A Universal Scheme for Transforming Binary Algorithms to Generate Random Bits from Loaded Dice

In this paper, we present a universal scheme for transforming an arbitrary algorithm for biased 2-face coins to generate random bits from the general source of an m-sided die, hence enabling the application of existing algorithms to general sources. In addition, we study approaches of efficiently generating a prescribed number of random bits from an arbitrary biased coin. This contrasts with most existing works, which typically assume that the number of coin tosses is fixed, and they generate a variable number of random bits.Comment: 2 columns, 10 page

Efficiently Generating Random Bits from Finite State Markov Chains

The problem of random number generation from an uncorrelated random source (of unknown probability distribution) dates back to von Neumann's 1951 work. Elias (1972) generalized von Neumann's scheme and showed how to achieve optimal efficiency in unbiased random bits generation. Hence, a natural question is what if the sources are correlated? Both Elias and Samuelson proposed methods for generating unbiased random bits in the case of correlated sources (of unknown probability distribution), specifically, they considered finite Markov chains. However, their proposed methods are not efficient or have implementation difficulties. Blum (1986) devised an algorithm for efficiently generating random bits from degree-2 finite Markov chains in expected linear time, however, his beautiful method is still far from optimality on information-efficiency. In this paper, we generalize Blum's algorithm to arbitrary degree finite Markov chains and combine it with Elias's method for efficient generation of unbiased bits. As a result, we provide the first known algorithm that generates unbiased random bits from an arbitrary finite Markov chain, operates in expected linear time and achieves the information-theoretic upper bound on efficiency

Optimum Power Controller for Random Number Generator in the Crypto Module of Ubiquitous Computing Environment

Abstract. Critical cryptography applications require the production of an unpredictable and unbiased stream of binary data derived from a fundamental noise mechanism, which is quite difficult to create with a stable random bit stream, as required for statistical randomness, when using a random generator with only a hardware component. However, since all electronic systems are influenced by a finite bandwidth, 1/f noise, and other non-random influences, perfect randomness cannot be preserved by any practical system. Thus, when generating random numbers using an electronic circuit, a low-power white noise signal is amplified, then sampled at a constant sampling frequency. Yet, it is quite difficult to create an unbiased and stable random bit stream, as required for statistical randomness, when using a random generator with only a hardware component and in especially it has occur the drift phenomena of input power. Therefore if the randomness of output bit stream is beyond limits range, it is applied the regulation of input power range to take the output bit stream, through the evaluation of randomness by constant period of output bit stream. Accordingly, this paper proposes a method for stabilizing the input power of a random number generator using optimum power control mechanism in crypto module hardware. As such, the proposed scheme is designed to reduce the statistical property of a biased bit stream and optimize the input power to a random number generator engine in crypto module engine for ubiquitous computing

Balanced Modulation for Nonvolatile Memories

This paper presents a practical writing/reading scheme in nonvolatile memories, called balanced modulation, for minimizing the asymmetric component of errors. The main idea is to encode data using a balanced error-correcting code. When reading information from a block, it adjusts the reading threshold such that the resulting word is also balanced or approximately balanced. Balanced modulation has suboptimal performance for any cell-level distribution and it can be easily implemented in the current systems of nonvolatile memories. Furthermore, we studied the construction of balanced error-correcting codes, in particular, balanced LDPC codes. It has very efficient encoding and decoding algorithms, and it is more efficient than prior construction of balanced error-correcting codes

Efficient Generation of Random Bits From Finite State Markov Chains

The problem of random number generation from an uncorrelated random source (of unknown probability distribution) dates back to von Neumann's 1951 work. Elias (1972) generalized von Neumann's scheme and showed how to achieve optimal efficiency in unbiased random bits generation. Hence, a natural question is what if the sources are correlated? Both Elias and Samuelson proposed methods for generating unbiased random bits in the case of correlated sources (of unknown probability distribution), specifically, they considered finite Markov chains. However, their proposed methods are not efficient or have implementation difficulties. Blum (1986) devised an algorithm for efficiently generating random bits from degree-2 finite Markov chains in expected linear time, however, his beautiful method is still far from optimality on information-efficiency. In this paper, we generalize Blum's algorithm to arbitrary degree finite Markov chains and combine it with Elias's method for efficient generation of unbiased bits. As a result, we provide the first known algorithm that generates unbiased random bits from an arbitrary finite Markov chain, operates in expected linear time and achieves the information-theoretic upper bound on efficiency