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Cryptology

Cryptology. Cryptography : A Historical Introduction. Prof. David Singer Dept. of Mathematics Case Western Reserve University. Vocabulary. Cryptography – secret messages Kryptos - Greek word for “hidden” or “covered” - graphy – Writing Cipher – an “encrypted” message

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Cryptology

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  1. Cryptology Cryptography: A Historical Introduction Prof. David Singer Dept. of Mathematics Case Western Reserve University

  2. Vocabulary • Cryptography – secret messages • Kryptos - Greek word for “hidden” or “covered” • -graphy– Writing • Cipher – an “encrypted” message • Code – words, numbers, or symbols replacing words, letters, or phrases

  3. Codes need not be secret

  4. Codes need not be secret

  5. Codes need not be secret

  6. Three types of Ciphers • 1. Concealment • Hide the message • 2. Substitution • Change the symbols in the message • 3. Transposition Scramble the order of the symbols

  7. Concealment • Example: Wax Tablets • Used by Demaratus, king of Sparta

  8. Substitution • Example: Caesar Cipher • Shift letters forward three steps

  9. Caesar cipher • Ciphertext • YHQL YLGL YLFL • Plaintext • venividivici

  10. ATBASHac,t A cipher used in the book of Jeremiah f h , j z u v s d c t k n b x g p m e r a , SHESHACH fa a becomes BABEL kc c

  11. Transposition • Example: Scytale (wooden staff) 7th century B.C.E.(?)

  12. Example: the Rail Fence TIUARSHENHJGSPEDOTEAE0SAOCEIHFHFUTE T***I***U ***A*** R***S***H***E***N *H*J*G*S*P*E*D*O*T*E*A*E*0*S*A*O*C **E***I***H***F****H***F***U***T***E

  13. Cryptanalysis This refers to the methods of breaking ciphers and cipher systems. The goal is to recover the plaintext message and/or the secret key.

  14. Basic Attack Methods • Brute Force • Try all possible keys until one unlocks the cipher. • This method works very well on the Caesar cipher! • The cryptographer tries to defeat this attack by having lots of keys.

  15. General Substitution Cipher • Replace letters with other letters by some table or other rule.

  16. General Substitution Cipher • There are (theoretically) 26!-1= 1x2x3x4x5x…x22x23x24x25x26-1 =403291461126605635583999999 possible substitution ciphers. Of course, if the rule is easy to guess, brute force still works:

  17. “The Secret Code”1942, Columbia Pictures

  18. Basic Attack Methods • Brute Force • Statistical analysis • Idea dates back at least to the 9th century Muslim scientist Abu Yusuf Ya’qub al-Kindi • Nice illustration in Edgar Allan Poe, The Gold Bug (1843)

  19. The Gold Bug Cipher • Attack is based on comparison of frequencies of ciphertext letters and frequencies of (English) plaintext letters. 53‡‡†305))6*;4826)4‡.)4‡);806*;48†8 ¶60))85;1‡(;:‡*8†83(88)5*†;46(;88*96 *?;8)*‡(;485);5*†2:*‡(;4956*2(5*—4)8 ¶8*;4069285);)6†8)4‡‡;1(‡9;48081;8:8‡ 1;48†85;4)485†528806*81(‡9;48;(88;4 (‡?34;48)4‡;161;:188;‡?;

  20. The Gold Bug Cipher Table of frequencies for cipher

  21. The Gold Bug Cipher Table of frequencies for English text

  22. The Gold Bug Cipher Poe writes:

  23. More subtleties “digrams” (and “trigrams”…)

  24. What method was used? • Are we looking at a substitution cipher or a transposition cipher? • What language is it written in? • Frequency analysis can answer these questions too.

  25. Cipher Bureau (1938)

  26. Thwarting the statistician • Leon Battista Alberti, De Cifris, ~1466

  27. Thwarting the statistician • Blaise de Vigenère , Traicté des Chiffres ou Secrètes Manières d'Escrire, 1586

  28. The Vigenère Tableau • Letters encrypted with different alphabets using keyword (fringe)

  29. Vigenère Example • I am a professor in the • B AK E RBAKERBAK ER BAK • K BX F HTPQJKUPC NF VIP • mathematics department • ERBAKERBAKE RBAKERBAKE • RSVIPRSVJNX VGQLWLOFYY

  30. Vigenère Example • KBXFHT PQJKUP CNFVIP RSVIPR SVJNX VGQLWL OFYY • We have destroyed the statistics! (e.g., the bold letters are a’s) • Vigenère’s system was le chiffreindéchiffrable(the unbreakable cipher) for 300 years.

  31. The unbreakable is broken Charles Babbage -- 1854

  32. The unbreakable is broken Babbage did not publish his solution (possibly by order of British Intelligence during the Crimean War.) But Friedrich Kasiski published his solution in 1863.

  33. The unbreakable is broken Key idea: look again at my cipher: KBXFHTPQJKUPCNFVIPRSVIPRSVJNX VGQLWLOFYY Notice the repetition of the string VIPRS. Why is it there?

  34. Another Look • I am a professor in the • B AK E RBAKERBAK ER BAK • K BX F HTPQJKUPC NF VIP • mathematics department • ERBAKERBAKE RBAKERBAKE • RSVIPRSVJNX VGQLWLOFYY

  35. Kasiski’s Attack • 1. Look for repeated strings • 2. Count the distance between beginnings of repeated strings. • 3. Guess length of keyword • 4. Divide and conquer!

  36. William Friedman • Developed a more sophisticated attack on Vigènere and other “polyalphabetic” ciphers. (1920) • Established a relationship between cryptanalysis and mathematics.

  37. What can we learn from history? • 1. Crypto is a constant struggle between cryptographer and cryptanalyst. • 2. Cryptosystems are absolutely unbreakable – until they are broken. • 3. Ignore Rule 2 at your peril.

  38. What can we learn from history? • Kerckhoffs’ Principle: The security of a cryptosystem must not depend on keeping secret the crypto-algorithm (=method.) The security depends only on keeping secret the key. • No cryptosystem can be assumed unbreakable forever.

  39. End of Historical Introduction

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