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- Title
Function Composition from Sine Function and Skew Tent Map and Its Application to Pseudorandom Number Generators.
- Authors
Palacios-Luengas, Leonardo; Marcelín-Jiménez, Ricardo; Rodriguez-Colina, Enrique; Pascoe-Chalke, Michael; Jiménez-Ramírez, Omar; Vázquez-Medina, Rubén
- Abstract
Featured Application: A pseudorandom number generator (PRNG) emulates to a truly random number generator in an interest interval and, its pseudorandomness depends on the size of the initial conditions space and the sensitivity to these conditions. A PRNG can be implemented through diverse strategies; but in cryptography applications, a PRNG must produce aperiodic number sequences with high linear complexity and a statistical distribution close to the uniform distribution. An approach to implement PRNGs is based on chaotic maps because they have inherent features, such as their highly sensitive dependence on initial conditions and the control parameters, their topological transitivity, ergodicity, aperiodicity and pseudorandomness properties. These features fully match with the practical implementation requirements of the PRNGs. Therefore, we propose a function composition based on skew tent map (STM) and the sine function that can be an effective alternative to implement PRNGs with high computational complexity that overcome pseudorandomness test suites. In cryptography, the pseudorandom number sequences must have random appearance to be used in secure information systems. The skew tent map (STM) is an attractive map to produce pseudorandom sequences due to its easy implementation and the absence of stability islands when it is in chaotic behavior. Using the STM and sine function, we propose and analyze a function composition to propose a pseudorandom number generator (PRNG). In the analysis of the function composition, we use the bifurcation diagram and the Lyapunov exponent to perform a behavioral comparison against the STM. We show that the proposed function composition is more sensitive to initial conditions than the STM, and then it is a better option than the STM for cryptography applications. For the proposed function we determine and avoid the chaos annulling traps. The proposed PRNG can be configured to generate pseudorandom numbers of 8, 16 or 32 bits and it can be implemented on microcontrollers with different architectures. We evaluate the pseudorandomness of the proposed PRNG using the NIST SP 800-22 and TestU01 suites. Additionally, to evaluate its quality, we apply tests such as correlation coefficient, key sensitivity, statistical and entropy analysis, key space, linear complexity, and speed. Finally, we performed a comparison with similar PRNGs that produce pseudorandom sequences considering numbers of 8 and 32 bits. The results show that the proposed PRNG maintains its security regardless of the selected configuration. The proposed PRNG has five important features: easy implementation, configurable to produce number with 8, 16 or 32 bits, high processing speed, high linear complexity, and wide key space. These features are necessary for cryptographic systems.
- Subjects
SINE function; RANDOM number generators; LYAPUNOV exponents; DISTRIBUTION (Probability theory); BIFURCATION diagrams
- Publication
Applied Sciences (2076-3417), 2021, Vol 11, Issue 13, p5769
- ISSN
2076-3417
- Publication type
Article
- DOI
10.3390/app11135769