???????? ?????????? ???????????????

????????????? (????????? ??? ? ?????????) ??? ???????????? ? ????????? ????? ???????? ????????? ??????? ?????, ??? ?????? ? ????????? ?????????? ????????? ?????? ???????????? ?????:

???????? ?????????? ??????????????? ??? ????????? ??????????????, ??????????? ??????????? ?????? ?, ??? ??????????? ? ??????? ?????????? ???????? ????????????? ?????? ????? ???????? ? ???????? ???????? ? ???????????? ???????? ???????? ^[1]? ?????????? ???????? ????????? ?? ??????????? ????????????? , ????? ??????? ?? ????????????? ????????? ???, ????? ??????? ?? ?????????? ??????????? ? ???????? ?????????? ?????????? ??????????????? ?????? ? ???????? ??????? ?????? ????????? ???????? ??????? ????? ? ??? ???????? ?????????? ??????????????? ^[2]?

???????? ???????? ??????????? ??????????? ???????? ??, ?? ???? ???????? ??????, ????? ? ?????????? ????????????????? ? ???????? ??????????? ?????, ???? ????? ?????, ????? ????? ???????????? ???????? ???????, ????? ?? ???????? ??????????? ??????? ????????? ????????????????? ???????? ????? ^[3]?

??????, ???????? ????? ? ?????????? ??????????? ?????????? ?????? ???????? ??????? ??? ??????? , ??????? ??????????? ????????? ?????? ??????????????????? ???????? ????????? ???????????????? ?????????? ???????? ????? ????????, ?? ???? ???????????? ???????? ???????, ????? ? ?????????? ??????????? ????????? ??????????? ???????????????????? ???????? ?????? ??????????? , ??? ??????? ? ???????????? ?????? ????????? ????? ??????????, ?? ????? ???????? ??????????? ????????? ??????????????, ???????? ?????????? ???????????? ?? ???????? ????????????? , ?????? ??????, ?? ??? ?????????? ? ?????????? ???????? ???????????????? ?????????? ?????, ??? ?? ???????? ??? ??? ????? ????? ?? ???????? ?????????? ??????????? ?????? ???????? ????? ?? ????? ???????? ??? ?????, ?? ?? ? ???????? ????????????????, ??? ???????? ???????? ? ??????????????? ???????????????? ??????????? ????????, ??? ????? ? ????????? ????? ???????? ?????????

?????? ????????????? ??????????? ????????? ????? ? ?????????????? ????????? ????? ?????????? ???????? ?????? ? ????????????????? ????????????? ??, ?? ???? ???????????? ???????? ??????, ????? ? ???????, ?? ?????? ??????????????? ?????????? ? ??????????????? ???, ???? ????????? , ?? ????? ???????? ???????, ?? ????? ????? ???? ???????????????/????????????? ?????, ??? ???????? ?????? ???????? ???????? ^[4]^[5]?

??????, ????????? ????????? ??????????? ????? ? ??????? ????????????? ?????????? ????? ? ??????? ???????? ??????? ?????????????? ??? ????????? ?????????? ???? ?????????? ??????????? ????? ? ????????? ??????? ???????? ???????? ?????????? ?????????? ???, ? ????????? ?????? ???????? ?????????? ????? ? ???????? ??? ???????????????? ?????????? ???????????????? ???????? ??????? ????????????? ???? ??? ?????????? ??????????? ?????? ? ?????? ???????? ???????, ???????? ??? ????????? ????? ? ???????? ???????????? ??????? ?????????????? ???, ????? ??? ????? ??????? ???????????????, ?? ???????? ???????? ????????? ?????? ??

???????? ?????????? ???????????? ??????????? ??????????????????? ????????????? ???????? ???????????? ??, ???????? ???????????? ?? ???????????????????, ????? ????????? ?? ???????????? ??????????????? ? ????????? ????????? ??????????????, ??????????? ? ?????????????????? ????? ??????? ?? ???????? ???????????? ???????????? ???, ???????? ?? Transport Layer Security (TLS), SSH , S/MIME ? PGP: ???? ???????? ?????????? ??????????? ????????? ?? ?????????? ??????? ? ????????????? (??????? Diffie?Hellman ?????????? ??????????), ????? ????????? ?? ?????? ????????????????? (??????? ?????? ????????????? ????????), ??? ????? ????????? ?? ??????? ?? (??????? RSA ): ????????? ???????? ?????????? ???? ????????? ???????????? ????????? ?????? ?, ??? ??? ???????? ????????????, ??? ?????????? ????? ???????? ?????? ^[6]? ??????? ????????????????? (??????? TLS-?, Secure Shell -?) ??????????? ?? ?? ???????? ??????????? , ?? ????????? ??????????? , ????? ????????? ??????????? ???????????? ?????? ?????? ?????? ?????????? ?????, ??? ????????? ???????????? ? ???????? ??????????? ??????

