Non-uniform birthday problem revisited: refined analysis and applications to discrete logarithms

2021 ◽  
pp. 106225
Author(s):  
Haoxuan Wu ◽  
Jincheng Zhuang ◽  
Qianheng Duan ◽  
Yuqing Zhu
Keyword(s):  
Discrete Logarithms ◽  
Birthday Problem

scholarly journals A non-uniform birthday problem with applications to discrete logarithms

2012 ◽  
Vol 160 (10-11) ◽  
pp. 1547-1560 ◽  
Author(s):  
Steven D. Galbraith ◽  
Mark Holmes
Keyword(s):  
Discrete Logarithms ◽  
Birthday Problem

scholarly journals On the birthday problem: some generalizations and applications

2003 ◽  
Vol 2003 (60) ◽  
pp. 3827-3840 ◽  
Author(s):  
P. N. Rathie ◽  
P. Zörnig
Keyword(s):  
Probability Distribution ◽  
Random Graph ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Exact Probability ◽  
Confluent Hypergeometric Functions ◽  
Birthday Problem ◽  
Exact Probability Distribution

We study the birthday problem and some possible extensions. We discuss the unimodality of the corresponding exact probability distribution and express the moments and generating functions by means of confluent hypergeometric functionsU(−;−;−)which are computable using the software Mathematica. The distribution is generalized in two possible directions, one of them consists in considering a random graph with a single attracting center. Possible applications are also indicated.

The Birthday Problem Revisited

1976 ◽  
Vol 7 (4) ◽  
pp. 39 ◽  
Author(s):  
Joe Dan Austin
Keyword(s):  
Birthday Problem

Poisson approximation for a sum of dependent indicators: an alternative approach

2002 ◽  
Vol 34 (03) ◽  
pp. 609-625 ◽  
Author(s):  
N. Papadatos ◽  
V. Papathanasiou
Keyword(s):  
Total Variation ◽  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Poisson Approximation ◽  
Total Variation Distance ◽  
Poisson Random Variable ◽  
Birthday Problem ◽  
Alternative Approach ◽  
Variation Distance

The random variablesX1,X2, …,Xnare said to be totally negatively dependent (TND) if and only if the random variablesXiand ∑j≠iXjare negatively quadrant dependent for alli. Our main result provides, for TND 0-1 indicatorsX1,x2, …,Xnwith P[Xi= 1] =pi= 1 - P[Xi= 0], an upper bound for the total variation distance between ∑ni=1Xiand a Poisson random variable with mean λ ≥ ∑ni=1pi. An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.

Seeing Double Voting: An Extension of the Birthday Problem

2008 ◽  
Vol 7 (2) ◽  
pp. 111-122 ◽  
Author(s):  
Michael P. McDonald ◽  
Justin Levitt
Keyword(s):  
Birthday Problem
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