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# 262 Class Note for CS 35500 at Purdue

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This 18 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 18 views.

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Date Created: 02/06/15

Introduction to Cryptography CS 355 Lecture 4 Ir 7 I Z The Vigen re Cipher CS 355 Fall 2005 Lecture 4 Lecture Outline Vigenere cipher Attacks on Vigenere Kasisky Test Index of Coincidence Frequency analysis CS 355 Fall 2005 Lecture 4 2 Towards the Polyalphabctic Substitution Ciphers Main weaknesses of monoalphabetic substitution ciphers each letter in the ciphertext corresponds to only one letter in the plaintext letter Idea for a stronger cipher 1460 s by Alberti use more than one cipher alphabet and switch between them when encrypting different letters Developed into a practical cipher by Vigenere published in 1586 CS 355 Fall 2005 Lecture 4 3 The Vigen re Cipher Definition Given m a positive integer P C 226 and K k1 k2 km a key we define Encryption ekp1 p2 pm p1k1 p2k2pmkm mod 26 Decryption dkc1 c2 cm c1k1 c2k2 cm km mod 26 Example Plaintext CRYPTOGRAPHY Key LUCKLUCKLUCK Ciphertext NLAZEI IBLJ J CS 355 Fall 2005 Lecture 4 Security of Vigenere Cipher Vigenere masks the frequency with which a character appears in a language one letter in the ciphertext corresponds to multiple letters in the plaintext Makes the use of frequency analysis more difficult Any message encrypted CS 355 by a Vigenere cipher is a collection of as many shift ciphe are letters in the key Fall 2005 Lecture 4 Vigenere Cipher Cryptanalysis Find the length of the key Divide the message into that many shift cipher encryptions Use frequency analysis to solve the resulting shift ciphers how CS 355 Fall 2005 Lecture 4 6 How to Find the Key Length For Vigenere as the length of the keyword increases the letter frequency shows less Englishlike characteristics and becomes more random Two methods to find the key 3 length C Kasisky test Index of coincidence Friedman CS 355 Fall 2005 Lecture 4 Kasisky Test Note two identical segments of plaintext will be encrypted to the same ciphertext if the they occur in the text at the distance A A20 mod m m is the key length Algorithm Search for pairs of identical segments of length at least 3 Record distances between the two segments A1 A2 m divides gcdA1 A2 CS 355 Fall 2005 Lecture 4 Example of the Kasisky Test Key KINGKINGKINGKINGKINGKING PT thesunandthemaninthemoon CT DPRYEVNTNBUKWIAOXBUKWWBT CS 355 Fall 2005 Lecture 4 9 Index of Coincidence Friedman Informally Measures the probability that two random elements of the nletters string x are iden cal Definition Suppose x x1x2xn is a string of n alphabetic characters Then lcx the index of coincidence is 10x Px 39 CS 355 Fall 2005 Lecture 4 10 Index of Coincidence cont Reminder binomial coefficient n quotl k kn k Consider the plaintext x and f0 f1 f25 are the frequencies with which A B Z appear in x and p0 p1 p25 are the probabilities with which A B Z appear in x We want to compute lcx CS 355 Fall 2005 Lecture 4 11 Index of Coincidence cont We can choose two elements out of the string of size n in ways For each i there are ways of choosing the elements to be i 2 S fi S S 2 22 21203 1 2f S 2 Cx n Ono 4 z 0 gn K2 CS 355 Fall 2005 Lecture 4 12 Index of Coincidence of English For English 8 25 and Id can be estimated pi 010 023 001 020 001 CS 355 Fall 2005 Lecture 4 Finding the Key Length y y1y2yn m is the key length lt y1 ymH gt yl lt7 ym2 yn m2 gt Y2 Q y2m yn gt ym CS 355 Fall 2005 Lecture 4 14 Guessing the Key Length If m is the key length then the text looks like English text i225 10yl z pr 0065 v1 sis m i0 If m is not the key length the text looks like random text and 10 z lily 26 xizziz 0038 120 26 26 26 CS 355 Fall 2005 Lecture 4 15 Summary Vigenere cipher is vulnerable once the key length is found a cryptanalyst can apply frequency analysis CS 355 Fall 2005 Lecture 4 16 Recommended Reading for This Lecture Trappe amp Washington Section 23 The Code Book Chapter 2 CS 355 Fall 2005 Lecture 4 17 Coming Attractions Enigma Machine Recommended Reading Trappe amp Washington 212 The Code Book Chapters 3 amp 4 CS 355 Fall 2005 Lecture 4 18

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