Determination of full cycle condition by linear congruence method

Teng Sun; Shenglin Li

doi:10.1117/12.2671256

29 March 2023 Determination of full cycle condition by linear congruence method

Teng Sun, Shenglin Li

Proceedings Volume 12594, Second International Conference on Electronic Information Engineering and Computer Communication (EIECC 2022); 125942G (2023) https://doi.org/10.1117/12.2671256
Event: Second International Conference on Electronic Information Engineering and Computer Communication (EIECC 2022), 2022, Xi'an, China

Abstract

As the most widely used pseudo-random number generation algorithm, the linear congruence algorithm has the characteristics of fast generation and can generate better random numbers in one-dimensional space. Random numbers are widely used in many fields, such as information security and communication, and it is important to study the generation of random sequences. However, the linear congruence method has some defects, for example, when the mode of the linear congruence method𝑚 takes 10, multiplier𝑎 takes 7, increment𝑐 takes 7 and the initial value𝑋₀ takes 7, the sequence obtained is: 7,6,9,0, 7,6,9,0, ..., which results in a sequence with a period of 4. In the linear congruence method𝑚 , the 𝑎 and 𝑐 are crucial to the size of the period of the whole sequence and will directly affect the security of the algorithm. In this paper, the conditions for the linear congruence method to reach the full cycle are given on the basis of previous work, and a rigorous mathematical proof is given.

Citation Download Citation

Teng Sun and Shenglin Li "Determination of full cycle condition by linear congruence method", Proc. SPIE 12594, Second International Conference on Electronic Information Engineering and Computer Communication (EIECC 2022), 125942G (29 March 2023); https://doi.org/10.1117/12.2671256

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