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The modern era in cryptography started some time in the late 70's or early 80's*. Previous eras include classical cryptography, which emphasized pencil and paper cryptosystems (such as the Playfair Cipher, Hill Cipher and Ceasar Cipher) and machine cryptography, which peaked during World War II with rotor-based machines such as Enigma.

Modern cyptography differs in two major respects from previous eras.

Not surprisingly, the first difference is that nearly all algorithms in this era are developed with eventual implementation on a computer (or in hardware) in mind.

The second difference is more fundamental: much of modern cryptography concerns itself with provably secure cryptographic constructions. Rather than the ad hoc techniques of the past, these systems can be proven unconditionally secure. Alas, the price of such security is that most of these systems are not efficient. This has lead cryptographers to base their cryptosystems on assumptions from the fields of number theory, computational complexity, and algebra. For example, these systems prove their security relative to the assumption that it is hard to factor integers (RSA) or find discrete logarithms in a cyclic group (Diffie-Hellman).

Almost none of these crytposystems will be truly known to be secure until the P versus NP question is settled. Until then, you can rest uneasily knowing that almost none of the cryptography in use by banks, governments, and web browsers has ever been proven to be secure!

In closing, I'd like to mention one other major difference between this era and those previous: popularity. When the government of the United States first called for proposals for a standard encryption algorithm to be used with unclassified data in the early 1970's, there was not one single response. IBM responded, albeit several years later to the second call, with what later became DES. In 1997, NIST made the annoucement it was soliciting suggestions on a new encryption standard, the AES. Fifteen serious submissions were fielded! (They eventually settled on one called Rijndael). The interest in cryptology has grown each year since, fueled by increased concerns about security, electronic privacy, and (I suspect) Neal Stephenson's excellent book, the Cryptonomicon.

*Arguably, modern cryptography started with Whitfield Diffie and Martin Hellman's groundbreaking 1976 paper, New Directions in Cryptography.

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