Devise a scheme of mapping arbitrary strings to (usually) distinct irrational numbers. This can serve as a hashing function. Possible implementation in a previous idea.
The CPU and memory difficulty of computing the forward direction of the hash can be arbitrarily increased by specifying that the hash is 256 bits of the binary expansion starting at, say, bit 1 billion. This is useful for applications like password hashing and the Bitcoin block chain.
Be careful about schemes for which precomputation can greatly accelerate things, BBP type formulae, and continued fractions being able to reverse a hash.
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