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2 1 (9/17) 2 (10/22) P2P 3 (11/12) 2 / 44

3 ogawa is.uec.ac.jp / 44

4 ARPANet (1969) 4 / 44

5 M. Blum ( ), Coin Flipping by Telephon ( ), / 44

6 6 / 44

7 7 / 44

8 Suica (JR ), PASMO ( ), Edy ( ) FeliCa (SONY) IC LAN SIM (NTT FOMA ), 8 / 44

9 SSL SSL (Secure Socket Layer) Web 9 / 44

10 IC (e-tax) (Felica, SONY) Suica DES DES 10 / 44

11 11 / 44

12 (1970 ) DES (Data Encryption Standard, 1977) AES (Advanced Encryption Standard 2001) (1976) RSA (1978) 12 / 44

13 , ABCDE FGHIJ KLMNO PQRST UVWXYZ DEFGH IJKLM NOPQR STUVW XYZABC HELLO KHOOR 13 / 44

14 (1) 1 (2) / 44

15 HELLO HELLO 15 / 44

16 = ABCDE FGHIJ KLMNO PQRST UVWXYZ TIEFH DJKLM GOQRC ASUVW YZBPXN E 12.7% T 9.1% E T 16 / 44

17 17 / 44

18 0 1 (ASCII) A B C Z / 44

19 = 0 = 1 (0) + (0) = (0) (0) + (1) = (1) (1) + (0) = (1) (1) + (1) = (0) (bit) = = = = 0 19 / 44

20 a = ) b = c = a b = a b..... a b b = a (b b) }{{} = a }{{} = a 20 / 44

21 (one-time pad) HELLO a = HELLO a = b = b = c = c = c = / 44

22 (Vernam, 1926) b 2. a a c = a b. 3. c b = (a b) b = a.. 22 / 44

23 (Shannon), 1948 (APPLE, BEACH,, HAPPY, HELLO,, ZEBRA, ) (1976, ) 23 / 44

24 24 / 44

25 / 44

26 Diffie-Hellman-Merkle (1976), (x ) (x ) (y ) (y ) x + y = 26 / 44

27 = 13 = = 13 =1 10+3=1 (mod 12) 12 1=13=25= (mod 12) mod 27 / 44

28 = 0 ( 1) = 1 ( 1) = 2 ( 1) 1=13=25= (mod 12) = =13 (mod 12) 25-1= =25 (mod 12) 12 0 = 5, 1 = 6, 2 = 7, 3 = 8, 4 = 9 (mod 5) = = 3 = 13 (mod 5) 4 1 = 9 6 = 3 (mod 5) 2 3 = 7 8 = 6 = 56 = 1 (mod 5) 28 / 44

29 y = a x a x a x y = a x = a a a }{{} x y = 10 x (a = 10) (x = 1) 10 1 = 10 (x = 2) 10 2 = = 100 (x = 3) 10 3 = = 1000 y = 10 x / 44

30 y = log a x [y = log a x x = a y ] a y x y a x x = a y = a a a }{{} y y = log 10 x (a = 10) x = 10 y (x = 10) 10 1 = 10 y = 1 (x = 100) 10 2 = 100 y = 2 (x = 1000) 10 3 = 1000 y = 3 y = log 10 x / 44

31 y y = a x (mod p) x y = 10 x (mod 7) (p = 7 ) x y = 10 x y = 10 x (mod 7) y = a x (mod p) y x x = 1, x = 2,, x = 6 p 31 / 44

32 y = a x (mod p) p 1024 x y p a y = a x (mod p) y = a x (mod p) x 32 / 44

33 = = 33 / 44

34 / 44

35 RSA Diffie-Hellman (1976) 1978 (Rivest-Shamir-Adleman) 1960, (Ellis), 1973, (Cocks), RSA 1974, (Williamson), Diffie-Hellman-Merkle 35 / 44

36 36 / 44

37 A B B A 37 / 44

38 = 1. a = 0 a = 1 a a 2. a a 3. a a a = a 38 / 44

39 a / 44

40 a = 0 a = 1 a, b c = a b a, b b a a c a b = 0 b = 1 b, a a c = a b 40 / 44

41 c = 0 c = 1 50% 1 a b 2 41 / 44

42 1 a b a b c = a b a c b c = a b 2 b a b a 42 / 44

43 ,,, (Simon Singh, The Code Book, 1999).,, BP, 1978.,,, 2008.,,,1997.,,, / 44

44 44 / 44

(Requirements in communication) (efficiently) (Information Theory) (certainly) (Coding Theory) (safely) (Cryptography) I 1

(Requirements in communication) (efficiently) (Information Theory) (certainly) (oding Theory) (safely) (ryptography) I 1 (Requirements in communication) (efficiently) (Information Theory) (certainly) (oding