The European Physical Journal Special Topics

, Volume 223, Issue 8, pp 1679–1697 | Cite as

Statistical tests and chaotic synchronization based pseudorandom number generator for string bit sequences with application to image encryption

  • Longjie Hao
  • Lequan MinEmail author
Regular Article Chaos Based Image Encryption, Stream Cipher and Authentication
Part of the following topical collections:
  1. Chaos, Cryptography and Communications


Recently, a stream encryption scheme using d-bit segment sequences has been proposed. This scheme may generate key avalanche effect. The randomness tests of d-bit segment pseudorandom number generator will be important for implementing such a scheme. Firstly this paper extends Beker and Piper’s binary pseudorandom sequence statistical test suite to d-bit segment sequences case. Secondly, a novel 3-dimensional polynomial discrete chaotic map (3DPDCM) is proposed. The calculated Lyapunov exponents of the 3DPCDM are 0.213, 0.125 and − 3.228. Using the 3DPDCM constructs a 6-dimensional generalized synchronization chaotic system. Based on this system, a 8-bit segment chaotic pseudorandom number generator (CPRNG) is introduced. Using the generalized test suite tests 100 key streams generated via the 8-bit PRNG with different initial conditions and perturbed system parameters. The tested results are similar to those of the key streams generated via RC4 PRNG. As an application, using the key streams generated via the CPRNG and the RC4 PRNG encrypts an RGB image Landscape. The results have shown that the encrypted RGB images have significant avalanche effects. This research suggests that the requirements for PRNGs are not as strict as those under the traditional avalanche criteria. Suitable designed chaos-based d-bit string PRNGs may be qualified candidates for the stream encryption scheme with avalanche effect.


European Physical Journal Special Topic Test Suite Encrypt Image Pseudorandom Number Generator Generalize Synchronization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.School of Mathematics and Physics, University of Science and Technology BeijingBeijingChina

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