Lecture22

Lecture22 - Algorithms in Systems Engineering IE170 Lecture...

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Algorithms in Systems Engineering IE170 Lecture 22 Dr. Ted Ralphs
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IE170 Lecture 22 1 References for Today’s Lecture Required reading CLRS Chapter 31 References Koblitz, A Course in Number Theory and Cryptography , Second Edition (1999).
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IE170 Lecture 22 2 Cryptography Cryptography is the study of methods for sending messages in an encoded form that can (hopefully) only be interpreted by the intended recipient. The original message is said to be in plaintext and the encoded message is said to be in ciphertext . All commonly used cryptographic methods are based on specifying a one-to-one function that transforms plaintext into ciphertext. To get back the original message, we simply apply the inverse transformation. To put it more precisely, let P be the set of all plaintext messages and C be the set of all encrypted messages. A crytosystem is a one-to-one mapping f : P → C , whose inverse maps C back to P . Note that in many cryptosystems, we have P = C .
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IE170 Lecture 22 3 Message Units Let’s assume that our plaintext message is composed from an alphabet of N characters. Most cryptosystems work by dividing the original message into message units , which are then individually enciphered. A message unit is typically defined to be a block of k letters for some positive k . For ease of defining the transformation, we can convert each message unit to a unique integer by interpreting it as a k -digit number base N . We can then make the simplifying assumption that the message units consist simply of integers from 0 to N k - 1 .
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IE170 Lecture 22 4 A Simple Cryptosystem Let’s first consider message units of length 1. A cryptosystem then consists essentially of specifying a permutation of the letters of the alphabet (we may or may not include the spaces also). To keep things simple, we want to be able to easily encrypt and decrypt
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Lecture22 - Algorithms in Systems Engineering IE170 Lecture...

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