Triple Pendulum Based Nonlinear Chaos Generator and its Applications in Cryptography

Abstract

A nonlinear chaos generator scheme derived from a mechanical triple pendulum physical system is proposed here. The chaotic behavior of the proposed generator is validated against various standardized tests, such as the Lyapunov exponents test, bifurcation diagrams, sensitivity to parametric and to initial values, ergodicity, key space and sensitivity, histogram, correlation, NPCR and UACI, collision test, etc. and compared with existing contemporary methods. The generated chaotic map is utilized to develop various cryptography applications, such as PRNG and symmetric key encryption schemes, which are realized on an FPGA and an ASIC. Chaos-based PRNG is validated successfully using $NIST-SP800$ benchmarks. The proposed encryption scheme illustrates its usage in low power, high throughput applications, where the power consumption, resource utilization, and throughput are $1.785\times $ , $1.825\times $ , and $2.396\times $ better than other known contemporary chaos-based encryption methods. The average power and area of its ASIC implementation at 180-nm technology are 61.8836 mW and 0.20374 mm2 at 250 MHz.

Keywords

• Nonlinear system
• triple pendulum
• chaotic map
• pseudo random number
• symmetric cryptosystem
• differential state-space model