Modern schemes for exchanging secret messages, such as the one-time pad and public key procedures that we saw in Chapter 4, rely on the sender and receiver to possess certain “keys.” Such keys are simply large numbers that have been carefully constructed so as to have special mathematical properties. If the appropriate keys are known, then any encrypted messages are easily unscrambled. But without the keys it is computationally intractable, at least with any classical computer, to crack a coded message. Consequently, the integrity of these cryptosystems relies on the keys being kept secret.
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