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Classical Cryptography

Classical Cryptography. What is cryptography?. kryptos – “hidden” grafo – “write” Keeping messages secret Usually by making the message unintelligible to anyone that intercepts it. The Problem. Private Message. Bob. Alice. Eavesdropping. Eve. The Solution. Private Message.

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Classical Cryptography

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  1. Classical Cryptography

  2. What is cryptography? • kryptos – “hidden” • grafo – “write” • Keeping messages secret • Usually by making the message unintelligible to anyone that intercepts it

  3. The Problem Private Message Bob Alice Eavesdropping Eve

  4. The Solution Private Message Private Message Encryption Decryption Scrambled Message Bob Alice Eavesdropping Eve

  5. What do we need? • Bob and Alice want to be able to encrypt/decrypt easily • But no one else should be able to decrypt • How do we do this? • Keys!

  6. Using Keys Nonsense Encryption Decryption Ciphertext Plaintext Plaintext

  7. What is a cipher? • A cipher is an algorithm for encryption/decryption • Kerckhoff’s Principle: All details of the cipher should be public • Eve still shouldn’t be able to decrypt messages unless she has the secret key

  8. The Shift Cipher • We “shift” each letter over by a certain amount Plaintext five red balloons f + 3 = I i + 3 = L v + 3 = Y … Key = 3 Encryption Ciphertext ILYH UHG EDOORRQV

  9. The Shift Cipher cont. • To decrypt, we just subtract the key Ciphertext ILYH UHG EDOORRQV I - 3 = f L - 3 = i Y - 3 = v … Key = 3 Decryption five red balloons Plaintext

  10. What’s wrong with the shift cipher? • Not enough keys! • If we shift a letter 26 times, we get the same letter back • A shift of 27 is the same as a shift of 1, etc. • So we only have 25 keys (1 to 25) • Eve just tries every key until she finds the right one

  11. The Substitution Cipher Plaintext Ciphertext • Rather than having a fixed shift, change every plaintext letter to an arbitrary ciphertext letter

  12. The Substitution Cipher cont. Plaintext five red balloons Key = f = A i = L v = R … Encryption ALRD HDS XGOOYYBW Ciphertext

  13. The Substitution Cipher cont. • To decrypt we just look up the ciphertext letter in the table and then write down the matching plaintext letter • How many keys do we have now? • A key is just a permutation of the letters of the alphabet • There are 26! permutations • 403291461126605635584000000

  14. Breaking the Substitution Cipher • If we could do 1 000 000 calculations per second, it would take over 12.7x1012 years to try all possible keys • The universe is about 13.7x109 years old • Trying all possible keys is probably not going to work

  15. Frequency Analysis • In English (or any language) certain letters are used more often than others • If we look at a ciphertext, certain ciphertext letters are going to appear more often than others • It would be a good guess that the letters that occur most often in the ciphertext are actually the most common English letters

  16. Letter Frequency • This is the letter frequency for English • The most common letter is ‘e’ by a large margin, followed by ‘t’, ‘a’, and ‘o’ • ‘J’, ‘q’, ‘x’, and ‘z’ hardly occur at all

  17. Frequency Analysis in Practice • Suppose this is our ciphertext • dq lqwurgxfwlrq wr frpsxwlqj surylglqj d eurdg vxuyhb ri wkh glvflsolqh dqg dq lqwurgxfwlrq wr surjudpplqj. vxuyhb wrslfv zloo eh fkrvhq iurp: ruljlqv ri frpsxwhuv, gdwd uhsuhvhqwdwlrq dqg vwrudjh, errohdq dojheud, gljlwdo orjlf jdwhv, frpsxwhu dufklwhfwxuh, dvvhpeohuv dqg frpslohuv, rshudwlqj vbvwhpv, qhwzrunv dqg wkh lqwhuqhw, wkhrulhv ri frpsxwdwlrq, dqg duwlilfldo lqwhooljhqfh.

  18. Ciphertext distribution English distribution In our ciphertext we have one letter that occurs more often than any other (h), and 6 that occur a good deal more than any others (d, l, q, r, u, and w) There is a good chance that h corresponds to e, and d, l, q, r, u, and w correspond to the 6 next most common English letters

  19. Frequency Analysis cont. • If we replace ‘e’ with ‘h’ and the 6 next most common letters with their matches, the ciphertext becomes • an intro???tion to ?o?p?tin? pro?i?in? a ?roa? ??r?e? o? t?e ?i??ip?ine an? an intro???tion to pro?ra??in?. ??r?e? topi?? ?i?? ?e ??o?en ?ro?: ori?in? o? ?o?p?ter?, ?ata repre?entation an? ?tora?e, ?oo?ean a??e?ra, ?i?ita? ?o?i? ?ate?, ?o?p?ter ar??ite?t?re, a??e???er? an? ?o?pi?er?, operatin? ???te??, net?or?? an? t?e internet, t?eorie? o? ?o?p?tation, an? arti?i?ia? inte??i?en?e.

  20. Modern Cryptography • Frequency analysis was the best cryptanalysis until the invention of computers • Next time • Modern ciphers • Cryptography wins WWII • Fighting the man

  21. The End

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