2007
DOI: 10.1109/tcsi.2007.890622
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A Class of Maximum-Period Nonlinear Congruential Generators Derived From the Rényi Chaotic Map

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Cited by 81 publications
(60 citation statements)
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“…(1b) where D controls attractor size [3]. The Euler approximation (with step size h = 2 −k ) is applied:…”
Section: A Digital Realizationmentioning
confidence: 99%
See 1 more Smart Citation
“…(1b) where D controls attractor size [3]. The Euler approximation (with step size h = 2 −k ) is applied:…”
Section: A Digital Realizationmentioning
confidence: 99%
“…Chaos theory is thus considered attractive for many recent applications and especially PRNG implementations due to the high sensitivities within system dynamics [1]- [16]. The digital realizations of the 1D discrete chaotic maps presented in [2], [3] are slow and large due to multiplication and have only one dimensional output. Numerically solved multidimensional continuous-time chaotic systems [4], [5] eliminate such drawbacks, provide multiple outputs and also have multiplier-free architectures.…”
Section: Introductionmentioning
confidence: 99%
“…Therefore, a fully digital approach to chaos generators is necessary for applications requiring repeatable oscillators, including cryptography and spread-spectrum communication. However, digital implementations of chaos-based pseudo-random number generators [25][26][27][28][29] have remained reliant on 1-D discrete chaotic maps. This notion is natural given the direct application in the digital do-main but resulting systems have the following drawbacks: a) They are slow and large due to multiplication, b) They have low throughput due to 1-D output and c) They suffer from windows of periodicity that require more complex architectures to overcome.…”
Section: Introductionmentioning
confidence: 99%
“…800-22 test suite [40] to indicate statistical randomness. The resulting PRNGs enjoy high-throughput when compared to other chaosbased designs [25][26][27][28][29] in spite of implementation on a previousgeneration Xilinx Virtex 4 FPGA. All systems are designed in Verilog HDL and experimentally verified with logic utilization less than 1.73% and throughput up to 15.59 Gbits/s for the native chaotic systems and up to 8.77 Gbits/s for the resulting PRNGs.…”
Section: Introductionmentioning
confidence: 99%
“…Chaotic oscillators have been emphasized for applications in random number generation [1]- [6] wherein the repeatable, reliable and high-performance chaotic sources required for these applications [7] are difficult to realize using analog circuits with chaos degradation due to established issues of PVT-sensitivity [8]. In particular, multi-scroll chaos generators have been exhaustively studied [9]- [12], wherein the limitations on the dynamic range of analog components and low supply voltages has restricted the number of scrolls that can be realized due to complex circuitry needed for control [13] unless mixed-signal approaches are used [14].…”
Section: Introductionmentioning
confidence: 99%