Checksums are well known and a simple version can be gotten by dividing message into 32 bit groups and anding these groups together.
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This is designed for fault tolerance and ensures that data was not garbled in transmission
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Such checksums or hashes (designed properly) cannot be inverted and represent a unique fingerprint of original message.
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A secret checksum combines this process with a secret key and produces a MIC (message integrity code) which can be decoded and checked
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This can be used with either a ciphertext or plaintext message and guarantees that information is stored or transmitted faithfully
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Note encrypting a message does not guarantee that it is not changed!
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MIC with plaintext is used by bank electronic fund transfer
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