?????????????? [ ???????? | ???????? ???? ]

????? 1970-???????? ?????? ????? ???????????? ??????????? ??????????? ??? ???????? ?????? ???????????, ???????? ????? ???????????? ??????? ???????????? ? ??????? ????? ????????? ??? ?????? ?????????, ?????? ?? ??????? ??????, ????? ??????? ?? ???? ? ?????? ????? ???? ????????? ?, ?? ????????????? ???? ????????? ??????? ??????? ???? ? ?????????? ???????????? ??????? ???? ???-?? ?????? ????, ?????? ????????? ???????? ????????????, ??????? ?????? ????? ???????? ??? ??????? ????? ?????? ?? ? ??? ???? ??????? ? ????????????, ???? ?? ???????????? ???? ???????? ?, ??? ??? ?????? ???????? ???????? ???, ??? ??? (?????? ??????? ???????????? ???????? ) ?????????? ????? ??????? ??? ????????????, ??? ???????????????????? ?????????? ?? ??? ??????????? ??????? ??????? ?????, ????????????? ???????? ????? ?????????????? ????? ????????? ? ??????? ???????

? ?????????????, ???????? ?????????? ??????????? ???????? ?????????? ????? ?? ???????? ? ??? ????????, ? ????? ???????????? ???????? ?????????? ???? ? ?????? ?????? ??? ????? ???????

???????? ?????????? ?????????? ??????????? ????????????????? ??????? ??.

???????? ???????? ??????????? , ??? ??????? ????????????????? ?????????? ? ?????????? ??????? ???????? ????????? ?????? ??????? ? ??????????? ???????????? ??????? ???????????????????? ???????????? ??? ????? ????????? ???? ???? ??????, ?? ????? ???????????? ???????? ??????, ??, ????????, ?????????? ?, ?? ??? ??????? ???????????? ? ?, ????????, ???????? ??????? ??? ?????? ????? ?? ????? ? ??????????? ??????????????? ?????????????? ?????????? ????? ^[7]?
?????? ????????????????? , ???????? ????????????????? ??????????? ? ????????? ???????? ???????? ? ????? ? ???????? ?????????????? ??????, ?? ????? ???? ????????? ???????? ???????? ??? ????????? ?????????? ?, ?? ????????? ????? ????? ???? ???????? ???????, ?, ????????, ??? ????????? ?, ?? ?? ???? ???????? ??????? ??? ?????? ????? ?? ??? ?????????? ?, ?? ??????????????? ?????????? ? ???? ??? ??????????????? ?????, ???? ?? ????????? ?? ??????? ???????? ??? ??????????????? ?????, ??? ?????? ? ??????? ????? ???????? ?????? ?????????????

?????? ????? ? ?????????????/????????? ??? ?????, ?? ??????? ???????? ??????? ??????? ?, ???????? ??? ???? ? ? ????????? ? ??????? ????? ??? ????????????????, ? ??? ?? ??????? ??? ?????????? ???? (???????? ?, ???????) ?????? ????? ??????? ??? ?? ???? ???????? ???????????, ??? ??????

???????? ?????????? ?????????????? (PKI) , ????? ??? ??? ?? ???? ?????? ??????, ????? ?????? ?? ????? ????????? ?????????, ????????? ?? ?????????? ???????? ???????????????? TLS-? ??????? ? ??? ???? ?? ????????? ?, ?? PKI ????????? (????????? ?????????, ??????????? ? ??????????) ???????? ? ????? ?????????????? ???????

≪??????????? ???≫, ??? ???????????????? ? ???????????????? ???????????? ????????? ? ??? ?????????? ???????? ???????? ?????????? ???? ?????? ????????? ?????????????? PGP-? ??????????? ? ??? ?????????? ? ?????? ???????? ????????? ??????????? ( DNS ) ???????????? ????????? ?????? ?????????? DKIM ????????? ???????? ??????????? ? ??? ??????????

????????? [ ???????? | ???????? ???? ]

???????? ?????????? ??????????? ????????? ?????? ??????? ????????? ??????????????? ???????????? ? ` ????????????? ?????????? ?????? ????????????????, ??? ????????? ??????????? ?` ???????????? ??????? ???????? ???????, ??? ????? ? ????????? ????? ??????? ?????????? ???????? ?????????

???????? ?????????? ????????????? ??? ??? ???????????? ?????? ??????????????? ?? ?????? ????????????? ????????? ????? ?? ??????????? ????????? ??????????? ?????????? ??????

?? ??????? ??????????? ??????????? ?? ?????? ?????????????????? ?????????????, ?? ???????? ???? ?? ????? ???????????? ???????? ????????? ??? ??????????????? ?? ????????????????

??? ????? ??? ????????? ?????? ???????????? ???????? ?? ?????? ?????? ?????? , ??????????? ?????????? ?????? ????????????, ???????? ???????????? ??????????????? ? ?????????? ???????????????????

?????????? ???????????????? [ ???????? | ???????? ???? ]

???? ?? ????????? ?????????? ???????????? ????? ???? ??? ????? ???????? ??, ??? ????????????, ????????? ? ?????????? ????????/???????? ????????? ?????????? ?????????? ????????? ???????? ?????? ???????????? ? ??????????? ?????, ??? ????????? ???????????? ? ???????? ?????? ?????????????? ???????? ????????? ????????? ????? ???? ?????????????? ???????? ??????? ???????? ?????????? ?????????? ????????? ?????? PGP, SSH ? SSL/TLS ????????? ???????? ??????????? ?? ??? ???????????. ????????, ????? ??????? ?? ?????????? ???????????????? ? ???????? ????????? ?????????????? ??? ??????? ?????????? ???????????? ??????? ?????? ???????? ???????? ???????? ???????? ?????????? ??????????????? ?????, ???? ?????????????, ?? ?? ?????????, ?? ???????? ??????? ??????? ????????????? ??????, ??????? ?????? ???? ??? ??? ???????????? ?????????? ???????????? ???, ???????? ??????? ?????????? ???????? ?????????? ?????????????? ????????? ????? ????? ????????????????, ??? ????????? ?????????? ??????????? ????????? ???? ?????? ???? ??????

