• Journal of the Korea Society of Computer and Information
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• v.18 no.2
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• pp.19-30
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• 2013

We study sub-Peres functions that are defined recursively as Peres function for random number generation. Instead of using two parameter functions as in Peres function, the sub-Peres functions uses only one parameter function. Naturally, these functions produce less random bits, hence are not asymptotically optimal. However, the sub-Peres functions runs in linear time, i.e., in O(n) time rather than O(n logn) as in Peres's case. Moreover, the implementation is even simpler than Peres function not only because they use only one parameter function but because they are tail recursive, hence run in a simple iterative manner rather than by a recursion, eliminating the usage of stack and thus further reducing the memory requirement of Peres's method. And yet, the output rate of the sub-Peres function is more than twice as much as that of von Neumann's method which is widely known linear-time method. So, these methods can be used, instead of von Neumann's method, in an environment with limited computational resources like mobile devices. We report the analyses of the sub-Peres functions regarding their running time and the exact output rates in comparison with Peres function and other known methods for random number generation. Also, we discuss how these sub-Peres function can be implemented.

• Journal of the Korea Society of Computer and Information
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• v.17 no.12
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• pp.149-158
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• 2012

Proposed is a hybrid randomizing function using two asymptotically optimal randomizing functions: Elias function and Peres function. Randomizing function is an mathematical abstraction of producing a uniform random bits from a source of randomness with bias. It is known that the output rate of Elias function and Peres function approaches to the information-theoretic upper bound. Especially, for each fixed input length, Elias function is optimal. However, its computation is relatively complicated and depends on input lengths. On the contrary, Peres function is defined by a simple recursion. So its computation is much simpler, uniform over the input lengths, and runs on a small footprint. In view of this tradeoff between computational complexity and output efficiency, we propose a hybrid randomizing function that has strengths of the two randomizing functions and analyze it.