6D (PhD) Thanos Stouraitis PhD, professor
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1 D (PhD).....,, Thanos Stouraitis PhD, professor, 2017
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35 [77]. - h = h. -. :,,. - h,, -. -.,, [78]. RSA, DSA. [79]., , RSA, ,, El Gamal Signature Algorithm (EGSA) DSS (Digital Signature Standard) [80]. EGSA DSA : ,,.,, 1994 [74, 80] , DSA [74] ,, ё ,, ё [17]. 35
36 Elliptic Curve Digital Signature Algorithm (ECDSA),,, DSA, ё,,, [81] «..» «..», , ( ) 52,8. ( 2.1) [82] ,9., [82-83]. 60,0 52,8 50,0 40,0 40,0 30,0 22,5 20,0 13,0 10,0 3,6 6,9 0, The Statistics Portal,, : ,6% ( 2.2) [84]. 36
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38 e-gov RSA,. GOST ( ),. e-gov,,., [21,66] ( ) ( ). ( ),, ( ), [42,85]. =,,, (2.1),,,, [42]. : = [ i ], =,, (2.2) [ i ]. (2.2), i- <.. (2.1),. : P =.,, 38
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40 ; ; ;. [37-40], [97-100]. 2.3 ( ) GF(2) [23-25]., [97].,..,.,... [24-26]. [23]., ( ). 40
41 .. [24-26]. x, x,, S x, (2.1) x -, =,. S. S P x = = x, =, S = S.,,. x,, x, x,, S x [24-26]: x = x, x,, S x, (2.2) x = x d x, =,. S ( ). ( x ) x, x,, S x,.. (2.2).. S : =. (2.3) (2.3) -. (2.3), -,, S = S -. [24-26]. (2.3) S,. 41
42 . [24-26]. x, x,, S x, ит м x, - x, S - S x. ( 2.2), (2.3). (2.3) x [23,97]: x = S = x x, x = P S x i x x, =, S. (2.4) x, (2.4) ( ) MD4 (Message Digest 4), MD5 (Message Digest 5) SHA (Secure Hash Algorithm) [85,101]. MD4 MD5 128 (16 ). SHA 160 (20 ). 42
43 [24-26,97].,.. S+ x, S+ x,, S+U x. x, x,, S x., U,..,.,,,,, U d, d,, d U. ( (2.3)) [24-26,97]: U U =, (2.5) d,, =,, U -, U = U, -. (2.5). ( ) S+ x, S+ x,, S+U x x S+ x, S+ x,, S+U x. - h( x ) : h( x ) = ( S+ x, S+ x,, S+U x ), (2.6) h( x ) S+ x d S+ x, =., U ,., DSA. - [78,80]
44 g = d, А, В, С ± h, ±, ±. DSS (Digital Signature Standard,, 1994) (, 1994.) [34, 75, 93]. DSS SHA DSA (Digital Signature Algorithm) [80]. DSA (Digital Signature Algorithm) ( ) 1991.,.,,. DSA. DSA, DSS, А = h, В =, С =, DSA 320. DSA -. [9,85]. DSA. р q: L < < L,,, 9 < <, - g = h / d, h -, < h <, h d >.. = g b d.,, g h : h = h. 2,.. 3 : = g d d. 4 Д h +, = :,. 5 = h + d, d =. 44
45 6,,., 2, 4,, h + = d., 4. r., : = h d.., r,.. -. [9,85].,,,,. 1 < < < < h = h. 3 = d. 4 : z = h d z = d. 5 : = ( g z z d ) d. 6 =,,.. : =.. DSA ,. DSA.,.,. -..,,,. 45
46 DSA , [24-26,97]. DSA [ ]. x, x,, S x, (2.7) x -, =,. S. P x = x x S x = S.,, [ ]. x,, x, x,, S x : x = x, x,, S x, (2.8) x = x d x, =,. S (2.8) x [16,32]: x = S = x x, x = P S x i x x, =, S. (2.9) x, (2.9). ( ) g x, g x,, g S x., g x, i =1,2,,S. g x x, x,, S x [ ]: 46
47 g x = g x, g x,, g S x, g x = g x ( d x ), i=1,2,,s. [, ] x x. x : x = x, x,, S x, x g b x d( x ), =,. S - h x, 2.4. [, ]. x, [109]: x = ( x, x,, x ), x g x d( x ) d( x ), =,. S - h x (2.6) x : x = ( x, x,, x ), x h x + x d( x ), =,. S x, x.. ( x, x x, x. - h x. x = ( x, x,, x ). z x = h x x d x z x = ( x x ) d x. x = ( x, x,, x ). 47
48 x = x,,.... : - - ; - -, ; -. x, x,, S x,. 2.6 ё..,. «e-gov»,,.,.. ( ): 1) ; 2). x, x,, S x. ( ).,.. S+ x, S+ x,, S+U x.. DSA - x, x... 48
