Converting random bits into random numbers

Koo, Bonwook; Roh, Dongyoung; Kwon, Daesung

doi:10.1007/s11227-014-1202-1

Cited by 3 publications

(3 citation statements)

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“…Recently, ISO/IEC JTC 1/SC 27/WG 2, responsible for standardizing cryptography and security mechanisms within ISO/IEC, decided to incorporate the two conversion methods for random number generation developed by Koo et al [8], the simple partial discard method and the complex partial discard method, into the standard. The partial discard methods discard less bits than discard methods and guarantee a uniform output.…”

Section: B Conversion Methods For Random Number Generationmentioning

confidence: 99%

Applying the Simple Partial Discard Method to Crystals-Kyber

Roh,

Jung

2024

IEEE Access

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In some cryptographic applications random numbers are required (e.g., when generating cryptographic keys and generating digital signatures). To obtain random numbers, we usually first get random bits and then convert them into random numbers. Several methods to convert a sequence of random bits into a sequence of random numbers are known and some of them are standardized. Recently, ISO/IEC JTC 1/SC 27/WG 2 decided to add two more methods, the simple partial discard method and the complex partial discard method, to the existing four standard methods. Meanwhile, CRYSTALS-Kyber is the only public-key encryption and key-establishment algorithm selected for the post-quantum cryptography standardization project by NIST (National Institute of Standards and Technology). It uses an algorithm called Parse that takes a byte stream as input and outputs a polynomial of degree d with coefficients in Z q (for some positive integer d and prime q) using the simple discard method to generate key pairs. In this paper, we apply the simple partial discard method to Parse. We show that using the simple partial discard method instead of the simple discard method can reduce the number of bits required by up to 12%. We also show that in some cases, by using the simple partial discard method instead of the simple discard method, a polynomial can be generated up to 8% faster experimentally.INDEX TERMS Conversion methods for random number generation, CRYSTALS-Kyber, Simple discard method, Simple partial discard method.

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Section: B Conversion Methods For Random Number Generationmentioning

confidence: 99%

Applying the Simple Partial Discard Method to Crystals-Kyber

Roh,

Jung

2024

IEEE Access

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“…As the ideas of these algorithms are very simple, it is no wonder that similar ideas also appeared in computer science literature but in different guises; see Barker and Kelsey [2007], Flajolet et al [2011], Koo et al [2014], and Ressler [1992] and the references therein. We will comment more on this in the next section.…”

Section: Introductionmentioning

confidence: 93%

“…Mean We see that the minor difference in Algorithm FYvN results not only in higher mean but also larger variance, making FYvN less competitive in modern practical applications although it was used, for example, by Moses and Oakford to produce tables of random permutations [Moses and Oakford 1963]. Also the procedure von-Neumann in Algorithm 4, as one of the simplest and most natural ideas of simulating a uniform by coin tossing, was independently proposed under different names in the literature; see, for example, Granboulan and Pornin [2007] and Koo et al [2014]; in particular, it is called "Simple Discard Method" in National Institute of Standards and Technology (NIST) [Barker and Kelsey 2007] "Recommendation for random number generation using deterministic random bit generators." Thus, we also include the analysis of FYvN in this article, although it is less efficient in bit complexity.…”

Section: Algorithmmentioning

confidence: 99%

Generating Random Permutations by Coin Tossing

Bacher

Bodini

Hwang

et al. 2017

ACM Trans. Algorithms

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Several simple, classical, little-known algorithms in the statistics and computer science literature for generating random permutations by coin tossing are examined, analyzed, and implemented. These algorithms are either asymptotically optimal or close to being so in terms of the expected number of times the random bits are generated. In addition to asymptotic approximations to the expected complexity, we also clarify the corresponding variances, as well as the asymptotic distributions. A brief comparative discussion with numerical computations in a multicore system is also given.

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