λ(t) (t) t ( ) (Mean Time to Failure) MTTF = 0 R(t)dt = /λ 00 (MTTF) MTTF λ = 00 MTTF= /λ MTTF= 0 2 (0 9 ) =0 7 () MTTF=

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1 R(t) t R(0) =, R( ) =0 λ(t) t R(t) λ(t) = R(t) dr(t) t, R(t) = exp ( λ(t)dt) dt 0

2 λ(t) (t) t ( ) (Mean Time to Failure) MTTF = 0 R(t)dt = /λ 00 (MTTF) MTTF λ = 00 MTTF= /λ MTTF= 0 2 (0 9 ) =0 7 () MTTF= 0 4 ().4.3 fail-safe 2

3 fault-avoidance fault-tolerance () 2 () R R d R d = R 2 +2R( R) =2R R 2 0 R R d R 2 3 R R t R t = R 3 +3R 2 ( R) = 3R 2 2R 3 R >/2 R t >R (R </2 R t <R ) 3

4 .4 ) 2) 3) ) N t =0n(t) t dn dt = φ(n n(t)) n(t) =N( exp ( φt)) (Jelinski,Z.)- (Moranda,P.B.) n(t) =N( exp ( φt a )) (Sulert,A.N.) 2) C (Calibration error) c e E E = Ce/c (Mills,H.D.) 3) (Halstead,M.H.).5 (Computer Virus) 2 () (2) 4

5 A A A E 0 q=0.9 p=0. 0 q=0.9 p=0. p =0. bit ( 0.) 8 =0.43 p =0.0 bit ( 0.0) 8 =0.92 p =0.000 bit ( 0.000) 8 = bit 000 ( 0.000) 8000 =0.449 () () 5

6 () () () (2) 2.2 =(000000) =(00000) =(000000) =(00000) =(0000) (, )=, (, )=4 d min ()d min 2 (2)d min 3 6

7 d min 2 d min ()d min 2t + t (2)d min 2t + s + t (t + s) ) 2) 2.3 ( ) =(0000) =(000) 2 =(000) 3 =(00) 4 =(0) 5 =() 0 5 7

8 9 =(00) u =(X,X 2,X 3,X 4 ) v =(X,X 2,X 3,X 4,X 5,X 6,X 7 ) X 5 = X + X 2 + X 3 X 6 = X + X 2 + X 4 X 7 = X + X 3 + X 4 (X,X 2,,X 5,X 6,X 7 )=(X,X 2,X 3,X 4 )G v = ug 000 G= : =0 0 0=0 +0= 0=0 0+= 0 =0 +=0 = 2 6 =(00) (00) v = (000) = v v =(X,X 2,,X 5,X 6,X 7 ) e =(e,e 2,,e 7 ) r =(r,r 2,,r 7 ) r = v + e 8

9 X 5 = X + X 2 + X 3 X 6 = X + X 2 + X 4 X 7 = X + X 3 + X 4 X +X 2 +X 3 +X 5 = 0 X +X 2 +X 4 +X 6 = 0 X +X 3 +X 4 +X 7 = 0 ( 2 =) H= vh T = (H) H (), (0), (0), (0), (00), (00), (00) (000) 0 rh T =(v + e)h T = vh T + eh T = eh T rh T s r e = ( ) s = (000) e = (000000) s = (00) e = (000000) s = (00) e = (000000) s = (00) e = (000000) s = (0) e = (000000) s = (0) e = (000000) s = (0) e = (000000) s = () s e r = v + e v = r e v = (X,X 2,,X 5,X 6,X 7 ) u = (X,X 2,X 3,X 4 ) k n k n k n n 2 n k

10 u =(X,X 2,X 3,X 4 ) G v =(X,X 2,,X 6,X 7 ) v = ug (G ) e =(e,e 2,,e 6,e 7 ) r =(r,r 2,,r 6,r 7 )=v + e H s = rh T s = rh T =(v + e)h T = eh T (vh T =0) s e v = r e u G,H ),, () 2) ( ) 3),,, ( ) 2.4 () 00 0