????? ?????? [ ???????? | ???????? ???? ]

?????? ????????????? ??? ?????? ????? ?????????????, ?????? ? ?????????? ???????? ????? ???????? ???? ????????? ?????????? ????????? ??? ????????????? (????? ??, ????? ???????? ????????? ?? ???????) ??? ??????? ???????? ???? ??????????????, ????????????? ??????? ????? ??? ?, ?? ?????? ? ??????? ?????? ???????? ???????? ???????????????????? ??? ???????????????, ??????????????? ? ????, ????????? ????????

??????????? [ ???????? | ???????? ???? ]

???????? ?????????? ????? ????????? ??????????? ?????? ?? ≪????? ??????? ?????????? ??????? ?????????≫ ^[8]? ??????????????, ???? ?????????? ???????????? ?, ??? ??????????? ???????? ????? ????????? ??????????? ??????, ??? ???? ?????? ?????? ??????? ? ≪???????????? ??????≫, ?????????? ? ????? ????????? ??????????????? ??? ????????? ????????? ??????? ????? ? ???????? ???????? ???????? ????? ????? ??????? ???? ??? ???????????? ????? ?? ? ??????? ??????? ??? ????? ???? ???????????? ?????????, ???? ?????? ? ???????? ???? ???? ????????? ?????????????? (??????? ????? ????? ?????????)? ???? ?????? ? ??????? ??????????? ?? ???????? ??????? ?????? ???????? ?????????? ??????????? ????????????? ??? RSA , ?? ElGamal ?????????????? ?????? ?? ????????????, ????? ??? ????? ???? ??, ??? ???? ???? ????????? ^[9]? ??????? ?? ???? ??????????? ?????????? ??, ??????? ????????? ????????? ?????

???????? ????? ??????? ???????????? ?? ????????? ???????????? ????????? ???????? ???????????? ?????? ??? ????????? ????????? ???? ??????? ?, ?? ≪????????? ????????????≫ ????????? ???????? ? ^[10]? ?????? ????? ???????????? ?????????????? ???????, ???????? ?????????? ???????????? ????? ? ?????? ????? ???????? ????? ????????????? ?????, ????? ??????????? ?? ?????????????? ?????????? ??????????? ?????? ?????? ????????? ????? ????? ????? ?? ??????????? ??????????? ????????????????? ?? ???????????? ?????? ?????????????, ?????? ?? ??? ?????????????? ???????????? ??????

???????? ?????????? ???????????? [ ???????? | ???????? ???? ]

????????? ?????????? ??????????? ??? ??? ????????? ????????????? ????????????? ? ≪????? ????????≫ ????????? ????????????????, ????? ???????? ?????????? ????????????????? ???????????? ? ?????? ????? ?????? (≪????? ????????≫) ? ????????? ????????? ?? ???????? ?????? ???????? ????????? ??????????? ?????? ??????????? ???????????????????? ? ???????????? ???? ? ????? ????????? ???????????, ????????? ? ?????????????? ?????????? ??????? ???????????? ??????????????? ?????? ?????????? ???? ???????? ??????????, ??????? ???????? ????????????

????? ??, ?? ????????????????? ???????? ?, ??? ????????? ?????????? ?? ??????, ?? ????? ? ????? ?????????? (??? ??????? ? ≪sniffing≫ ): ??? ?????????? ?????????? ?? ????????? ???????? ????????? ?????????? ??????????? ????????????????? ???????? ????????? ?, ??? ??????????????? ??? ????? ??????? ??? ?????????? ????????? ?????? ^[11]?

≪????? ????????≫ ?????????? ????? ? ????? ????? ??????????? ??????????? ????????????? ??????????????????? ??????????????? ????????? ??????????????, ?????? ????? ???? ? ???????, ??? ????????? ??????????? ? ???????? ?????????????? , ???????? ?? ???????? ??????? , ????????? ??? ????? ????: ??? ????????? ?????????? ????? ? ?????? ???????? ???? ???????????????, ??? ?? ?? ???? ?????????? ???????? ???????????????? ?????????? (ISP) ????????? ??????? ?????????? ????? ? ??????????? ???? ??????? ≪????-?????≫ ??????????? ???????? ??????? ???????? ????? ????????? ????? ?????? ???????, ???? ?? ??? ?????????? ? ISP-? ???????????? ????????? ???????? ?????? ?????? ??????????? ????????? ?????????? ??????????? ?? ????? ???? ???

