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History

Symmetric Encryption. History. Crypto. History. David Kahn, “The code breakers” (1996). Symmetric Ciphers. Few Historic Examples (all badly broken). 1. Substitution cipher. k :=. Caesar Cipher (no key).

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History

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  1. Symmetric Encryption History Crypto

  2. History David Kahn, “The code breakers” (1996)

  3. Symmetric Ciphers

  4. Few Historic Examples (all badly broken) 1. Substitution cipher k :=

  5. Caesar Cipher (no key)

  6. Whatis the size of key space in the substitution cipher assuming 26 letters? 26 factorial)

  7. How to break a substitution cipher? What is the most common letter in English text? “X” “L” “E” “H”

  8. How to break a substitution cipher? • Use frequency of English letters • Use frequency of pairs of letters (digrams)

  9. An Example UKBYBIPOUZBCUFEEBORUKBYBHOBBRFESPVKBWFOFERVNBCVBZPRUBOFERVNBCVBPCYYFVUFOFEIKNWFRFIKJNUPWRFIPOUNVNIPUBRNCUKBEFWWFDNCHXCYBOHOPYXPUBNCUBOYNRVNIWNCPOJIOFHOPZRVFZIXUBORJRUBZRBCHNCBBONCHRJZSFWNVRJRUBZRPCYZPUKBZPUNVPWPCYVFZIXUPUNFCPWRVNBCVBRPYYNUNFCPWWJUKBYBIPOUZBCUIPOUNVNIPUBRNCHOPYXPUBNCUBOYNRVNIWNCPOJIOFHOPZRNCRVNBCUNENVVFZIXUNCHPCYVFZIXUPUNFCPWZPUKBZPUNVR E IN THE AT T A trigrams digrams

  10. 2. Vigener cipher (16’th century, Rome) k = C R Y P T O C R Y P T O C R Y P T (+ mod 26) m = W H A T A N I C E D A Y T O D A Y c = Z Z Z J U C L U D T U N W G C Q S suppose most common = “H” first letter of key = “H” – “E” = “C”

  11. 3. Rotor Machines (1870-1943) Early example: the Hebern machine (single rotor) A B C . . X Y Z K S T . . R N E E K S T . . R N N E K S T . . R key

  12. Rotor Machines (cont.) Most famous: the Enigma (3-5 rotors) # keys = 264 = 218

  13. 4. Data Encryption Standard (1974) DES: # keys = 256 , block size = 64 bits Today: AES (2001), Salsa20 (2008)(and others)

  14. END END END

  15. Consider the weight update: Which of these is a correct vectorized implementation?

  16. Suppose q is at a local minimum of a function. What will one iteration of gradient descent do? Leave q unchanged. Change q in a random direction. Move q towards the global minimum of J(q). Decrease q.

  17. Fig. A corresponds to a=0.01, Fig. B to a=0.1, Fig. C to a=1. Fig. A corresponds to a=0.1, Fig. B to a=0.01, Fig. C to a=1. Fig. A corresponds to a=1, Fig. B to a=0.01, Fig. C to a=0.1. Fig. A corresponds to a=1, Fig. B to a=0.1, Fig. C to a=0.01.

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