An 8-bit integer true periodic orbit PRNG based on delayed Arnold’s cat map

Abstract

Designing a pseudo-random number generator (PRNG) exhibiting true periodic orbits with large periods is promising for embedded applications. Implementing chaotic behaviors on a finite precision digital platform using conventional unsigned integer or floating-point arithmetic yields short period limit-cycles. It leads the output to diverge from the true chaotic orbits. This paper presents an unsigned integer encoded PRNG based on the delayed quantized Arnold’s Cat Map (QACM) that exhibits true periodic orbits with large periods. The proposed PRNG is obtained by delaying one of the 2-D QACM outputs with a linear feedback shift register (LFSR) thereby increasing its period. By investigating its period, we show that the periodicity increases with an increase in the delay and bit-precision. We also present the proposed PRNG unit’s hardware architecture and its synthesis results targeting on a Xilinx Zynq 7000 Field Programmable Gate Array (FPGA) with 8-bit precision and delay δ=58. Further, we synthesize the design using 90 nm CMOS technology for ASIC realization. The synthesis results demonstrate the throughput as 2.208 Gbps and 5.46 Gbps at 138 MHz and 342 MHz operating frequency on FPGA and ASIC respectively. We experimentally evaluate the performance of random numbers using the NIST 800-22-1 tests along with the correlation and key sensitivity tests.