???? ???????? ≪????-?????≫ ????????????? ??????? ??????????????? ?? ????? ?????? ???????? ?????????, ??? ????? ????? ?????? ???????? ????????? ????????? ≪????-?????≫ ????????????? ????? ?? ???????? ??????????? ????????, ?? ????? ???? ???????? ?? ?? ????? ? ??????, ???????? ??? ???????, ??? ?????? ?, ?? ?? ??????????? ????????? ???????? ??, ???? ?? ????????? ????? ?????????? ??? ?? ?????? ?? ????? ? ????????? ?????????? ???? ????????? ???????????????????, ???????? ??? ≪?? ???? ? ???? ??? ???????≫? ??? ??????????? ?? ???? ??????? ??? ????????, ≪????? ????????≫ ????????????? ?????? ???????????? ?? ????? ??? ???????, ??? ??????????????? ??????????????? ????????? ??????????? ? ???????? ???? ??? ??????? ??????. ??????? ??????? ???????? ???????? ????????? ??????? ????? ???????? ????????? ??????, ???????? ?????????? ????? ???? ?? ?????????, ??? ????????? ?????? ??????????? ???????????? ???????????? ??????????? ? ?????????? ?????? ^[12]^[13]^[14]?

???????? ?????? ?????????????? [ ???????? | ???????? ???? ]

???? ????????????? ???????? ????????????? ???? ???????? ? ???????? ??????? ??????????????? (PKI) ????????????. ?? ???? ?????, ??????????????????? ? ????????????, ????? ????????? ?? ?????? ?????????? ?????????, ???????????, ?????????, ????????????, ??????? ? ?????? ????????? ? ???????? ?????????? ??????????? ??????????? ?????? ??????????????, ?? ????????? ????? ?????? ?????

??????? ????????? ???? ??????????? ??????? ???? ? ?????? ????? ???????? ????????, ?? ?????? ?????? ??????? ? ???????????? ????????????, ???????? ? ???????? ??????? ???????????? ???????? ???????????, ?????????? ????? ????????????? ????????????????, ? ????? ???????????? ??? ?????????????? ????????? ????? ????? ????????????, ?????? ?????????? ???????????????????? ??????? ??? ????????????? , ??????, ??????????? ? ≪??????????????? ?????????? ????????????≫ ????? ?????? PKI ?????????????? ? ????? ???????????? ?? ?????????????? ????? ???????????????? ????????? ?????, ?????????, ??????? ???????, ????????? ??????????????? ????????????? ??????????, ?? ????? ? ??????? ??? ??????????????? ???? ????? ???? ???????? ??????? ????? ???????? ????? ?????, ????? ? ????????? ≪????? ????????≫ ????????? ?????? ?????? ???????????, ?????? ???????? ?????? ??????????? ?? ???????????? ???????? ????????? ?????????????? ????????? ??????????, ?? ???????????? ? ??????????? ????????? ? ??????? ??? ???????????? ? ?????????? ??????? (???????? ? ????????), ????? ? ???????????? ??????, ???????? ? ?????? ????????????

?????? ?? ??????? ? ????????? ??????????? ??? ????????? ???????? ????????? ?? ?????????? ???????? ?? TLS-? ? ??? ?????? SSL -?, ????? ????????? ???????????? ?? ??? ????????? ??????????? ??????????????? ?????????? ????? (??????? ?????? ????? ????????? ?????? ???????? ??????? ?????????? ?????)?

???? ??????? ?????????? ?????? ????????? ???????????????, ???????? ?????????? ??????????? ??????????? ???? ? ????? ????? ????????????? ??????????? ??????????????? ? ???? ????????????? (????????? ?????? ????????? ??????, ??? ???????? ? ?????????? ?????????? ???), ???????????? ?? ??????? ???????? ?????????? ????????????? ?????????? ?????? ????????? ???????? ?????????? ?????? ?????????? ????????? ????? ?? ?? ???? ???? ??????????, ????? ??????? ???????? ?????????? ???? ? ?????? ?????? ??? ?????????? ??? PKI ??????? ????????????? ????? ????? ???????? ???????? ????? ??????????? ???????? ??????? ???????? ? ??? ????????? ???????????? ?, ??? ???????? ? ≪????? ????? ????≫? ???????? ?????? ???????? ????????? ?????? ?????????

????????? [ ???????? | ???????? ???? ]

?????? ?????????? ????? ??? ????????? ????????? ???????? ????????? ?????????? ???????? ??.

Diffie-Hellman ?????????? ?????????? ???????????????
DSS (Digital Signature Standard) ? ?????? ????????????? ????????, ??? ???????? ? ?????? ????????????? ?????????
???????
????????? ???? ???????????????
?????? ??????????? ?????????? ???????? ???????????? ???????
Paillier ?????? ????????
RSA ?????????? ???????? (PKCS#1 )
Cramer?Shoup ??????????????
YAK ?????????? ?????? ???????????? ???????????????

????????? ???????? ???????????? ??????????, ????? ??? ???????? ??? ?????????, ???????? ??.

???????????, ???? ?? ???????, ????????? ???????? ???????????? ?????????? ???????? ??.

Merkle?Hellman ???????? ??????????????

????????? ?????????? ??????????? ?????????? ??????????????????? ?????????? ???????? ??.

