現(xiàn)代密碼學(xué) 第二版 楊波 課后答案khdaw

1、 1.E11,23(m11m+23 (mod 26THE NATIONAL SECURITY AGENCY D11,23(c11-1(c-23 (mod 26M=19 7 4 13 0 19 8 14 13 0 11 18 4 2 20 17 8 19 24 0 6 4 13 2 24 C= E11,23(M11*M+23 (mod 26=24 22 15 10 23 24 7 21 10 23 14 13 15 19 9 2 7 24 1 23 11 15 10 19 1=YWPKXYHVKXONPTJCHYBXLPKTB11*19 1 mod 26D(c19*(c-2319c+5 (mod

2、 26CM=D(C19C+5 (mod 26= THE NATIONAL SECURITY AGENCY2.ifm=D(cedD(e=i853a+b (mod 26a=3b=22m=D(cc=4 3 18 6 8 2 10 23 7 20 10 11 25 21 4 16 25 21 10 23 22 10 25 20 10 21 2 20 7 =ifyoucanreadthisthankateahcer4.C i AM i + B (mod 26 A22B0dontelni Adont = (3,14,13,19 => elni = (4,11,13,8a bAc d43(mod261

3、114a bc d1313(mod26819a bc d1013923A20 17ENCYedsgickx*c+b (mod 26a*c+b (mod 26if(mod 264 13 2 2419 7 4 13 0 19 8 14 13 0 11 18 4 2 20 17 8 19 24 0 6 4 13 2 24ckxhuklzveqzvkxwedsgickxhuklzveqzvkxwkzukvcuh6 D(d=f4a+b (mod 26 D(d=f3c+22 (mod 263c+22 (mod 260 23 7 20 10 11 252 (mod 26m=3*c+22 (mod 2624

4、14 20 2 0 13 1=8 5 24 14 20 2 0 13 17 4 0 3 19 7 8 18 19 7 0 13 10 0 19 4 0 7 2 4 17nreadthisth 1. 3c3=14(a1,a2,a3=(1,0,1f(a1,a2,a3 = a1c2a2c1a3c1=0c2=0f(a1,a2,a3 = a1101101 (3c1=0c2=1f(a1,a2,a3 = a1a210111* (7c1=1c2=0f(a1,a2,a3 = a1a310100* (7c1=1c2=1f(a1,a2,a3 = a1a2a310101010 (23.n=4f(a1,a2,a3,a4

5、=a1a41a2a3(a1,a2,a3,a4=(1,1,0,1(a1,a2,a3,a4f(a1,a2,a3,a41 1(1,0,1,1 1 1(0,1,1,14. m=2s LFSR(01s+1s+101m+31(,m ms a a a aLFSR121, 1m k m k m m km+1, m+21121121121122211sm m m m jjsm m m m jja c a c a c a ca c a c a c a cm+33122134114312341211101010 0m m m m m m msm m jja c a c a c a c a c a c ac c c

6、c c c cm+30 1.M1(1,1,1,1 01101111011 11011 1(1,1,1,0 1 11 15m+2s00121,(0,1,.,0,1 sa c a c a c a k1 1.(1MM DESY = DES K(XY=DES K(XA B(A B=AB(iDES IP IP-1E P PC1PC2N=PO(MN=PO(MPO(PO(M= PO(M(iiLSN=LS (MN=LS(M(LS (M=LS(M(1(K1,K16K KG(K1,K16=KG(K(K1',K(iiia b(a b= a1(b1=a bA B=A(ivDES1,i ii i i iL RR

7、 L F R K,(F R K P S E R K''111(, (i(ii(,' (, ' (iii(, (,(Ki i i i i i i iii i i ii iY DES X Y DES XR L F R KL F R K L F R KF R K F R KP S E R K''1''11'''111'''11''11( (ii ii i i ii i i i i ii i i ii iP S E R KE R K E R Kiii E R K E R K

8、E R KE R K E R KE R E R(2 DES256(1k K1/2kK1/2k K1/2kK1/2K1/2K1/2256/2=255(2E k0(x=y x y E DESk0b1=(aB(A11''16'=KG(Kb=ab= aB=A BF''''Ki i i i i'('('111LR F R K(,11111K 1/2k K 1/2(i E k (x=y 1y 1=y k 0=k k 0K 1/2 (ii E k (x =y 2y 2=y k= k 0k 0= k k 0K 1/2(x,yK 1

9、/22552.DEST 64T(L,R=(R,LT 2(L,R=(L,RT 2=II DESi f i 11111(,(,i i i i i i i f L R L F R K R 211111*(,(,(,(,(,(,i i i i i i i i ii i i ii i i i i i i f L R L F R K R f L F R K R L F R K F R K R L R 2i f I DES1(c DES m IP f T f T f IP m (* 11(*(#13.DESECB CBC C 1P 1P 2(1 P 2116151216I DES IP f T c T f

10、f IP DES DES (m m 1(c ( (# DES 3-11? P1C i24.8CFB1(64+8-1/8= 89 CFB 1. 3.Fermat 3201 mod 11(a b mod n = (a mod n(b mod n mod n Fermat310 1 mod 11 (310k 1 mod 113201 mod 11= (310203 mod 11 = ( (31020 mod 11(3 mod 11 mod 11 = 3 4. Euclid 67 mod 119q g u v 119 1 0 67 0 1 1 52 1 -1 1 15 -1 2 3 7 4 -7 2

