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Cryptology Terminology plaintext - text that is not encrypted. ciphertext - the output of the encryption process. key - the information required to convert between plaintext and ciphertext. cryptanalysis - the art of breaking ciphers. cryptography - the art of designing ciphers. cryptology - the field of cryptanalysis and cryptography.

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Substitution Ciphers Caesar cipher Each letter is alphabetically shifted by k letters Very easy to break (just 26 different codes) Monoalphabetic substitution Each plaintext letter is assigned a different ciphertext letter. 26! different codes are possible. Still easy to break

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Defeating Monoalphabetic Ciphers Distribution of letters in English text ETAONRISHLGCMUFYPWBVKXJQZ Build a histogram Distribution of digrams two letter combinations th, in, er, re, an Distribution of trigrams the, ing, and, ion Detecting probable words or phrases

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Transposition Ciphers Reorder the letters rather than change them Use a key to determine number and order of columns

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Defeating Transposition Ciphers These ciphers are also easily defeated See if the letters have the expected distribution Guess words that are probably in the message and see what pairs of letters appear in the message. Use this information to guess the number of columns For a cipher with key length k, try all pairs of columns and see if the digram distribution matches the expected distribution.

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One-time Pads An unbreakable cipher Each side has the same long text or random bit string. This is the pad. The “pad” is combined with the ciphertext to decode the message. Example 1 - The “Beale Treasure” - Bedford County Numbers identify the first letter of words in the declaration of independence. When in the course of human events it becomes necessary 10, 2, 4, 7 is “nice”

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Another way to use a one-time pad Example 2: Add the ith letter of this slide to the ith letter of your message, then divide by the size of your alphabet and record the remainder. my message one-time pad (‘m’+’o’) mod 127, (‘y’+’n’) mod 127, (‘ ‘+ ‘e’) mod 127

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One-time Pad with Bit Strings (the xor trick) Temp = a; a = b; b = Temp; a = b xor a // encrypt a using b (and b using a) b = a xor b // decrypt a using b a = a xor b // decrypt b using a

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One-time Pad with Bit Strings Exclusive Or the ASCII plaintext with corresponding bits in the random bit string 01001010 (plaintext) 10000110 (ciphertext) 11001100 (random) 10000110 (ciphertext) 01001010 (plaintext)

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Problems with One-Time Pads The pad must be long It will eventually run out The pad must be random Otherwise it might be guessed The pad must be distributed It can be captured It is sensitive to lost characters Losing a single character makes the ciphertext unreadable

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Secret-Key Algorithms Transpositions and substitutions Product ciphers

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DES Encryption Standard Based on IBM “Lucifer” encryption technique Plaintext is encrypted in blocks of 64 bits 56-bit key, 19 distinct stages Decryption/encryption use the same key

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Problems with DES The original “Lucifer” code used 128 bit keys, rather than 56-bit keys. Exhaustive search of 2 56 (approx 7x10 17 ) keys can be done with powerful computer systems Chinese Lottery idea (Quisquater and Girault) 1.2 billion chips in TV’s and Radios Chinese government broadcasts the ciphertext and each appliance checks its part of the search space. Solution found in about 60 seconds Appliance with the matching key announces that the owner has won the Chinese lottery.

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Public Key Algorithms 1976, Diffie and Hellman Make the encryption key and algorithm public Anyone can encrypt messages, but only you can decrypt them Trapdoor (one-way) functions Requirements D(E(P)) = P It is exceedingly difficult to deduce D from E E cannot be broken by a chosen plaintext attack

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RSA Algorithm Rivest, Shamir, Adleman (RSA) Based on the difficulty of factoring large numbers (200-digits and larger) Factoring a 200-digit number requires 4 billion years of computer time at 1 usec/instruction.

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Problems with Public Key Encryption It is slow The keys are large Public keys are often used to exchange keys for other encoding schemes

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CS 6262 Spring 02 - Lecture #7 (Tuesday, 1/29/2002) Introduction to Cryptography.

CS 6262 Spring 02 - Lecture #7 (Tuesday, 1/29/2002) Introduction to Cryptography.

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