S/MIME
GPG, OpenPGP -? ??????????? ? ???????? ????????
EMV, EMV ????????? ??????
IPsec
PGP
ZRTP , ??????? VoIP ???????????????
????????????? ????? ??????????????? ????????????? ? IETF-? ? ??? ???????? Secure Socket Layer-? ??????
SILC
SSH
Bitcoin
Off-the-Record Messaging

??????????? [ ???????? | ???????? ???? ]

?????????????? ??? ?????????? ????????? ????? ??????? ????????? ??? ????????, ??? ????? ??????????? ??????, ???? ?? ???????????? ?????? ???????, ???????? ? ??? ?? ??? ?????????? ??? ???????? ???????????? ??? ???????, ??? ????????? ????? ??????? ???? ? ???????????? ?????? ?????, ????? ?? ??????????? ?????????? ??????????????????? ??????????? ?????? ?????????? ??????? ??? ????????? ????????? ?? ?? ???? ????????? ????????? ????????????????

???????? [ ???????? | ???????? ???? ]

?? 1874 ??????? ≪????????? ????????????≫ ?????? ??????? ?????? ????? ^[15] ???? ??

????????? ?????? ? ????, ?? ??? ????? ????? ??? ????????????? ??????? 8616460799 ???? ^[16]? ?? ??? ????????? ?? ????????, ?? ?????? ???? ???? ???? ????? ????? ^[17]?

?????? ?? ????????? ?????????? ???????????? ???? ?????????????? ??? ? ?????????? ???????? ???????? ?????????????? ??????, ??? ???????????? ?? trapdoor ???????? ????????? ?????? 1996 ??????? ???????? ??????????? ??????? ?. ??????? ????. ≪?????? ????????? ?? RSA ????????? ???????? ??????????????????? ???????? ?????????? ?????????? ?????, ??? ??, ???????, ??? ??????? ???????? ?????????? ?????????????? ????????≫ ^[18]?

??????????? ??????????? [ ???????? | ???????? ???? ]

1970 ???????? ????? ?. ?????? ? ????????? ???????????, ??????? ????????????? ????????????? ???????????? ??????? ???????????? ( GCHQ ) ???????? ≪?? ?????? ???????????≫ ???????????????? (???? ??????? ? ???????? ?????? ????????????), ???? ?????????? ?????? ??? ????????????? ???????????????? ^[19]^[20]? 1973 ???????? ??? ????????? ??????? ????? ??????? ???, ???? ?????? ?????? ????? RSA ?????????? ????????? ????? ≪?? ?????? ???????????≫ ????????? ?????, ??? 1974 ???????? GCHQ-? ??? ??? ??????????? ? ?????????? ??????? ?. ??????????? ?????? ???, ??? ???? ?????? ? ????? Diffie-Hellman ?????????? ??????????? ?????? ????????? ? ??? ??? ??????? ????????????? ??????????????? ^[21]? ????? ???????????????????? ?? ?????? ???????? ?????????????? ? ???? ??????? ???????? ?? ????? ?????????? ?????????? ????????????? ???????? ?????????? ?????????????? ??????? ?????? ? ???????? ?? ?? ??????????????? ???????

?? ?? ???????? ?? ???????????? ???????? ??????????? ?????... ??? ???? ????????? ???? ? ???????????? ???????? ????? ??? ???????, ???? ??? ????????????? ????? ??? ??????????? ????????? ????? ???????????? ??????? ???????-??? ?????? CERN-? ????? ??? ???????????? ????????????????? ?????????, ??? ???????????? ? ?????????? Arpanet-? ?????… ??????? ???????? ?????? ???????????????? ??????? ? ?? ??? ????????
???? ???????? ^[21]

??? ????????????????????? ??????????????? ??????????? 27 ????, ????? ?? ??????????????? ????????????? ?????????? ????????????? ?????? 1997???????? ^[22]?

??????????? ??????????? [ ???????? | ???????? ???? ]

1976 ???????? ????????? ?????????? ??????????????? ??????????? ???????? ????? ? ?????? ??????? ??????, ?????, ???????? ???????? ?????????? ??????? ?????????? ???? ?????? ??????????, ???????????? ???????? ?????????? ?????????????? ??????? ??????????? ?????????? ??? ??????, ??? ??????????? ? ?????????? ???????? ???????, ?????? ?????? ????? ??????????? ?????????? ?????????? ^[23]? ?? ?????? ??????????? ????????? ?????? ??? ????????? (???? ?? ??????) ???? ????? ??? ????????? ?????? ?????? ????????? ?????? ????? ???????? ????????? ???????? ???????????? ?????? ≪???????? ?????????? ???????????? ????????≫ ?????? ?????? ????? ?????? ??????????? ? ????????????? 1974 ???????? ? ??????????? ????? 1978 ????????? ?? ????????? ???????????? ???????? ? ????????? ??? ????? ?????????????? ???, ??? ????????????? ?????? ????? ??? 2000 ????? ???????????? ???? ^[24]?

1977 ???????? ????? ??????? ????????????? ??????????? ??????? ?? ??? ??????? , ??? ?????? ? ??????? ???????? , ????????? MIT-???? ?????? ??????????? ?????????? ?? ????? ????????? 1978 ???????? ?????? ???????? ≪Scientific American≫ ?????????, ? ????????? ?????? ? ?????? ????? RSA ? ????? ????????? ????????????? ^[25]? RSA-? ??????????? ? ????????? ?????? ????? ??? ??? ???? ????? ????????? ???????????? ? ?????????? ?????? ????????? ?? ???????? ?????????? ???????????, ?? ???????? ?????????? ?????? ??????????????????? ??? ??????????????? ?????? ? ??? ?????? ????? ?????????? ???????? ??????????? ???, ?????, ??? ????? ?????? ??????????? ????????? ??????? ??? (?????? ????????? ????????????? ?????? ? ???? ????? ???? ???? ???????? ???????. ????? ???????? ?? ???????? ??????????, ?? ??? ????? ????? ? ???????)? ????????? ??????????????? ??????????? ? ≪Mathematical Games≫ ?????????? Scientific American-? 1977 ??????? ???????? ???????? ^[26]?

