Symmetric Encryption Crypto History Dan Boneh History David
Symmetric Encryption Crypto History Dan Boneh
History David Kahn, “The code breakers” (1996) Dan Boneh
Symmetric Ciphers Dan Boneh
Few Historic Examples (all badly broken) 1. Substitution cipher k : = Dan Boneh
Caesar Cipher (no key) Dan Boneh
What is the size of key space in the substitution cipher assuming 26 letters?
How to break a substitution cipher? What is the most common letter in English text? “X” “L” “E” “H”
How to break a substitution cipher? (1) Use frequency of English letters (2) Use frequency of pairs of letters (digrams) Dan Boneh
An Example UKBYBIPOUZBCUFEEBORUKBYBHOBBRFESPVKBWFOFERVNBCVBZPRUBOFERVNBCVBPCYYFVUFO FEIKNWFRFIKJNUPWRFIPOUNVNIPUBRNCUKBEFWWFDNCHXCYBOHOPYXPUBNCUBOYNRVNIWN CPOJIOFHOPZRVFZIXUBORJRUBZRBCHNCBBONCHRJZSFWNVRJRUBZRPCYZPUKBZPUNVPWPCYVF ZIXUPUNFCPWRVNBCVBRPYYNUNFCPWWJUKBYBIPOUZBCUIPOUNVNIPUBRNCHOPYXPUBNCUB OYNRVNIWNCPOJIOFHOPZRNCRVNBCUNENVVFZIXUNCHPCYVFZIXUPUNFCPWZPUKBZPUNVR B 36 E N 34 U 33 P 32 C 26 T A NC 11 PU 10 UB 10 UN 9 IN AT UKB 6 RVN 6 FZI 4 THE trigrams digrams Dan Boneh
2. Vigener cipher (16’th century, Rome) k = C R Y P T O C R Y P T 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” (+ mod 26) first letter of key = “H” – “E” = “C” Dan Boneh
3. Rotor Machines (1870 -1943) Early example: the Hebern machine (single rotor) A B C. . X Y Z key K S T. . R N E E K S T. . R N N E K S T. . R Dan Boneh
Rotor Machines Most famous: the Enigma (cont. ) (3 -5 rotors) # keys = 264 = 218 Dan Boneh
4. Data Encryption Standard DES: Today: (1974) # keys = 256 , block size = 64 bits AES (2001), Salsa 20 (2008) (and others) Dan Boneh
END END Dan Boneh
Consider the weight update: Which of these is a correct vectorized implementation?
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.
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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