TY - JOUR
T1 - Some Polynomial Chaotic Maps Without Equilibria and an Application to Image Encryption with Avalanche Effects
AU - Min, Lequan
AU - Yang, Xiuping
AU - Chen, Guanrong
AU - Wang, Danling
PY - 2015/8/8
Y1 - 2015/8/8
N2 - This study uses seven four-dimensional four-variable polynomial chaotic maps without equilibria in combination with generalized chaos synchronization (GCS) theorem to construct eight-dimensional bidirectional discrete generalized chaos synchronization (8DBDGCS) systems without equilibria. By combining the 8DBDGCS system with the GCS theorem, a 12-dimensional GCS system is designed. Numerical simulation verifies the chaotic dynamics of the 12-dimensional GCS system, which is used to design a 216-word chaotic pseudorandom number generator (CPRNG). The SP-8002 test suite is used to test the randomness of four 100-key streams consisting of 1 000 000 bits generated respectively by the CPRNG, a six-dimensional GCS-based CPRNG, the RC4 algorithm and the ZUC algorithm. The results show that the randomness performances of the two CPRNGs are promising, suggesting that there are no significant correlations between the key stream and the perturbed key streams generated via the 216-word CPRNG. In addition, theoretically the key space of the CPRNG is larger than 21195. The CPRNG is used with an avalanche-encryption scheme to encrypt an RGB balloon image, demonstrating that the CPRNG is able to generate the avalanche effects which are similar to those generated via ideal 216-word CPRNGs.
AB - This study uses seven four-dimensional four-variable polynomial chaotic maps without equilibria in combination with generalized chaos synchronization (GCS) theorem to construct eight-dimensional bidirectional discrete generalized chaos synchronization (8DBDGCS) systems without equilibria. By combining the 8DBDGCS system with the GCS theorem, a 12-dimensional GCS system is designed. Numerical simulation verifies the chaotic dynamics of the 12-dimensional GCS system, which is used to design a 216-word chaotic pseudorandom number generator (CPRNG). The SP-8002 test suite is used to test the randomness of four 100-key streams consisting of 1 000 000 bits generated respectively by the CPRNG, a six-dimensional GCS-based CPRNG, the RC4 algorithm and the ZUC algorithm. The results show that the randomness performances of the two CPRNGs are promising, suggesting that there are no significant correlations between the key stream and the perturbed key streams generated via the 216-word CPRNG. In addition, theoretically the key space of the CPRNG is larger than 21195. The CPRNG is used with an avalanche-encryption scheme to encrypt an RGB balloon image, demonstrating that the CPRNG is able to generate the avalanche effects which are similar to those generated via ideal 216-word CPRNGs.
KW - avalanche-encryption scheme
KW - bidirectional generalized synchronization
KW - Chaotic map without equilibrium
KW - pseudorandom number generator
KW - randomness test
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84941241693&origin=recordpage
U2 - 10.1142/S0218127415501242
DO - 10.1142/S0218127415501242
M3 - 21_Publication in refereed journal
VL - 25
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
SN - 0218-1274
IS - 9
M1 - 1550124
ER -