49 : -, - ;. x, x,, S x,. 49
50 3 Щ Щ ,,,,, -,,.,,,., «giant step-baby step»,,,,,,..,,,,.,, ( ) [29].,.,,,. ( : b -, r -, l - ). DES - [9-11] =, =, =. DES [110, 111]. 50
51 Triple DES DESX =, =, = ; - DES, [ ]. IDEA =, =, =., [112]. RC5 - = ; ;, =, = [112,115]. [116], = = = =, =, = [ ]., DES [ ]., - S- DES -.,,. Blowfish - 64-, (Schneier) 1993.,. XOR 32- (XORs and additions on 32-bit words). ( 448 ) (subkey arrays). 32- DES [120]. AES (Rijndael), [76,12]. 100 (Triple DES IDEA..).,,., [122]. DES, S.W.I.F.T., VISA EUROPAY,, -.,,,. 51
52 3.1,,, MIPS DES Triple DES 128 (112) IDEA RC5 128, , 40 Blowfish AES 128, 192 (Rijndael) 256, IBM. 20, 25%, DES Lai Massey. Joan Daemen Vincent Rijmen. ( NIST) ,5, (Schneier) (Feistel) 32- DES Joan Daemen Vincent Rijmen. ( NIST).,.,... ( 3.2).
53 RSA, ( ).. [26-27]. - (El-Gamal) [22, 34].. DSS [19, 80], [74].. (elliptic curve) [35] RSA DSA El-Gamal ( - ) (. ), MIPS 2, , RSA, RSA 1977., DSS -. DSA- DSS.. : 53
54 ; ; [123] [122].. [81].,..,,.. -. ( ) h = h, = , ( ). DSA SHA-1 SHA-2., 3.3., DSA ECDSA, DSA ECDSA. DSA ECDSA. DSA ECDSA - SHA
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68 14 BelT [ ]: : ( : ). 15 O.z DSt 1105: // І.., ґ є...:, What are ANSI X9.30 and ANSI X9.31? // Digital Signature Standard (DSS) // techtarget.com/definition/digital-signature-standard: El Gamal Signature Algorithm // liljanab/isas/course_materials/elgamalsign.pdf: // (" ") / ,... : // , :....: : : , ,..,..,.., // :, ,.. // :,. - :, ,.. // , ,.. // ,..,.. :. -.: -, , : -,
69 30.., :, , :, : :, Beth., Schaefer F. Non-super singular elliptic curves for public key cryptosystems // Advances in Cryptology - EUROCRYPT'91, Springer-Verlag P ElGamal T. A public key cryptosystem and a signature scheme based on discrete logarithms // IEEE Transactions on Information Theory Vol. IT- 31, P Koblitz N. Elliptic Curve Cryptosystems // Mathematics of Computation Vol. 48, Wilson S.., Menezes A., Tavares S., Meijer H. Authenticated Diffe- Hellman Key Agreement Protocols // Proc. SAC'98. - Lecture Notes in Computer Security Vol P Schinianakis D., Stouraitis T. Residue Number Systems in Cryptography: Design, Challenges, Robustness // Secure System Design and Trustable Computing, Springer Schinianakis D., Fournaris A., Michail H., Kakarountas A., Stouraitis T. An RNS implementation of an Fp elliptic curve point multiplier // IEEE Trans. Circuits Syst , I 56(6). - P Schinianakis D., Stouraitis T. A RNS Montgomery multiplication architecture // IEEE International Symposium on Circuits and Systems (ISCAS) P Schinianakis D., Stouraitis T. Hardware-fault attack handling in RNS-based Montgomery multipliers // IEEE International Symposium on Circuits and Systems (ISCAS) P // ,... -.:, (., ) // ,..,..,..,.,..,.. // , Pan Asian E-commerce Alliance Retrieved: Aug, 2016:
