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Computer Science 101 Cryptography Part I

Computer Science 101 Cryptography Part I. Notes based on. S. Singh, The Code Book: The Evolution of Secrecy from Mary, Queen of Scots to Quantum Cryptography . New York: Doubleday (1999) ‏. Terminology. Steganography – Hiding the message Under wax of wooden tablets Shaved heads

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Computer Science 101 Cryptography Part I

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  1. Computer Science 101CryptographyPart I

  2. Notes based on • S. Singh, The Code Book: The Evolution of Secrecy from Mary, Queen of Scots to Quantum Cryptography. New York: Doubleday (1999)‏

  3. Terminology • Steganography – Hiding the message • Under wax of wooden tablets • Shaved heads • Within hardboiled eggs – special ink • Invisible ink • Embedded in pictures or tunes

  4. Crypto: The Problem BOB ALICE EVE How do I love thee? Let me count the ways. I love thee to the depth and breadth and height My soul can reach, when feeling out of sight For the ends of Being and ideal Grace. I love thee to the level of every day's Most quiet need, by sun and candlelight. abca adf adCIFASFDSF adfafdasf daf pua,kjpui 8978*&( aadb adae-898 adsf9898b @!!l;kjadsfdsa *()_*()kasjdf*(abac 3(*_* ,DAD0-89adfafj &(D()8asdkljfasd;f(_cas adfdasfA(()*Aafdafdfas*( ADFSF9-898DFDFS ASFDFSDF(*DFSCDFS*(_*( DFS*(adfdsaf(*_)dafdas* ASFD9898-08DFSFDSad*(A(* abca adf adCIFASFDSF adfafdasf daf pua,kjpui 8978*&( aadb adae-898 adsf9898b @!!l;kjadsfdsa *()_*()kasjdf*(abac 3(*_* ,DAD0-89adfafj &(D()8asdkljfasd;f(_cas adfdasfA(()*Aafdafdfas*( ADFSF9-898DFDFS ASFDFSDF(*DFSCDFS*(_*( DFS*(adfdsaf(*_)dafdas* ASFD9898-08DFSFDSad*(A(* How do I love thee? Let me count the ways. I love thee to the depth and breadth and height My soul can reach, when feeling out of sight For the ends of Being and ideal Grace. I love thee to the level of every day's Most quiet need, by sun and candlelight.

  5. Terminology • Cryptography – Hiding the meaning • Transposition – letters rearranged • Rail fence • Wrap around wooden staff • Substitution – substitute letter for letter, etc. • Caesar cypher – shift • Key in front (remove repeats – example next)

  6. Example – Key at front • Suppose we used GEORGE BOOLE as key. Then our encoding would beABCDEFGHIJKLMNOPQRSTUVWXYZGEORBLMNPQSTUVWXYZACDFHIJK • Encoding "TOM WHALEY" would give CWUHNGTBJ • This worked for a few centuries (1st millenium AD)

  7. Muslim Scholars • Mathematics, statistics, linguistics • Abu Ja' far Muhammad ibn Musa Al-Khowasrizmi (algorithm) • Algebra • Cryptanalysis techniques described by al Kindi in 9th century

  8. Frequency Analysis • For a given language (e.g., English), it is known how often each letter occurs: LetterPercentage a 8.2 b 1.5 c 2.8 d 4.3 e 12.7 ... z 0.1

  9. Frequency Analysis • So Eve just counts percentages in ciphertext message, and decrypts it: Encrypted Percentage Decoded x 8.2 a c 1.5 b p 2.8 c t 4.3 d f 12.7 e ... b 0.1 z

  10. Frequency Analysis • Only have to encrypt part of the message, and then play “Wheel of Fortune”: _ o _ d_ I _ _ _e _ _ee _ _et _e _ _ _ _t t_e _ _ _s. • As length of ciphertext message increases, statistics become more applicable (less so for shorter messages)‏

  11. Frequency Analysis • Encrypting pairs helps a lot, but then we just use pairwise frequencies instead: PairPercentage aa 0.0001 ab 0.002 ac 0.003 ... zz 0.0005

  12. Vigenère Ciphers (1586)‏ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A A B C D E F G H I J K L M N O P Q R S T U V W X Y Z B B C D E F G H I J K L M N O P Q R S T U V W X Y Z A C C D E F G H I J K L M N O P Q R S T U V W X Y Z A B D D E F G H I J K L M N O P Q R S T U V W X Y Z A B C E E F G H I J K L M N O P Q R S T U V W X Y Z A B C D F F G H I J K L M N O P Q R S T U V W X Y Z A B C D E G G H I J K L M N O P Q R S T U V W X Y Z A B C D E F H H I J K L M N O P Q R S T U V W X Y Z A B C D E F G ... Z Z A B C D E F G H I J K L M N O P Q R S T U V W X Y • Alice uses a different row to encrypt each letter • She and Bob use a keyword to switch rows....

