Tree Algorithms for Unbiased Coin Tossing with a Biased Coin

Stout, Quentin F.; Warren, Bette

doi:10.1214/aop/1176993384

Cited by 46 publications

(50 citation statements)

References 5 publications

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“…, 25}. Since |P k | = 26 = 2 1 + 2 3 + 2 4 , P k is partitioned in three sets: set V k,1 contains the 2 4 elements {0, 1, . .…”

Section: Indexer Designmentioning

confidence: 99%

“…Thus, mapping T H → 0, HT → 1, while discarding the events T T , HH, generates a sequence of truly random bits even if the original coin is biased. More efficient algorithms for generating random bits from a biased coin were proposed by various authors [2][3][4][5]. See [6] for a more comprehensive bibliography, where the problem to generate random bits from a correlated source is considered.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Elias schemes for efficient harvesting of truly random bits

Bernardini

Rinaldo

2017

Int. J. Inf. Secur.

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The problem of generating a sequence of true random bits (suitable for cryptographic applications) from random discrete or analog sources is considered. A generalized version, including Vector Quantization, of the classical approach by Elias for the generation of truly random bits is introduced, and its performance is analyzed, both in the finite case and asymptotically. The theory allows us to provide an alternative proof of the optimality of the original Elias' scheme. We also consider the problem of deriving random bits from measurements of a Poisson process and from vectors of iid Gaussian variables. The comparison with the scheme of Elias, applied to geometric-like non binary vectors, originally based on the iso-probability property of permutations of iid variables, confirms the potential of the generalized scheme proposed in our work.

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“…, 25}. Since |P k | = 26 = 2 1 + 2 3 + 2 4 , P k is partitioned in three sets: set V k,1 contains the 2 4 elements {0, 1, . .…”

Section: Indexer Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized Elias schemes for efficient harvesting of truly random bits

Bernardini

Rinaldo

2017

Int. J. Inf. Secur.

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“…Elias [4] proposed a method of extracting unbiased bits from biased Markov chains. Stout and Warren [5] and Juels et. al.…”

Section: Introductionmentioning

confidence: 96%

Unbiased Random Sequences from Quasigroup String Transformations

Markovski

Gligoroski

Kocarev

2005

Fast Software Encryption

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Abstract. The need of true random number generators for many purposes (ranging from applications in cryptography and stochastic simulation, to search heuristics and game playing) is increasing every day. Many sources of randomness possess the property of stationarity. However, while a biased die may be a good source of entropy, many applications require input in the form of unbiased bits, rather than biased ones. In this paper, we present a new technique for simulating fair coin flips using a biased, stationary source of randomness. Moreover, the same technique can also be used to improve some of the properties of pseudo random number generators. In particular, an improved pseudo random number generator has almost unmeasurable period, uniform distribution of the letters, pairs of letters, triples of letters, and so on, and passes many statistical tests of randomness. Our algorithm for simulating fair coin flips using a biased, stationary source of randomness (or for improving the properties of pseudo random number generators) is designed by using quasigroup string transformations and its properties are mathematically provable. It is very flexible, the input/output strings can be of 2-bits letters, 4-bits letters, bytes, 2-bytes letters, and so on. It is of linear complexity and it needs less than 1Kb memory space in its 2-bits and 4-bits implementations, hence it is suitable for embedded systems as well.

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“…Numerous improvements on von Neumann's original idea have been studied over the decades ( [1,7,9,12], to mention but a few). Our method handles, however, an extra restriction: the players are not able to know the actual result of each coin toss, instead they are only aware of whether each toss produced the same result as the previous one along a sequence of independent tosses.…”

Section: Introductionmentioning

confidence: 99%

Blind-friendly von Neumann’s Heads or Tails

Sá¹,

Figueiredo

2014

The American Mathematical Monthly

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The toss of a coin is usually regarded as the epitome of randomness, and has been used for ages as a means to resolve disputes in a simple, fair way. Perhaps as ancient as consulting objects such as coins and dice is the art of maliciously biasing them in order to unbalance their outcomes. However, it is possible to employ a biased device to produce equiprobable results in a number of ways, the most famous of which is the method suggested by von Neumann back in 1951. This paper addresses how to extract uniformly distributed bits of information from a nonuniform source. We study some probabilities related to biased dice and coins, culminating in an interesting variation of von Neumann's mechanism that can be employed in a more restricted setting where the actual results of the coin tosses are not known to the contestants.

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Tree Algorithms for Unbiased Coin Tossing with a Biased Coin

Cited by 46 publications

References 5 publications

Generalized Elias schemes for efficient harvesting of truly random bits

Generalized Elias schemes for efficient harvesting of truly random bits

Unbiased Random Sequences from Quasigroup String Transformations

Blind-friendly von Neumann’s Heads or Tails

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