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Cryptology

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.

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Cryptology

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  1. 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.

  2. 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

  3. 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

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

  5. 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.

  6. 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”

  7. 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

  8. 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

  9. 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) 11001100 (random) 10000110 (ciphertext) 01001010 (plaintext)

  10. 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

  11. 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

  12. Problems with DES • The original “Lucifer” code used 128 bit keys, rather than 56-bit keys. • Exhaustive search of 256 (approx 7x1017) 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.

  13. 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

  14. 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.

  15. 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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