  13. Vigenère Ciphers • E.g., keyword FADE: Keyword F A D E F A D E F A D E F A D Plaintext h o w d o i l o v e t h e e l Ciphertextm A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z D E F G H I J K L M N O P Q R S T U V W X Y Z A B C E F G H I J K L M N O P Q R S T U V W X Y Z A B C D F G H I J K L M N O P Q R S T U V W X Y Z A B C D E

  14. Vigenère Ciphers • E.g., keyword FADE: Keyword F A D E F A D E F A D E F A D Plaintext h o w d o i l o v e t h e e l Ciphertextm o A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z D E F G H I J K L M N O P Q R S T U V W X Y Z A B C E F G H I J K L M N O P Q R S T U V W X Y Z A B C D F G H I J K L M N O P Q R S T U V W X Y Z A B C D E

  15. Vigenère Ciphers • E.g., keyword FADE: Keyword F A D E F A D E F A D E F A D Plaintext h o w d o i l o v e t h e e l Ciphertextm o z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z D E F G H I J K L M N O P Q R S T U V W X Y Z A B C E F G H I J K L M N O P Q R S T U V W X Y Z A B C D F G H I J K L M N O P Q R S T U V W X Y Z A B C D E

  16. Vigenère Ciphers • E.g., keyword FADE: Keyword F A D E F A D E F A D E F A D Plaintext h o w d o i l o v e t h e e l Ciphertextm o z h A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z D E F G H I J K L M N O P Q R S T U V W X Y Z A B C E F G H I J K L M N O P Q R S T U V W X Y Z A B C D F G H I J K L M N O P Q R S T U V W X Y Z A B C D E

  17. Vigenère Ciphers • E.g., keyword FADE: Keyword F A D E F A D E F A D E F A D Plaintext h o w d o i l o v e t h e e l Ciphertextm o z h t A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z D E F G H I J K L M N O P Q R S T U V W X Y Z A B C E F G H I J K L M N O P Q R S T U V W X Y Z A B C D F G H I J K L M N O P Q R S T U V W X Y Z A B C D E

  18. Vigenère Ciphers • Now the code for a word is different each time. • Alice must send Bob a new key often, or Eve may figure it out – weakness! • Babbage (1854) : two instances of a common word (the, and, ...) will occasionally look the same: Keyword K I N G K I N G K I N G K I N G K I N G K I N G Plaintext t h e s u n a n d t h e m a n i n t h e m o o n CiphertextD P R Y E V N T N B U K W I A O X B U K W W B T • Then use W-o-F techniques to decode.

  19. Vigenère Ciphers • Solution: Use a key the length of the whole message: Keyword P L M O E Z Q K I J Z L R T E A V C R C B Y N N Plaintext t h e s u n a n d t h e m a n i n t h e m o o n CiphertextI S Q G Y M Q X L C G P D T R I I V Y G N M B A • Bob & Alice share a “one-time-pad” of keys, one for each new message (or new day, week, ...)‏ • Problem: making lots of truly random keys • People are lazy and will make patterns in keys • Truly random numbers are difficult to generate automatically (a huge field)‏

  20. Vigenère Ciphers • Cracked by Charles Babbage in 1854 • Common word will occasionally be encrypted the same way.

  21. The Enigma Machine (1926-1945)‏ • Alice types on keyboard. • Scramblers (rotors) randomly wire keyboard to lamps. • Lamp shows encrypted letter. • Scrambler rotates as Alice types. • Scramblers can be removed and swapped with each other. • Add a plugboard to randomize some of the keyboard/scrambler connections.

  22. The Enigma Machine • If Eve doesn't have an Enigma machine, she'll never decode a message. • Assuming she has an exact copy of the machine, there are: • 26*26*26 = 17,576 possible configurations of three scramblers • Six possible orders of three scramblers for each such config • Millions or billions of ways of wiring plugboard • Therefore over 10,000,000,000,000,000 possible ways of setting up the machine • So Eve must get an Enigma machine, and intercept the updated Bob/Alice scrambler/plugboard settings.

  23. Cracking the Enigma: Rejewski, Turing • A combination of espionage, genius, and brute force: • Get hold of an enigma machine or blueprints • Obtain some knowledge about what's being transmitted to eliminate most possibilities for initial setup: • Part of initial setup was sometimes specified in message itself • Early-morning messages had the word weather in specific places (crib: AXQEPAZ = weather)‏ • Military messages are more rigidly structured (predictable) than everyday language.

  24. Cracking the Enigma: Rejewski, Turing • A combination of espionage, genius, and brute force: • Build a model of how the machine operates, to eliminate more possibilities • Isolate components; e.g., ignore the plugboard, and build a model of the scramblers. • Check correlations between input and output: • Put in M1, get C1 • Put in M2, get C2 • M1 is to C1 as M2 is to C2 • Check every remaining possibility.

  25. If you'll tell me yours,I'll tell you mine.

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