11、1 -9 1616 67-15.gcd(4655, 1207512075 = 24655 + 2765 4655 = 12765 + 1890 2765 = 11890 + 875 1890 = 2875 + 140 875 = 6140 + 35140 = 435+0 gcd(4655, 12075=356.1mod 51mod 7x x a 1=2, a 2=1, a 3=1, m 1=3, m 2=5, m 3=7, M=m 1m 2m 3=105,M 1=M/m 1=35, M 1-1 mod m 1 = 35-1 mod 3 = 2, M 2=M/m 2=21, M 2-1 mod

12、m 2= 21-1 mod 5 = 1, M 3=M/m 3=15, M 3-1 mod m 3 = 15-1 mod 7 = 1x (M 1M 1-1a 1 + M 2M 2-1a 2 + M 3M 3-1a 3 mod M(3522+2111+1511 mod 105176 mod 10571 mod 105 10.RSA (e,n=(5,35C=10M(1 = 11 1 = 119 mod 119 = 16 119(-9 + 67gcd(42mod31mo xn=35 -> p=5, q=7 (n=(p-1(q-1=24d e -1 mod (n5-1 mod 24 5 mod 2

13、4 . ( 55 1 mod 24M C d mod n 105 mod 35 512.RSA (e,n=(77, 221 (1160k2 4 8 16 32 64 72 76 77 160k mod 221185 191 16 35120 35118 217 23nn(2d(11601616064 mod 221 (16064 - 16016 mod 221 = 0 16016(16048 1 mod 221 = 0 16048 = 1 mod 221Euler 4-7ord n (160 | 48 (n(n=48k (n(n nk=4(n=192<221(n=192(n=(p-1(q

14、-1, n=pq p q 1317 p-q = sqrt(p+q2- 4n, n (2d d e -1 mod 77 5 - 192 2 = 1 13.ElGamalg=7(1B A k=2M=30(2AM=30C=(59, C 2C 2(1 C 1g k mod p = 72 mod 71 = 49 C 2y B k M mod p = (3230 mod 71= 57C=(C 1, C 2=(49, 57 (2 7k mod 71 = 59 k k=3C 2 = (3k 30 mod 71 = (3330 mod 71 = 29 18.E 11(1,6y 2x 3+x+6 mod 1110

15、5 mod 355 = 4 + 1 = (1012 bi=0, d <- d*db i - 1 0 1 bi=0, d <- d*d* d 1 10 30 5k 221221 p+q = n - (n + X 2 - 30X + 224n, p = (= 221 = 1 n = 221 = 13=48k+ 1 = 221 - 192 +(n + 1 = 221 - 192 + 1 = 30 221 = 0 - 30X + 221 = 0 = (p+q + (p-q /2p = (p+q + (p-q /2, q =(p+q - (p-q /2= 1317(n = 77-1 mod

16、192 mod 192 = 5(p=71y B =3kx1 2 3 4 5 6 7 8 9 10 x 3+x+6 mod 1168538484974mod 11NoNoyesyesNoyesNoyesyesNoyesy 4, 7 5, 6 2, 9 2, 9 3, 8 2, 9E 11(1, 6 O, (2, 4, (2, 7, (3, 5, (3, 6, (5, 2, (5, 9, (7,2, (7, 9, (8, 3, (8, 8, (10, 2, (10, 9 19.G=(2, 7E 11(1,62G 3Ga=1, b=6, p=11, y 2x 3+x+6 mod 112G = G +

17、 G,22+1/(27-1 mod 11 = 4x3=(82 2G = (5, 23G = 2G + G = (5, 2 + (2, 7,(8*7=1 mod 11x3=(22 3G = (8, 3 20.ElGamal E 11(1,6G=(2,7An A =7(1AP A(2BP m =(10,9k=3C m(3A C mP m(1 A P A = n A G = 7G = (7, 2 (2 C 1=kG = 3G = (8, 3C 2=P m + kP A =(10,9 + 3(7, 2 = (10,9 + (3, 5 = (10, 2C m =C 1, C 2 = (8,3, (10,

18、 2 (3C 2 - n A C 1= (P m + kP A n A (kG = (10, 2 7(8,3 = (10, 9 = P m1 = 2/3 7 mod 11=2 -2-2 mod 11=5, y3= 8(2-5-7 mod 11=23 mod 11=5/8 mod 3 mod 11 = 8 -5-2 mod 11 = (-3 mod 11 = 8 (-8 mod 11 = 3 y3=2(5-8-2 mod 11 = (-8 mod 11 = 3 8 mod 11=13/14 mod 11 = 2/3 mod 11 = 8 ( 3od 11=5*7 mod 11mod 11=5/(-3 mod 11=5/8 mod 11=5*7 mod 11= 2 = 3 1. 6.1.3CBC DES 0CFB 1 CFB 2 CFB M=D 1D 2D N(1 CBC DESCFBj64CFB 3(212DESIVD1, P1 D2, .(3CBCDESO N =E K (D N O N-1CFB P M Z 64640C M =E K (C M-1Z 64=E K (C M-1P M-1=D NM=D 1D 2.D N ,DES/CFBj=64,IV