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Complexity Theory - Cryptography by Chuck Introduction One important yet practical application of complexity theory is cryptography It has become one of the main tools for privacy trust electronic payments and other forms of security It is no longer just a military tool and the advantages it provides should be used to the fullest extent This paper will discuss basic terminology and popular methods of cryptography Terminology Cryptography is the science of scrambling text so that no one can read it except for the intended recipient The art of breaking ciphers without the proper key is called cryptanalysis Cryptography deals with the secure message digital signatures authentication and other similar applications Cryptology is the branch of mathematics that studies the foundation of cryptographic methods The process of transforming plaintext into a form that is meaningless to anyone that might intercept it is called encryption The process of decoding the message is called decryption This can be done by using an encryption algorithm a decryption algorithm and a secret or private key The sender uses the encryption algorithm to encode the message and the receiver uses the decryption algorithm and the key to decode the message A third party intercepting the encoded message will have worthless data unless they can figure out the decryption algorithm and obtain a key To best ensure that the key is kept safely out of the hands of the third party it is never to be sent with the encoded message History of Cryptography The study of cryptography dates back thousands of years to the hieroglyphs of early Egyptian civilization Cryptography has been used by such figures as Julius Caesar Charlemagne Louis XIV and Mary Queen of Scots More recently Alan Turing the inventor of the Turing machine led a group of British mathematicians who broke the German code used in World War II for sending instructions to U-boats patrolling the
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