1970-????????? ? ??? ??????? ?? ???????????, ?????? ?????????????, ?????????? ????????????? ? ??? ????????? ??? ???????????? ? ???????????????, ???????? Rabin ??????????????? , ElGamal ??????????? , DSA - ? ????????? ???? ??????????? ?

?????????????????? [ ???????? | ???????? ???? ]

↑ Bernstein, Daniel J.; Lange, Tanja (2017 ?? ?????????? 14). ≪Post-quantum cryptography≫ . Nature (????????). 549 (7671): 188?194. Bibcode : 2017Natur.549..188B . doi : 10.1038/nature23461 . ISSN 0028-0836 . PMID 28905891 . S2CID 4446249 .
↑ Stallings, William (1990 ?? ?????? 3). Cryptography and Network Security: Principles and Practice (????????). Prentice Hall. ?? 165. ISBN 9780138690175 .
↑ Menezes, Alfred J. ; van Oorschot, Paul C. ; Vanstone, Scott A. (1996 ?? ?????????). ≪8: Public-key encryption≫. Handbook of Applied Cryptography (PDF) . CRC Press. ???? 283?319. ISBN 0-8493-8523-7 . ??????? ? 2022 ?? ?????????? 8-?? .
↑ Menezes, Alfred J. ; van Oorschot, Paul C. ; Vanstone, Scott A. (1996 ?? ?????????). ≪8: Public-key encryption≫. Handbook of Applied Cryptography (PDF) . CRC Press. ???? 425?488. ISBN 0-8493-8523-7 . ??????? ? 2022 ?? ?????????? 8-?? .
↑ Bernstein, Daniel J. (2008 ?? ?????? 1). ≪Protecting communications against forgery≫. Algorithmic Number Theory (PDF) . Vol. 44. MSRI Publications. §5: Public-key signatures, pp. 543-545 . ??????? ? 2022 ?? ?????????? 8-?? .
↑ Alvarez, Rafael; Caballero-Gil, Candido; Santonja, Juan; Zamora, Antonio (2017 ?? ??????? 27). ≪Algorithms for Lightweight Key Exchange≫ . Sensors (????????). 17 (7): 1517. doi : 10.3390/s17071517 . ISSN 1424-8220 . PMC 5551094 . PMID 28654006 .
↑ ≪Asymmetric encryption≫ . IONOS Digitalguide (????????) . ??????? ? 2022 ?? ??????? 2-?? .
↑ Paar, Christof; Pelzl, Jan; Preneel, Bart (2010). Understanding Cryptography: A Textbook for Students and Practitioners . Springer. ISBN 978-3-642-04100-6 .
↑ Mavroeidis, Vasileios, and Kamer Vishi, "The Impact of Quantum Computing on Present Cryptography" , International Journal of Advanced Computer Science and Applications , 31 March 2018
↑ Shamir, Adi (1982 ?? ????????). ≪A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem≫ . 23rd Annual Symposium on Foundations of Computer Science (SFCS 1982) : 145?152. doi : 10.1109/SFCS.1982.5 .
↑ Tunggal, Abi (2020 ?? ???????? 20). ≪What Is a Man-in-the-Middle Attack and How Can It Be Prevented - What is the difference between a man-in-the-middle attack and sniffing?≫ . UpGuard . ??????? ? 2020 ?? ??????? 26-?? .
↑ Tunggal, Abi (2020 ?? ???????? 20). ≪What Is a Man-in-the-Middle Attack and How Can It Be Prevented - Where do man-in-the-middle attacks happen?≫ . UpGuard . ??????? ? 2020 ?? ??????? 26-?? .
↑ martin (2013 ?? ???????? 30). ≪China, GitHub and the man-in-the-middle≫ . GreatFire . ?????????? ?????????? 2016 ?? ???????? 19-?? . ??????? ? 2015 ?? ??????? 27-?? .
↑ percy (2014 ?? ?????????? 4). ≪Authorities launch man-in-the-middle attack on Google≫ . GreatFire . ??????? ? 2020 ?? ??????? 26-?? .
↑ Jevons, William Stanley, The Principles of Science: A Treatise on Logic and Scientific Method p. 141, Macmillan & Co., London, 1874, 2nd ed. 1877, 3rd ed. 1879. Reprinted with a foreword by Ernst Nagel , Dover Publications, New York, NY, 1958.
↑ This came to be known as "Jevons's number". The only nontrivial factor pair is 89681 × 96079.
↑ Principles of Science , Macmillan & Co., 1874, p. 141.
↑ Golob, Solomon W. (1996). ≪On Factoring Jevons' Number≫ . Cryptologia . 20 (3): 243. doi : 10.1080/0161-119691884933 . S2CID 205488749 .
↑ Ellis, James H. (1970 ?? ???????). ≪THE POSSIBILITY OF SECURE NON-SECRET DIGITAL ENCRYPTION≫ (PDF) . {{ cite journal }}: Cite journal requires |journal= ( ?????????? )
↑ Sawer, Patrick (2016 ?? ????? 11). ≪The unsung genius who secured Britain's computer defences and paved the way for safe online shopping≫ . The Telegraph .
↑ ^21,0 ^21,1 Espiner, Tom (2010 ?? ?????????? 26). ≪GCHQ pioneers on birth of public key crypto≫ . www.zdnet.com .
↑ Singh, Simon (1999). The Code Book . Doubleday. ???? 279 ?292.
↑ Diffie, Whitfield ; Hellman, Martin E. (1976 ?? ????????). ≪New Directions in Cryptography≫ (PDF) . IEEE Transactions on Information Theory . 22 (6): 644?654. CiteSeerX 10.1.1.37.9720 . doi : 10.1109/TIT.1976.1055638 . ?????????? (PDF) ?????????? 2014 ?? ????????? 29-??.
↑ ≪Asymmetric encryption≫ . IONOS Digitalguide (????????) . ??????? ? 2022 ?? ??????? 9-?? .
↑ Rivest, R.; Shamir, A.; Adleman, L. (1978 ?? ???????). ≪A Method for Obtaining Digital Signatures and Public-Key Cryptosystems≫ (PDF) . Communications of the ACM . 21 (2): 120?126. CiteSeerX 10.1.1.607.2677 . doi : 10.1145/359340.359342 . S2CID 2873616 . ?????????? ? ?????????? (PDF) 2008 ?? ?????????? 17-?? . ??????? ? 2023 ?? ?????? 2-?? .
↑ Robinson, Sara (2003 ?? ??????). ≪Still Guarding Secrets after Years of Attacks, RSA Earns Accolades for its Founders≫ (PDF) . SIAM News . 36 (5). ?????????? ? ?????????? (PDF) 2017 ?? ???????? 16-?? . ??????? ? 2023 ?? ?????? 2-?? .

