8.5. Summary
For our purposes, three aspects of cryptography require study. Classical cryptography uses a single key shared by all involved. Public key cryptography uses two keys, one shared and the other private. Both types of cryptosystems can provide secrecy and origin authentication (although classical cryptography requires a trusted third party to provide both). Cryptographic hash functions may or may not use a secret key and provide data authentication.
All cryptosystems are based on substitution (of some quantity for another) and permutation (scrambling of some quantity). Cryptanalysis, the breaking of ciphers, uses statistical approaches (such as the Kasiski method and differential cryptanalysis) and mathematical approaches (such as attacks on the RSA method). As techniques of cryptanalysis improve, our understanding of encipherment methods also improves and ciphers become harder to break. The same holds for cryptographic checksum functions. However, as computing power increases, key length must also increase. A 56-bit key was deemed secure by many in 1976; it is clearly not secure now.
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