- ( know-how " "), - -/286 1,5 , - . - 300 200 , 500 1 000 . "," : - , - , - () , - . "". " " P , P-1 2*Q, Q , " " P , P-1 160 Q( Q 2 ), x 1< x < Q. " " , u , - Q ( R.Shnorr). PC/AT-286 , 16MHz , - . P - 512 . +----------------------------------------------------------------------------+ | | | | | | +-----------------------------------------------------------+ | | | | | | | | +----------------------------------------------------------------------------+ | | 1.0101 | 0.9885 | 0.3223 | 0.2975 | 0.2966 | 0.2899 | +----------------------------------------------------------------------------+ | | | | | | | | | | 2.2286 | 2.7520 | 0.8153 | 1.0166 | 0.5065 | 0.7050 | | | | | | | | | +----------------------------------------------------------------------------+ | | | | | | | | | | | 4.9641 | | 1.6883 | | 0.9643 | | | | | | | | | +----------------------------------------------------------------------------+ | | 2.2973 | | 0.7076 | | 0.2832 | | | | | | | | | | +----------------------------------------------------------------------------+ | | 128 | 192 | 40 | 104 | 27 | 91 | | | | 128 | | 40 | | 27 | +----------------------------------------------------------------------------+ | | | | | | | | | | 0.9013 | 4.5693 | 0.2777 | 2.1599 | 0.2903 | 1.6585 | | | | | | | | | +----------------------------------------------------------------------------+ | | | | | | | | | | | 4.0532 | | 1.4292 | | 1.6388 | | | | | | | | | +----------------------------------------------------------------------------+ " " , - . , - , - . . " " . 1.4. . " " - x x x b = g mod P , .. " - " b g P, - . - P ( - ) +-------------------------------------------------------------------------+ | P | | | | | ( ) | | | | | | x | | CRAY (10**9 /c) | | | | ( ) | | +-------------------------------------------------------------------------+ | | 12 | 6 | | | 128 | 2*10 | 7*10 | | | | 16 | 8 | | | 200 | 10 | 10 | | | | 17 | 9 | | | 256 | 9*10 | 10 | | | | 24 | 12 | | | 512 | 4*10 | 3*10 | | | | 34 | 17 | | | | 1024 | 10 | 10 | | | | | 41 | 20 | | 100 | | 1500 | 10 | 8*10 | | | | 47 | 24 | | | | 2000 | 7*10 | 10 | | | | | 50 | 25 | | | | 2200 | 10 | 10 | | | | | | | +-------------------------------------------------------------------------+ - - " " , , - - 10 ( CRYPTO`82-92, EUROCRYPT`84-92, ..). , " " P 200 - 250 , - , - 30 - 50 , , , - P 500 . 1000 ( 1500) "" . , - , - , , x . , "- " "" . - , -22 , . 2. . , - "" (1976 ), , . , 70- ( , - ..) . , . , - " ". , - , , - . , , , , . - , 1973 - (DES). , . " " , 1989 , 28147-89. , "", .. " ". - , , , . 1989 - FEAL-4 FEAL-8. - . 2.1. DES. DES 64 . . - - . DES, .. (., , [ 7 ] ) [ 2,3 ]. , DES 1973 - - . , DES - 56 , "". " " - , DES. , DES - : - ( - DES PC-AT/286 - 50 /.); - DES " " ( - , 64 ), - ). 2.2. 28147-89. ( 28147-89) 1989 . , (DES). 28147-89 64 . - 2, 32 . . DES - . 28147-89 , .. - . , , , .. - . , - - , , , . , " " , 28147-89 -/286 , - - DES, . - , , . 2.3. "". , " " , DES, 28147-89. , - - 2 - , - / - 2 . : - ( : ); - - ( : - "" / PC/AT-286 - 200-220 /); - : . ( - ) - : . , " " - 3. / - "" . 2.4. . , .. - (" ") - - - . , (DES) - 20 18 10 , . , DES 𝂌 CRAY, 9 (10 ) , 30 7 ( - 3*10 ). - 𝂌, 12 , CRAY, .. 10 ./., , "" DES . , 1973 -, DES . ( 28147-89) 1989 1990-1991 - "Kami" "" - . 1992 "- ", "" " ", , DES. , 28147-89 , , () , - - . , - . " " 28147-89 - , , 50 10 , . "", DES 28147, - 70 , 10 . 50 DES , 10 , 70 - 10 , , . - , - . 3. . , ( ) - . , - . , - , - : (, , ) - , . , , - . , , ... , . , 1976 . ., 1, . , , - , , . - ( ), - - . "". ( ), , , " RSA". - ( ). 3.1. - . , - / , . - ( ) . - - , . , (!) , , . . , - - / . - (). - - . , , P. , 1976 , , , , , - , - 1.4. - " " . 3.2. . , - - , , . , : ( - ), , , .. , . - 2. , - . : , , ... . - - , - - . 3.3. "". " " - - , . , , - P, - - - , 1.3. - - , - . P - , . P , (DSS), - P , 16 2 , . , P , - "" . P , , . , P - "" P. - . 3.4. . , .. - , , "" - . - " " - 1976 . - . - 1.4. - . , " ". 1. , , P 510 , , 24 10 ( 1000 100 - 9 10 ./. ). 2. ( ) - : 18 - (DES) - 10 , 50 - 28147-89 - 10 , 70 - "" - 10 . 3. ( ) - P 510 , , - , - , 24 10 . . " " 1. W. Diffie, M. Hellman, " New directions in cryptography ", IEEE Trans. Informat. Theory, vol. IT-22, pp.644-654, Nov.1976. 2. Federal Register , "Encryption algorithm for computer data protection", vol.40, no.52, pp.12134-12139, Mar.17, 1975. 3. "Data encryption standard(DES)", National Bureau of Standards (U.S.), Federal information Service, Springfield , VA , Federal Information Processing Standard Publication,46, Apr. 1977. 4. R. Rivest, A. Shamir, L. Adleman, "A method for obtaining di- gital signatures and public key cryptosystems", Commun. ACM, vol. 21, no. 2, pp. 120-126, Feb. 1978. 5. T. ElGamal, "A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms", IEEE Trans. Informat. Theory , vol. IT-31, no.4, pp.469-472, Nov.1985. 6. Federal Register , "A Proposed Federal Information Processing Standard for Digital Signature Standard(DSS), vol.56, no.169, Aug.30, 1991. 7. A. Konheim , " Cryptography. A Primer" John Wiley & Sons, New York, 1983.  * *   .  () ......... . , .............................. ( - ), , ; - ; , ; - , -- ; , - , , - , : I. () , () . II. , () , - - () , . III. - , () , ............... . , ............................ , - , - () , - , . ............................ . - ................. , , - . IV. , , . . () - , .......................... . V. ... , , , - . .......................... . ___________________________________________________ __________________________ (_____________) .. ___________________________________________________ __________________________ (_____________) .. . . . . . . . . . . . . . . . . . . . . . . . . .   , , , - - .......................... . 1. , , , ( ), . , , - - , . 2. - ( ), - . .58 /1/ , , , . , , - , . ____________________ /1/ 31 1991 . (- . 1991. N 26. .733). -