CryptRndTest (version 1.2.2)

topological.binary: Topological Binary Test

Description

Performs Topological Binary Test of Alcover et al. (2013) to evaluate the randomness of an RNG. No additional goodness-of-fit test is applied after calculation of test statistic of Topological Binary Test.

Usage

topological.binary(x, B, alpha = 0.05, critical.value)

Arguments

x

a matrix that includes random data in base-2 format. See details for further information.

B

the length of words (B-bit).

alpha

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

critical.value

a value used to decide whether to reject the null hypothesis at the significance level of alpha. See details for further information.

Value

statistic

calculated value of the test statistic.

result.TBT

returns 0 if H0 is rejected and 1 otherwise.

Details

The argument x should be entered as a matrix of bits of dimension $B$x$k$, where $k$ is the number of words (integers) generated by the RNG of interest.

The argument critical.value should be calculated regarding the value of B. For $B = 8,...,16$, values of critical.value are tabulated by Alcover et al. (2013) and calculation procedure of critical.value for the values greater than 16 is described therein. The tabulated values can be used if the number of words ($k$) is equal to $2^B$. Otherwise, it should be calculated over the given cumulative distribution function by Alcover et al. (2013). For example, if $k=10^4$, then critical.value$ = 9245$ and if $k=2*10^4$, then critical.value$ = 19999$.

Topological binary test is itself constitutes a goodness-of-fit test based on the number of different B-bit patterns among the non-overlapping B-bit blocks composed of the input sequence of bits.

References

Alcover, P.M., Guillamon, A., Ruiz, M.C., A new randomness test for bit sequences. Informatica (2013), 24(3), 339--356.

Examples

RNGkind(kind = "Super-Duper")
B=16                          # Bit length is 16.
k=5000                        # Generate 5000 integers.
dat=round(runif(k,0,(2^B-1)))
x=sfsmisc::digitsBase(dat, base= 2, B) #Convert to base 2
alpha = 0.05
critical.value=9245           #Obtained for B = 16
test=topological.binary(x, B, alpha, critical.value)
print(test)