Provable security and other problems in modern cryptography

A concept called provable security brings the rigor of mathematics to the art of cryptography.

Cryptography was originally a mystical art form with the goal of concealing information from unauthorized persons. For example, a simple method for encrypting messages was developed by Gaius Julius Caesar around the year 100 BC. The basic idea of the method was to shift each letter of a message by a fixed amount in the alphabet. This position then served as a secret key. For example, if Caesar were to encrypt Veni, vidi, vici with a secret key of 3, it would result in a ciphertext of Yhql, ylgl, ylfl.

However, the method was soon seen through, then improved, cracked again, and so on. In this way, over time, a kind of cat-and-mouse game developed between the designers of encryption methods and the attackers who cracked the methods in order to access the secret information. This dragged on until the discovery of provable security in the 1980s.

Provable security is a field that seeks to assess the security of systems through mathematical proofs . People often think of cryptography as a sea of digits and huge numbers, which it often is; however, for a mathematician, the goal is to sweep away the details and define the system symbolically in a way that lends itself to logical proof. The development of provable security has brought rigor to the ancient practice of cryptography, which was once considered more art than science.

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