HASH

HASH is a hashing function designed for compatibility with Anduin containers. Inputs are hashed to an eight-digit base-36 string.

Collision

Hashes, by nature of mapping an infinite input domain to a restricted output, have a probability of collision. In order to calculate the probability of collision, we can use an approximation of the birthday problem, derived from its Taylor series expansion.

$$p(k)\approx 1-e^{-\frac{k^2}{2n}}$$

Where $n$ is the cardinality of the hash space, or $36^8\approx 2.8\text{ trillion}$.

$k$ (Number of items)	Probability of collision
1000	0.0000001772351919
10000	0.0000177233637
100000	0.001770782387
1000000	0.1624172444
2000000	0.507834792
5000000	0.9880959927

This approximation only holds as long as the hash function follows a continuous uniform distribution. Below is an empirical result from hashing two datasets, showing that it does.