80 1. ALGEBRAIC THEMES All sorts of encryption/decryption rules have been used, from simple letter by letter substitutions to rules that transform the message as a whole. But one feature traditional methods of cryptography have in common is that if one knows the encryption rule or key , then one can also derive the decryption key. Therefore, the sender and recipient must somehow manage to transmit the key secretly in order to keep their communications secure. A remarkable public key cryptography system, based on properties of congruences of integers, circumvents the problem of transmitting the key. The trick is that it is impractical to derive the decryption key from the encryption key, so that the recipient can simply publish the encryption key; anybody can encrypt messages with this key, but only the recipient has the key to decrypt them. The RSA public key cryptography method was discovered in 1977 by R. Rivest, A. Shamir, and L. Adleman 10 and is very widely used. It’s a good bet that you are using this method when you use an automatic
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