Structural Properties of Cryptographic Sequences - Computational Intelligence in Security for Information Systems - page 196

Table 3. Results of NIST SP800-22 Statistical tests

Results of NIST Pseudorandom tests
P-Value

Test Review

Proposed
Cryptosystem

AES DES

Frequency 0.5955 0.9463 0.0155 Approved

Block-Frequency 0.3669 0.4559 0.7399 Approved

Cumulative-sums Forward 0.9357 0.924 0.3504 Approved

Cumulative-sums Reverse 0.7197 0.7791 0.07571 Approved

Runs 0.9357 0.9558 0.2368 Approved

Longest-Runs of Ones 0.6579 0.7597 0.6371 Approved

Rank 0.3505 0.3504 0.319 Approved

Spectral FFT 0.0428 0.0757 0.2896 Approved

Overlapping-templates 0.7792 0.3838 0.419 Approved

Non-Overlapping-templates 0.4461 0.5749 0.3838 Approved

Universal 0.3345 0.6786 0.924 Approved

Approximate Entropy 0.4012 0.7597 0.3504 Approved

Random-Excursions 0.5047 0.02818 0.2492 Approved

Random-Excursions-Variant 0.3789 0.1005 0.1453 Approved

Serial 0.8669 0.6371 0.01559 Approved

4 Conclusions

In this paper, it is proposed a cryptosystem that includes pseudorandom sequences
generators using 1-D chaotic maps. These generators have been built with piecewise
linear maps because they do not have stability islands in the chaotic region. The parti-
tion made on the definition interval of the 1-D chaotic map and its association with
the Extended ASCIII alphabet avoids the periodicity problems in the generated se-
quences. These problems are derived from the scaling and discretization of the chaotic
map used in cryptosystems. In summary, the implementation of a block chaotic
cryptosystem is shown, and its behavior is analyzed using the concepts of information
theory and the suite of random test of NIST SP800-22. The proposed chaotic crypto-
system was made using a 1-D chaotic tent map, which has not stability islands into
the chaotic region. The entropy and mutual information results show that the proposed
cryptosystem is a good alternative to affect the syntactic, semantic and the statistical
distribution of a plaintext. Cryptosystems as the one proposed in this paper can be
useful components in software applications that provide security to stored or commu-
nicated information, because they have similar behavior to the one of the algorithms
currently used, and they are designed with chaotic sequence generators, which are
aperiodic by definition.
Acknowledgments. The authors are grateful to the financial support of the SIP-IPN
20110670 and ICYTDF 270/2010 projects.