Hashing: Why & How?

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Why do we wish to reduce a long list to a short one? How to do it, so that the short list will identify the long list. How to do it so that it is impossible to identify the long list from the short one, and the implications of the fact that many long lists share the very same short list. Hashing configurations: straight encryption, MD4, MD5, SHA-1, SHA-2.

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