????????????? [ ???????? | ???????? ???? ]

Hirsch, Frederick J. ≪SSL/TLS Strong Encryption: An Introduction≫ . Apache HTTP Server . ??????? ? 2013 ?? ?????? 17-?? . . The first two sections contain a very good introduction to public-key cryptography.
Ferguson, Niels ; Schneier, Bruce (2003). Practical Cryptography . Wiley . ISBN 0-471-22357-3 .
Katz, Jon ; Lindell, Y. (2007). Introduction to Modern Cryptography . CRC Press . ISBN 978-1-58488-551-1 .
Menezes, A. J. ; van Oorschot, P. C.; Vanstone, Scott A. (1997). Handbook of Applied Cryptography . ISBN 0-8493-8523-7 .
IEEE 1363: Standard Specifications for Public-Key Cryptography
Christof Paar, Jan Pelzl, "Introduction to Public-Key Cryptography" , Chapter 6 of "Understanding Cryptography, A Textbook for Students and Practitioners". (companion web site contains online cryptography course that covers public-key cryptography), Springer, 2009.
Salomaa, Arto (1996). Public-Key Cryptography (2 ed.). Berlin: Springer . 275 . doi : 10.1007/978-3-662-03269-5 . ISBN 978-3-662-03269-5 . S2CID 24751345 .

??????? ???????? [ ???????? | ???????? ???? ]

Oral history interview with Martin Hellman , Charles Babbage Institute , University of Minnesota. Leading cryptography scholar Martin Hellman discusses the circumstances and fundamental insights of his invention of public key cryptography with collaborators Whitfield Diffie and Ralph Merkle at Stanford University in the mid-1970s.
An account of how GCHQ kept their invention of PKE secret until 1997

??????????? ???? ???????, ????? ?????????? ?? ≪???????? ?????????? ???????????????≫ ?????????

[1] Bernstein, Daniel J.; Lange, Tanja (2017 ?? ?????????? 14). ≪Post-quantum cryptography≫ . Nature (????????). 549 (7671): 188?194. Bibcode : 2017Natur.549..188B . doi : 10.1038/nature23461 . ISSN 0028-0836 . PMID 28905891 . S2CID 4446249 .

[2] Stallings, William (1990 ?? ?????? 3). Cryptography and Network Security: Principles and Practice (????????). Prentice Hall. ?? 165. ISBN 9780138690175 .

[hac-pke-3] Menezes, Alfred J. ; van Oorschot, Paul C. ; Vanstone, Scott A. (1996 ?? ?????????). ≪8: Public-key encryption≫. Handbook of Applied Cryptography (PDF) . CRC Press. ???? 283?319. ISBN 0-8493-8523-7 . ??????? ? 2022 ?? ?????????? 8-?? .

[hac-digsig-4] Menezes, Alfred J. ; van Oorschot, Paul C. ; Vanstone, Scott A. (1996 ?? ?????????). ≪8: Public-key encryption≫. Handbook of Applied Cryptography (PDF) . CRC Press. ???? 425?488. ISBN 0-8493-8523-7 . ??????? ? 2022 ?? ?????????? 8-?? .

