! ! ! yoshiko ! ! K=3 K ! abcdefghijklmnopqrstuvwxyz BRVKLNR abcdefghijklmnopqrstuvwxyz DEFGHIJKLMNOPQRSTUVWXYZABC DEFGHIJKLMNOPQRSTUVWXYZABC 3 K=3 yoshiko ! K=3 BRVKLNR abcdefghijklmnopqrstuvwxyz DEFGHIJKLMNOPQRSTUVWXYZABC 3 ! ! M K = 0 M−1 BRVKLNR ! K= 0 25 0: 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: BRVKLNR BRVKLNR BRVKLNR BRVKLNR BRVKLNR BRVKLNR BRVKLNR BRVKLNR BRVKLNR BRVKLNR BRVKLNR BRVKLNR BRVKLNR brvklnr aqujkmq zptijlp yoshiko xnrghjn wmqfgim vlpefhl ukodegk tjncdfj simbcei rhlabdh qgkzacg pfjyzbf ! K=0 13: BRVKLNR 14: BRVKLNR 15: BRVKLNR 16: BRVKLNR 17: BRVKLNR 18: BRVKLNR 19: BRVKLNR 20: BRVKLNR 321: BRVKLNR yoshiko" 22: BRVKLNR 23: BRVKLNR 24: BRVKLNR 25: BRVKLNR oeixyae ndhwxzd mcgvwyc lbfuvxb kaetuwa jzdstvz iycrsuy hxbqrtx gwapqsw " fvzoprv euynoqu dtxmnpt cswlmos 25 JYREWWCM ! K 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 ! F : ! F-1 :F F(a) = b ! F-1(b) =a F-1 M ! M! ! F ! M = 26 M! 10 120 F-1 ! ! Wikipedia 4 1000 ! ! ! ! ! ! ! ! ! B B ! ! A B B ! ! 1977 MIT Rivest, Shamir, Adleman ! x x mod m m ! 35 mod 3 = 2 8292 77 59417 136 ! 74 mod 12 = 7×7×7×7 mod 12 = 2401 mod 12 = 1 ! 74 ! 716 mod 12 mod mod ! 74 mod 12 = ((72 mod 12) × (72 mod 12) ) mod 12 = ((49 mod 12) × (49 mod 12)) mod 12 = (1 × 1) mod 12 = 1 xy+z mod m = ((xy mod m)×(xz mod m)) mod m (E, N) D 0 7 13 17 (E, N) = (3, 33) D=7 N-1 24 17 y = xE mod N x = yD mod N 173 mod 33 = 4913 mod 33 = 29 13 19 29 30 D 29 (E, N) = (3, 33) D=7 (E, N) = (3, 33) 1. 8 , 2. 17 D=7 8 297 mod 33 = ((293 mod 33)2 × (29 mod 33)) mod 33 = ((24389 mod 33)2 ×29) mod 33 = (22 × 29) mod 33 = 116 mod 33 = 17 29 (E, N) D N p q N = p×q E D E × D = k × LCM(p−1,q−1) + 1 E, D, k p=3, q=11 N = 33 LCM(p−1, q−1) =LCM(2,10) =10 k=2, E=3, D=7 LCM:" ! ! (E, N) D p, q (E, N) D p, q ! D ! D ! D ! z D x x = zD mod N ! D D 1, 2, ... p ! ! ! ! D D N q 512 21024 (E, N) D N ! E×D = k×LCM(p−1, q−1) + 1 ! ! p q k = 1, 2, ... ! ! ! Rivest p D N p q N = p×q q (1970) (129 ) 114381625757888867669235779976146 612010218296721242362562561842935 706935245733897830597123563958705 058989075147599290026879543541 ! ! 1600 3490529510847650949147849619903898 133417764638493387843990820577 " " " "× 3276913299326670954996198819083446 1413177642967992942539798288533 ! N 10 ! 10 ! ...
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