# book.stack: Book Stack Test In CryptRndTest: Statistical Tests for Cryptographic Randomness

 book.stack R Documentation

## 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`.

### Details

If `x` contains a sequence of bits, then `x` should be a matrix of BxN, where N is the number of words (integers) generated by the RNG of interest. Otherwise, `x` is an Nx1 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.

### 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.

### Author(s)

Haydar Demirhan

Maintainer: Haydar Demirhan <haydarde@hacettepe.edu.tr>

### 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)

```

CryptRndTest documentation built on April 22, 2022, 9:07 a.m.