[djb-forgery-5] Bernstein, Daniel J. (2008 ?? ?????? 1). ≪Protecting communications against forgery≫. Algorithmic Number Theory (PDF) . Vol. 44. MSRI Publications. §5: Public-key signatures, pp. 543-545 . ??????? ? 2022 ?? ?????????? 8-?? .

[6] Alvarez, Rafael; Caballero-Gil, Candido; Santonja, Juan; Zamora, Antonio (2017 ?? ??????? 27). ≪Algorithms for Lightweight Key Exchange≫ . Sensors (????????). 17 (7): 1517. doi : 10.3390/s17071517 . ISSN 1424-8220 . PMC 5551094 . PMID 28654006 .

[7] ≪Asymmetric encryption≫ . IONOS Digitalguide (????????) . ??????? ? 2022 ?? ??????? 2-?? .

[8] Paar, Christof; Pelzl, Jan; Preneel, Bart (2010). Understanding Cryptography: A Textbook for Students and Practitioners . Springer. ISBN 978-3-642-04100-6 .

[9] Mavroeidis, Vasileios, and Kamer Vishi, "The Impact of Quantum Computing on Present Cryptography" , International Journal of Advanced Computer Science and Applications , 31 March 2018

[10] Shamir, Adi (1982 ?? ????????). ≪A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem≫ . 23rd Annual Symposium on Foundations of Computer Science (SFCS 1982) : 145?152. doi : 10.1109/SFCS.1982.5 .

[11] Tunggal, Abi (2020 ?? ???????? 20). ≪What Is a Man-in-the-Middle Attack and How Can It Be Prevented - What is the difference between a man-in-the-middle attack and sniffing?≫ . UpGuard . ??????? ? 2020 ?? ??????? 26-?? .

[12] Tunggal, Abi (2020 ?? ???????? 20). ≪What Is a Man-in-the-Middle Attack and How Can It Be Prevented - Where do man-in-the-middle attacks happen?≫ . UpGuard . ??????? ? 2020 ?? ??????? 26-?? .

[martin-GF-13] rtin (2013 ?? ???????? 30). ≪China, GitHub and the man-in-the-middle≫ . GreatFire . ?????????? ?????????? 2016 ?? ???????? 19-?? . ??????? ? 2015 ?? ??????? 27-?? .

[percy-GF-14] rcy (2014 ?? ?????????? 4). ≪Authorities launch man-in-the-middle attack on Google≫ . GreatFire . ??????? ? 2020 ?? ??????? 26-?? .

[15] Jevons, William Stanley, The Principles of Science: A Treatise on Logic and Scientific Method p. 141, Macmillan & Co., London, 1874, 2nd ed. 1877, 3rd ed. 1879. Reprinted with a foreword by Ernst Nagel , Dover Publications, New York, NY, 1958.

[16] This came to be known as "Jevons's number". The only nontrivial factor pair is 89681 × 96079.

[17] Principles of Science , Macmillan & Co., 1874, p. 141.

[18] Golob, Solomon W. (1996). ≪On Factoring Jevons' Number≫ . Cryptologia . 20 (3): 243. doi : 10.1080/0161-119691884933 . S2CID 205488749 .

[19] Ellis, James H. (1970 ?? ???????). ≪THE POSSIBILITY OF SECURE NON-SECRET DIGITAL ENCRYPTION≫ (PDF) . {{ cite journal }}: Cite journal requires |journal= ( ?????????? )

[20] Sawer, Patrick (2016 ?? ????? 11). ≪The unsung genius who secured Britain's computer defences and paved the way for safe online shopping≫ . The Telegraph .

[zdnet-21] 21,0 ^21,1 Espiner, Tom (2010 ?? ?????????? 26). ≪GCHQ pioneers on birth of public key crypto≫ . www.zdnet.com .

[singh-22] Singh, Simon (1999). The Code Book . Doubleday. ???? 279 ?292.

[Diffie_1976-23] Diffie, Whitfield ; Hellman, Martin E. (1976 ?? ????????). ≪New Directions in Cryptography≫ (PDF) . IEEE Transactions on Information Theory . 22 (6): 644?654. CiteSeerX 10.1.1.37.9720 . doi : 10.1109/TIT.1976.1055638 . ?????????? (PDF) ?????????? 2014 ?? ????????? 29-??.

[24] ≪Asymmetric encryption≫ . IONOS Digitalguide (????????) . ??????? ? 2022 ?? ??????? 9-?? .

[rsa-25] Rivest, R.; Shamir, A.; Adleman, L. (1978 ?? ???????). ≪A Method for Obtaining Digital Signatures and Public-Key Cryptosystems≫ (PDF) . Communications of the ACM . 21 (2): 120?126. CiteSeerX 10.1.1.607.2677 . doi : 10.1145/359340.359342 . S2CID 2873616 . ?????????? ? ?????????? (PDF) 2008 ?? ?????????? 17-?? . ??????? ? 2023 ?? ?????? 2-?? .

[26] Robinson, Sara (2003 ?? ??????). ≪Still Guarding Secrets after Years of Attacks, RSA Earns Accolades for its Founders≫ (PDF) . SIAM News . 36 (5). ?????????? ? ?????????? (PDF) 2017 ?? ???????? 16-?? . ??????? ? 2023 ?? ?????? 2-?? .

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