix of $B$x$N$, where $N$ is the number of words (integers) generated by the RNG of interest. Otherwise, x is an $N$x$1$ vector of the words. Because bits will be converted to base-10 before application of the test, implementation time will be shorter with integer input. Optimal value of $N$, which also represents the length of sample that is composed of B-bit words, is obtained by the optimal length of sample composed of bits ($n$) that is given by Ryabko and Monarev (2005) as $n=B(2^(B/2))$. For example, if $B=16$, then $n=4096$ and the legth of alphabet is 65536. In this case, we need to enter 4096 bits or $N=4096/16=256$ integers. However, under the setting $B=32$, the length of alphabet is 2^32 and we need to enter 65536. Note that it is hard to implement the test for $B>32$ due to the memory overflows. Therefore, this test is applicable for smaller values of $B$. In this test, because there is no asymptotic theoretical distribution introduced, only chi-square test is applied as goodness-of-fit test.

References

Ryabko, B.Ya., Monarev, V.A., Using information theory approach to randomness testing. Journal of Statistical Planning and Inference (2005), 133, 95--110.

Examples

RNGkind(kind = "L'Ecuyer-CMRG")
B=8                 # Bit length is 8. 
n=B*(2^(B/2))       # Number of required bits.
N=n/B               # Number of integers to be generated.
x=round(runif(N,0,(2^B-1)))
k=2                   # Divide alphabet to two sub-sets.
alpha=0.05
test=book.stack(x, B, k, alpha, bit = FALSE)
print(test)