70 46.. : -. -.:, Biyashev R. G., Nyssanbayeva S. E., and Begimbayeva Ye. Y. The Development of a Structural Scheme of National Segment in a Protected Cross- Border Space // International Conf. on Advanced Material Science and Environmental Engineering (AMSEE 2016) P (Thomson Reuters). 48 Magzom M. M., Begimbayeva Ye. Ye., Biyashev R. G., Nyssanbayeva Modelling services infrastructure in the integrated system of cross-border information exchange // C Biyashev R. G., Nyssanbayeva S. E. and Begimbayeva Ye. Y. Development of the model of protected cross-border information interaction // Open Engineering, P (Scopus). 50..,..,.. // V , ,..,.. // C ,..,.. //.... " " ,..,.. // III «-2050». -, C // find=&type=blog&view=article&hid=227&page=1&rowinpage=10&menuid=0: // _k_modeli_pd-t.pdf:
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72 17/ // II ( ) // 73, // :, :, : , : -, Diffie W., Hellman M. New directions in cryptography// IEEE Trans. Inform. Theory P Rivest R., Shamir A., Adleman L. A method for obtaining digital signatures and public-key cryptosystems // Comm. ACM P FIPS PUB 186. Digital Signature Standard (DSS) // ,.. // Informatics and Mathematical Methods in Simulation. - Vol. 4 (2014), No P // // Share of companies using digital signature in Spain from 2009 to 2016 //
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74 , ,..,.. // C ,..,.. // C Maksat N. Kalimoldayev, Rustem G. Biyashev, Saule E. Nyssanbayeva, Yenlik Ye. Begimbayeva Modification of the digital signature, developed on the nonpositional polynomial notations // Eurasian Journal of Mathematical and Computer Applications Vol p (Scopus) ,..,.. DSA //..., , Biyashev R.G., Nyssanbayeva S.E., Begimbayeva Ye.Ye., Magzom M.M. Building modified modular cryptographic systems / International Journal of Applied Mathematics and Informatics. - Vol. 9, P Biyashev R.G., Nyssanbayeva S.E., Begimbayeva Ye.Ye., Magzom M.M. Modification of the cryptographic algorithms, developed on the basis of nonpositional polynomial notations // New developments in circuits, systems, signal processing, communications and computers. Proceedings of the International Conference on Circuits, Systems, Signal Processing, Communications and Computers (CSSCC 2015). - Vienna, Austria, P Biyashev R.G., Nyssanbayeva S.E., Begimbayeva Ye.Ye., A modification of the digital signature algorithm based on modular arithmetic //... «,» (CITech-2015), -. -,,, (86), C Biyashev R.G., Nyssanbayeva S.E., Begimbayeva Ye.Ye., A modication of the digital signature algorithm based on modular arithmetic // Abstracts of the International conference «Computational and Informational Technologies in Science, Engineering and Education» (September 24-27, 2015). - Almaty:, P ,..,..,..,..,.. // : ,
