The Zaslavsky maps based pseudorandom byte generator is a recent and secure cryptographic primitive. Extended security analysis of the generator is presented. We evaluated the output byte properties by period and linear complexity calculation and DieHarder and PractRand statistical packages. This gives the motivation to consider the Zaslavsky systems based pseudorandom byte generator as reasonable for basic cryptographic applications in encryption process.
Cryptanalysis is the study of analyzing cipher text, ciphers and cryptographic primitives with the aim of understanding how they operate and finding and improving methods for defeating or destroying them. Pseudorandom byte generators are distinct algorithms that use mathematical formulas to output bytes with random like properties.
The use of chaos maps as a secure cryptographic system in the last thirty
years has been at the prominence of dynamical equations. In [
Zaslavsky maps [
The aim of the article is to present new analysis of some cryptographic
properties of Zaslavsky maps based pseudorandom byte generator. In Section 2, the
steps of the generator are described. Section 3 presents calculations of the period
and the linear complexity, and DieHarder [
where The mathematical expression of the Zaslavsky equations is given by: yn+1 = mod(yn+ν(1+μzn)+ɛνμcos(2πyn),1) zn+1=e-r(zn+ɛcos(2πyn)
μ=1-e-r/r, (3) r = 3.0, ν = 400/3, and ɛ = 0.3. The generator under present study is based on two Zaslavsky chaotic systems. The initial parameters y1,0, y2,0, z1,0, and z2,0 are real numbers. With each iteration, four real values y1,i, y2,j, z1,i, and z2,j, are generated, then converted to 256 bit values, and XOR-ed. Pseudorandom byte m is outputted. (1) (2)
The period and linear complexity of two hundred sequences of length M=200,000
of the generator were computed using SAGE [
The DieHarder package (version 3.31.1) is a random number generator-testing suite. This testing and benchmarking software program consists tests presented in Table 1 and Table 2.
The DieHarder output results are presented in Table 1 and Table 2.
Assessment passed passed passed diehard rank 6x8 diehard bitstream diehard opso diehard oqso diehard dna diehard count 1s stream diehard parking lot diehard 2dsphere diehard 3dsphere diehard squeeze diehard sums diehard runs diehard craps Test name count the 1s byte marsaglia tsang gcd sts monobit sts runs sts serial rgb bitdist rgb minimum distance rgb permutations rgb lagged sum rgb kstest test dab bytedistrib dab dct dab filltree dab filltree2 dab monobit2
The second package is PractRand. We tested our pseudorandom scheme for bytes up to 224 bytes in length, Table 3 and Table 4.
The size of initial values can guarantee long period and good linear complexity of the output stream. All probability values, calculated from DieHarder and PractRand tests are in acceptable range of [0, 1). Based on these results we can conclude that all of statistical tests are passing successfully and the generator under present study is very suitable for critical cryptographic applications. 4
We have presented new security analysis of the Zaslavsky functions based pseudorandom byte generator. The results from the period, linear complexity, and DieHarder and PractRand statistical packages evaluation, indicate that the studied algorithm is reasonable for basic cryptographic applications in derivative encryption schemes. 5
This work is partially supported by the Bulgarian Ministry of Education and Science under the National Program for Research “Young Scientists and Postdoctoral Students”. This work is partially supported by the Scientific research fund of Shumen University under the grant No. RD-08-107/02.02.2021.