birthday collision approximation
estimates the probability of at least one collision when q random samples fall into N values.
symbols, variables and units
q: number of samples; N: equal probability output space size; probability is dimensionless.
applicable conditions and boundaries
Independent uniform sampling, approximation for large N; hash bias changes probabilities.
formula source code
The following is a copyable LaTeX expression.
P_{\mathrm{coll}}\approx1-e^{-q(q-1)/(2N)}Reference and Extended Learning
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birthday attackHash