75 110 Weiner M. Efficient DES key search. Technical Report TR-244, School of Computer Science. - Carleton University, p. 111 Odlyzko A.M. The Future of Integer Factorization. Cryptobytes // RSA Laboratories Vol. 1, 2. - P Bruce Schneier, Applied Cryptography: Protocols, Algorithms and Source Code in C // John Willey & Sons P Rogaway P. The security of DESX // Cryptobytes, RSA Laboratories Vol. 2, 2. - P Kaliski B., Robshaw M. Multiple encryption: weighing security and performance // Dr. Dobb s Journal P Rivest R.L. The RC5 Encryption Algorithm // Cryptobytes, RSA Laboratories Vol. 1, 1. - P Kaliski B., Yiqun Lisa Yin. On the Security of the RC5 Algorithm // Cryptobytes, RSA Laboratories Vol. 1, 2. - P // // , Intel x86 // Blowfish? // CryptFAQ. html Rogaway P. The security of DESX // Cryptobytes, RSA Laboratories Vol. 2, 2. - P Shannon C.E. Communication Theory of Secrecy Systems // Bell Systems Technical Journal P , - : ( ) / :...;.:.. -,
76 1...,..,.. DSA //...,. 50-, ,, ,..,.. //, 4, 2015, Biyashev R.G., Nyssanbayeva S.E., Begimbayeva Ye.Ye., Magzom M.M. Building modified modular cryptographic systems / International Journal of Applied Mathematics and Informatics. Vol. 9, P Biyashev R.G., Nyssanbayeva S.E., Begimbayeva Ye.Ye., Magzom M.M. Modification of the cryptographic algorithms, developed on the basis of nonpositional polynomial notations // New developments in circuits, systems, signal processing, communications and computers. Proceedings of the International Conference on Circuits, Systems, Signal Processing, Communications and Computers (CSSCC 2015), -Vienna, Austria, pp., Biyashev R.G., Nyssanbayeva S.E., Begimbayeva Ye.Ye., A modification of the digital signature algorithm based on modular arithmetic //... «,» (CITech-2015),,. 20,. -,,,, 3(86), 2015, Biyashev R.G., Nyssanbayeva S.E., Begimbayeva Ye.Ye., A modication of the digital signature algorithm based on modular arithmetic // abstracts of the International conference «Computational and Informational Technologies in Science, Engineering and Education» (September 24-27, 2015). Almaty:, 2015, p. 7...,..,..,.. // -,, -,. -, ,..,.. //., 2015, ,..,.. // III
77 «-2050»., 2015, C ,..,..,..,..,.. // : 80-., ,..,.. // V -,, 2016, Kalimoldayev Maksat N., Biyashev Rustem G., Nyssanbayeva Saule E., Begimbayeva Yenlik Ye. Modification of the digital signature, developed on the nonpositional polynomial notations // Eurasian Journal of Mathematical and Computer Applications, Vol. 4, Issue 2 (2016), p (Scopus) ,..,.. //, 4, 2016, c //., 2016, ,..,.. // ,. 2, Biyashev R.G., Nyssanbayeva S.E., Begimbayeva Ye.Ye. The Development of a Structural Scheme of National Segment in a Protected Cross-Border Space // Proceedings of the International Conference on Wireless Communications, Network Security and Signal Processing International Conference on Advanced Material Science and Environmental Engineering P (Thomson Reuters) 17. Biyashev R.G., Nyssanbayeva S.E., Begimbayeva Ye.Ye. Development of the model of protected cross-border information interaction // Open Engineering 2016, Open Eng. 2016; 6. p (Scopus, Thomson Reuters) ,..,..,.., ғ.. //, 2, 2017, Magzom M. M., Begimbayeva Ye. Ye., Biyashev R. G., Nyssanbayeva Modelling services infrastructure in the integrated system of cross-border information exchange //..., C
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