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This variation of the birthday problem is interesting because there is not a unique solution for the total number of people m + n. For example, the usual 50% probability value is realized for both a 32-member group of 16 men and 16 women and a 49-member group of 43 women and 6 men.
The problem in Equihash is to find distinct, -bit values ,,..., to satisfy () ()... = such that (...) has leading zeros, where is a chosen hash function. [1] In addition, there are "algorithm binding conditions" which are intended to reduce the risk of other algorithms developed to solve the underlying birthday problem being applicable.
The birthday attack can be modeled as a variation of the balls and bins problem. In this problem: Balls represent inputs to the hash function. Bins represent possible outputs of the hash function (hash values). A collision occurs when two or more balls land in the same bin (i.e., two inputs produce the same hash output).
To obtain the optimal solution with minimum computation and time, the problem is solved iteratively where in each iteration the solution moves closer to the optimum solution. Such methods are known as ‘numerical optimization’, ‘simulation-based optimization’ [ 1 ] or 'simulation-based multi-objective optimization' used when more than ...
OptimJ is a mathematical Java-based modeling language for describing and solving high-complexity problems for large-scale optimization. Perl Data Language, [22] [23] also known as PDL, an array extension to Perl ver.5, used for data manipulation, statistics, numerical simulation and visualization.
The birthday problem asks, for a set of n randomly chosen people, what is the probability that some pair of them will have the same birthday? The problem itself is mainly concerned with counterintuitive probabilities, but we can also tell by the pigeonhole principle that among 367 people, there is at least one pair of people who share the same ...
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A related problem, somewhat similar to the Birthday paradox, is that of determining the size of the input set so that we have a probability of one half that there is a solution, under the assumption that each element in the set is randomly selected with uniform distribution between 1 and some given value. The solution to this problem can be ...