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A new two-dimensional mutual coupled logistic map and its application for pseudorandom number generator. (English) Zbl 1435.37054
Summary: Given that the sequences generated by logistic map are unsecure with a number of weaknesses, including its relatively small key space, uneven distribution, and vulnerability to attack by phase space reconstruction, this paper proposes a new two-dimensional mutual coupled logistic map, which can overcome these weaknesses. Our two-dimensional chaotic map model is simpler than the recently proposed three-dimensional coupled logistic map, whereas the sequence generated by our system is more complex. Furthermore, a new kind of pseudorandom number generator (PRNG) based on the mutual coupled logistic maps is proposed for application. Both statistical tests and security analysis show that our proposed PRNG has good randomness and that it can resist all kinds of attacks. The algorithm speed analysis indicates that PRNG is valuable to practical applications.
MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
65C10 Random number generation in numerical analysis
94A60 Cryptography
65P20 Numerical chaos
Software:
TestU01
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