11 M E C D M K K 2 (encryption) C = E k (M) (decryption) M = D k2 (C) M = D k2 (E k (M)) (M = E k (D k2 (M)) ) E 3 (M) =M + 3 (mod 26) (M =0,,..., 25) D 3 (M) =M 3 (mod 26) (M =0,,..., 25) ABCDEFGHIJKLMNOPQRSTUVWXYZ THUVICWBNFSPODZGJXQALYMRKE MESSAAGE OIQQTTWI 26 = ,

12 space I R A J S B K T C L U D M V E 0.03 N W F O X G P Y H Q Z () n ( ( ) ) 2345 n = n (n ) DES 973 () 977 (Data Encryption Standard) 64 (8 ) ( ) 6 )980 (977 Hellman ) 2) ) 2

13 ( ) (00 ) : ( ) E A A D A A A Β M E C D M B B ( ) ( ) ()C = E A (M) D A (C) =M D A (E A (M)) = M (2)E A D A (3)E A (D A (M)) = M 3

14 man crypt CRYPT() USER COMMANDS CRYPT() NAME crypt - encode or decode a file SYNOPSIS crypt [ password ] DESCRIPTION crypt encrypts and decrypts the contents of a file. crypt reads from the standard input and writes on the standard output. The password is a key that selects a particular transformation. If no password is given, crypt demands a key from the terminal and turns off printing while the key is being typed in. crypt encrypts and decrypts with the same key: example% crypt key <clear.file >encrypted.file example% crypt key <encrypted.file pr will print the contents of clear.file. Files encrypted by crypt are compatible with those treated by the editors ed(), ex() and vi() in encryption mode. The security of encrypted files depends on three factors: the fundamental method must be hard to solve; direct search of the key space must be infeasible; "sneak paths" by which keys or cleartext can become visible must be minimized. crypt implements a one-rotor machine designed along the lines of the German Enigma, but with a 256-element rotor. Methods of attack on such machines are widely known, thus crypt provides minimal security. The transformation of a key into the internal settings of the machine is deliberately designed to be expensive, that is, to take a substantial fraction of a second to compute. However, if keys are restricted to (say) three lower-case letters, then encrypted files can be read by expending only a substantial fraction of five minutes of machine time. Since the key is an argument to the crypt command, it is potentially visible to users executing ps() or a derivative command. To minimize this possibility, crypt takes care to destroy any record of the key immediately upon entry. No doubt the choice of keys and key security are the most vulnerable aspect of crypt. FILES /dev/tty for typed key SEE ALSO des(), ed(), ex(), ps(), vi(), makekey(8) RESTRICTIONS This program is not available on software shipped outside the U.S. 995//2 (3) DES DES 2 50 RSA (Rivest-Shamir-Adleman ) 0 (n ) n p, q n = pq E(M) =M e (mod n) D(C) =C d (mod n) X ed = X (mod n) e d 4

15 ( ) p (a, p) = a p = (mod p) (a, p) a p (a p = a (mod p) a ) a, 2, 3,,p () a, 2a, 3a, (2) p (2) (ka = ma + np p k, m, n p ) () (2) p p a p (p )! = (p )! (mod p) (p )! p a p = (mod p) () () (a, r) = a φ(r) = (mod r) φ(r) r r p, q φ(pq) =(p )(q ) e d (p )(q ) e u, v, x, y ue + v(p ) = xe + y(q ) = (u x)e = v(p ) + y(q ) p q m e (p )(q ) u x m w t d u x = w(p ) + t(q ) u w(p ) = x + t(q ) ed = eu ew(p ) = (ew + v)(p ) = (mod p ) 5

16 ed = ex + et(q ) = +(et y)(q ) = (mod q ) X ed = X (mod p) X ed = X (mod q) X ed = X (mod n) n (p, q ) 50 () : p = q =3 n = 43 e =7 d =43 M =5 M M 7 = C (mod 43) C 5 7 = 7825 = 47 (mod 43) = = 5 (mod 43) 5 n p q () e d n 00 n p q 50 p, q n = pq p q A A S = D A (M) C = E B (S) B 6

17 C D B (C) =D B (E B (S)) = S S (S ) E A (S) =E A (D A (M)) = M ()S D A A (2)C S D B ( ) (3)S E A M 3 ) k k(k ) 2 2k k = 00 k(k ) 2 = 4950 k = 000 k(k ) 2 = ) RSA )D A E A 2)n 00 7

(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