A New Pseudorandom Bit Generator Based on Mixing Three‐Dimensional Chen Chaotic System with a Chaotic Tactics

Abstract

In this paper, a new chaotic system is proposed based on mixing three-dimensional Chen chaotic system with a chaotic tactics. This new system is proved to be chaotic under Wiggins' chaos definition and can generate chaotic sequences with high complexity. Furthermore, we propose a new pseudorandom bit generator (PRBG) based on this new system. A coding algorithm is used to make the sequences uniform. Both statistical and security tests are provided to show the generated sequences are with good randomness and high complexity to withstand attacks.

Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

“…In addition, Figure 19 depicts the autocorrelation and cross-correlation plots for a bit sequence of length , generated for parameter values . For random sequences, the auto-correlation should have a delta like form, and the cross-correlation should be close to zero [ 5 , 13 ]. This is indeed verified.…”

“…The field of chaos theory expands to numerous applications related to cryptography, secure communications, engineering, physics, economics, robotics, control, and many more; see, for example, References [ 1 , 2 , 3 , 4 , 5 ] and the references therein. Chaotic systems, being deterministic systems with a high sensitivity to initial conditions and parameter changes, constitute an excellent basis for efficiently modelling complex natural phenomena, as well as adding complexity to security related applications.…”

“…The resulting map presents more complex chaos related phenomena compared to the classic map as mentioned above, as well as achieves a higher value for its Lyapunov exponent. Furthermore, to showcase the applicability of the map to chaos related applications, the problems of pseudo random bit generation [ 4 , 5 , 10 , 11 , 13 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 ] and image encryption [ 4 , 7 , 9 , 14 , 15 , 33 , 35 , 39 , 44 , 45 , 46 , 47 , 48 ] are considered. It is seen that the bit sequence generated from the modified map using a simple rule passes all 15 tests of the National Institute of Standards and Technology (NIST) statistical test suite [ 49 ].…”

The Establishment and Dynamic Properties of a New 4D Hyperchaotic System with Its Application and Statistical Tests in Gray Images

“…At present, research on 1D chaos, such as Logistic mapping [ 5 , 6 , 7 ]; 2D chaos, such as Henon mapping [ 8 , 9 , 10 ]; and 3D chaos, such as Rossler chaotic attractor [ 11 , 12 , 13 ], Chua [ 14 , 15 , 16 ], and Chen [ 17 , 18 , 19 ], have been very extensive and mature. With the development of chaos theory, many people began to study high-dimensional chaotic attractors, such as 4D chaotic attractor subsystems [ 20 , 21 , 22 , 23 ], 5D chaotic attractor subsystems [ 24 , 25 , 26 , 27 ], and 6D chaotic attractor subsystems [ 28 ].…”

The Eigenvalue Complexity of Sequences in the Real Domain

“…Nowadays, many physical systems can be used in cryptography for its complex dynamical properties, such as chaos-based cryptography [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. However, chaotic systems are based on the real number field R n , and the cardinality of the state variable is infinite.…”