1. Dan Boneh Symmetric Encryption History Crypto

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

3. Dan Boneh Symmetric Ciphers

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

5. Dan Boneh Caesar Cipher (no key)

6. Template vertLeftWhite1 What is the size of key space in the substitution cipher assuming 26 letters?

7. Template vertLeftWhite2 How to break a substitution cipher? What is the most common letter in English text? “X” “L” “E” “H”

8. Dan Boneh How to break a substitution cipher? (1) Use frequency of English letters (2) Use frequency of pairs of letters (digrams)

9. Dan Boneh An Example UKBYBIPOUZBCUFEEBORUKBYBHOBBRFESPVKBWFOFERVNBCVBZPRUBOFERVNBCVBPCYYFVUFO FEIKNWFRFIKJNUPWRFIPOUNVNIPUBRNCUKBEFWWFDNCHXCYBOHOPYXPUBNCUBOYNRVNIWN CPOJIOFHOPZRVFZIXUBORJRUBZRBCHNCBBONCHRJZSFWNVRJRUBZRPCYZPUKBZPUNVPWPCYVF ZIXUPUNFCPWRVNBCVBRPYYNUNFCPWWJUKBYBIPOUZBCUIPOUNVNIPUBRNCHOPYXPUBNCUB OYNRVNIWNCPOJIOFHOPZRNCRVNBCUNENVVFZIXUNCHPCYVFZIXUPUNFCPWZPUKBZPUNVR B36 N34 U33 P32 C26  E  T  A NC11 PU10 UB10 UN9  IN  AT UKB6 RVN6 FZI4  THE digrams trigrams

10. Dan Boneh 2. Vigener cipher (16’th century, Rome) k = C R Y P T O C R Y P T O m = W H A T A N I C E D A Y T O D A Y C R Y P T (+ mod 26) 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. Dan Boneh 3. Rotor Machines (1870-1943) Early example: the Hebern machine (single rotor) ABC..XYZABC..XYZ ABC..XYZABC..XYZ KST..RNEKST..RNE KST..RNEKST..RNE EKST..RNEKST..RN EKST..RNEKST..RN NEKST..RNEKST..R NEKST..RNEKST..R key

12. Dan Boneh Rotor Machines (cont.) Most famous: the Enigma (3-5 rotors) # keys = 26 4 = 2 18

13. Dan Boneh 4. Data Encryption Standard (1974) DES: # keys = 2 56, block size = 64 bits Today: AES (2001), Salsa20 (2008) (and others)

14. Dan Boneh END END END

15. Template vertLeftWhite1 Consider the weight update: Which of these is a correct vectorized implementation?

16. Template vertLeftWhite1 Suppose  is at a local minimum of a function. What will one iteration of gradient descent do? Leave  unchanged. Change  in a random direction. Move  towards the global minimum of J(  ). Decrease .

17. Template vertLeftWhite2 Fig. A corresponds to  =0.01, Fig. B to  =0.1, Fig. C to  =1. Fig. A corresponds to  =0.1, Fig. B to  =0.01, Fig. C to  =1. Fig. A corresponds to  =1, Fig. B to  =0.01, Fig. C to  =0.1. Fig. A corresponds to  =1, Fig. B to  =0.1, Fig. C to  =0.01.

18. Template vertLeftWhite2

19. Template block2x2White1 Ordering of buttons is: 13 24