A Chaos Robustness Criterion for 2D Piecewise Smooth Map with Applications in Pseudorandom Number Generator and Image Encryption with Avalanche Effect

This study proposes a chaos robustness criterion for a kind of 2D piecewise smooth maps (2DPSMs). Using the chaos robustness criterion, one can easily determine the robust chaos parameter regions for some 2DPSMs. Combining 2DPSM with a generalized synchronization (GS) theorem, this study introduces a novel 6-dimensional discrete GS chaotic system. Based on the system, a 216-word chaotic pseudorandom number generator (CPRNG) is designed. The key space of the CPRNG is larger than 2996. Using the FIPS 140-2 test suit/generalized FIPS 140-2 test suit tests the randomness of the 1000 key streams consists of 20,000 bits generated by the CPRNG, the RC4 algorithm, and the ZUC algorithm, respectively. The numerical results show that the three algorithms do not have significant differences. The CPRNG and a stream encryption scheme with avalanche effect (SESAE) are used to encrypt an image. The results demonstrate that the CPRNG is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs. The SESAE with one-time-pad scheme makes any attackers have to use brute attacks to break our cryptographic system.

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A Stream Encryption Scheme with Both Key and Plaintext Avalanche Effects for Designing Chaos-Based Pseudorandom Number Generator with Application to Image Encryption

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127416500917 ◽

2016 ◽

Vol 26 (05) ◽

pp. 1650091 ◽

Cited By ~ 8

Author(s):

Dandan Han ◽

Lequan Min ◽

Guanrong Chen

Keyword(s):

Chaotic System ◽

Pseudorandom Number ◽

Pseudorandom Number Generator ◽

Encryption Scheme ◽

Number Generator ◽

Test Results ◽

Avalanche Effect ◽

Text Segment ◽

Text Word ◽

Test Suit

Based on a stream encryption scheme with avalanche effect (SESAE), a stream encryption scheme with both key avalanche effect and plaintext avalanche effect (SESKPAE) is introduced. Using this scheme and an ideal [Formula: see text]-word ([Formula: see text]-segment) pseudorandom number generator (PRNG), a plaintext can be encrypted such that each bit of the ciphertext block has a change with the probable probability of [Formula: see text] when any word of the key is changed or any bit of the plaintext is changed. To that end, a novel four-dimensional discrete chaotic system (4DDCS) is proposed. Combining the 4DDCS with a generalized synchronization (GS) theorem, a novel eight-dimensional discrete GS chaotic system (8DDGSCS) is constructed. Using the 8DDGSCS, a [Formula: see text]-word chaotic pseudorandom number generator (CPRNG) is designed. The keyspace of the [Formula: see text]-word CPRNG is larger than [Formula: see text]. Then, the FIPS 140-2 test suit/generalized FIPS 140-2 test suit is used to test the randomness of the 1000-key streams consisting of 20[Formula: see text]000 bits generated by the [Formula: see text]-word CPRNG, the RC4 algorithm PRNG and the ZUC algorithm PRNG, respectively. The test results show that for the three PRNGs, there are 100%/98.9%, 99.9%/98.8%, 100%/97.9% key streams passing the tests, respectively. Furthermore, the SP800-22 test suite is used to test the randomness of four 100-key streams consisting of 1000[Formula: see text]000 bits generated by four PRNGs, respectively. The numerical results show that the randomness performances of the [Formula: see text]-word CPRNG is promising, showing that there are no significant correlations between the key streams and the perturbed key streams generated via the [Formula: see text]-word CPRNG. Finally, using the [Formula: see text]-word CPRNG and the SESKPAE to encrypt two gray-scale images, test results demonstrate that the [Formula: see text]-word CPRNG is able to generate both key avalanche effect and plaintext avalanche effect, which are similar to those generated via an ideal CPRNG, and performs better than other comparable schemes.

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