Given a message m, the hash h(m) must satisfy
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It can be calculated relatively quickly
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Given h(m), it cannot be be inverted (to find m) by any practical method
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Even though many m's will be transformed to the same h(m), this will in practice never happen and it is impossible in practice to find two m's that give the same h(m)
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As hash function is known, the security of a hash comes from the unknown message.
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Messages can be made unknown by concatenating plaintext with a secret key before applying h(m)
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These are called one-way transformations as hashes cannot be inverted
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Practical methods involve a strange combination of anding and permutations which ensures the cryptography safety of method
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Message Digests (such as MD2 MD4 MD5 -- MD is Message Digest with 128 bit output -- or SHS -- Secure Hash Standard with 160 bit output output) are used in Public key Systems to reduce computational complexity of encryption (see previous foil)
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