￾ "!"#%$&$(')$(* +-,.,"/10123!547698&,": $(;(6< ,.=&8?>A@ BDCFEHGI KJ LK >NMOEQPR J S UTV >? J WDX E YZ J 1 J >? [ \M U>^]`_ _ a E b( c 1 Z J U 7 J >& U K edfd3dhgUifjfi khg1lOj m3nhg1ofdOj mfpfkOqfr3rsgUifjRt nOj3i [ uM U K wv U J KWx 7 y y Vz{ J v| A KTK } T~ O 7 J ~ Ky KT U J TwP K U€ QJ ? @A R ‚fƒ M. K 7 U€ J- ^vQ J W{ „  U€ PH K>O J … J W† ‡ Z „ U€J v y€ FTK B| f ^TV Q ^ A K U J Qyˆc KE ￾ € O 7 JW R J ` ‰ Š3 KJ WD D@ €J W €J v „c y‹ € y †TV Œ Q @A 3 ‚f>ˆ 3TK Q BO J vI w U RW c TK J v T K { w K JŽ A K U J y c U †  A K U J5T K ` J v ‰TK B > „ 7 ‚f J v Ky KT QJ €T-T K Œ ‘PR y€ Q@ y€ † U ’ ’PR y^@ B K U sz{‹ c U€ h A K U ~ U€ QJ J7z{ U‹ €J v~ Q [ Mˆ U K U E &ŠOTK K < •z{ K U ‰ ‘PH K 1V U€W W KJ@ BŽ ‰ U O TK } T- O 7 J5 @A ‘PH > ‰ 1 J W W™TK BO v xJ €T Q [ \M U K Z y€ K % š € h Ky KT U J ThP K U€ QJ ƒ ›F Kœ  € @O 3 ‚ŒJ QJ BD ‡ F 7 ‘B @A Z K 3W c TK W‰ & U J U ~œ KW‰ J† QJ BD Q u @ B J Bž 7 K QJ >h Ky KT U J T‰ „ 7 TV J TK y >h€J TKy c W J vŸ RT BN J v > 7 TK U } y ~ J v > J W KT W €J vQ>% š@ B5 J B€J Q 7 J 1 U v Œ e ’ ’PR ys 1BO ‡ 7>?z{œ c ~ U€ A K U ~ U€ QJ J7z{ U‹ €J v~ Q { c @ y € U K UE ￾ 7T J J † Q [ M {W R …J ~ Š3 KJ Wx -T BN J vD …v J K U ysW ‡ @ c J > Q ~ ` J >N Q T K ` J v•J ’z¡ze ‚f >N ^ y KEhX A KT €} Te O 7€ U Jx „c 1 {@O @< J KWD J7z{ U‹ €J v~ Q [ \M U K Z Uc TV T BN J v E ¢T ] _ _Q£•@ BŽ [^ ¤M >¥¦J T E . Chapter Overview of Cryptography Contents in Brief 1.1 Introduction §?§N§?§?§?§&§?§?§?§&§?§?§&§?§?§?§&§?§?§?§N§?§?§&§?§?§?§&§ 1 1.2 Information security and cryptography §?§&§?§?§?§N§?§?§&§?§?§?§&§ 2 1.3 Background on functions §?§?§&§?§?§&§?§?§?§&§?§?§?§N§?§?§&§?§?§?§&§ 6 1.4 Basic terminology and concepts §?§?§&§?§?§?§&§?§?§?§N§?§?§&§?§?§?§&§ 11 1.5 Symmetric-key encryption §?§&§?§?§&§?§?§?§&§?§?§?§N§?§?§&§?§?§?§&§ 15 1.6 Digital signatures §?§?§&§?§?§?§&§?§?§&§?§?§?§&§?§?§?§N§?§?§&§?§?§?§&§ 22 1.7 Authentication and identification §?§&§?§?§?§&§?§?§?§N§?§?§&§?§?§?§&§ 24 1.8 Public-key cryptography §?§?§&§?§?§&§?§?§?§&§?§?§?§N§?§?§&§?§?§?§&§ 25 1.9 Hash functions §?§?§?§&§?§?§?§&§?§?§&§?§?§?§&§?§?§?§N§?§?§&§?§?§?§&§ 33 1.10 Protocols and mechanisms §?§&§?§?§&§?§?§?§&§?§?§?§N§?§?§&§?§?§?§&§ 33 1.11 Key establishment, management, and certification §N§?§?§&§?§?§?§&§ 35 1.12 Pseudorandom numbers and sequences §?§&§?§?§?§N§?§?§&§?§?§?§&§ 39 1.13 Classes of attacks and security models §?§?§&§?§?§?§N§?§?§&§?§?§?§&§ 41 1.14 Notes and further references §&§?§?§&§?§?§?§&§?§?§?§N§?§?§&§?§?§?§&§ 45 1.1 Introduction Cryptography has a long and fascinating history. The most complete non-technical account of the subject is Kahn’s The Codebreakers. This book traces cryptography from its initial and limited use by the Egyptians some 4000 years ago, to the twentieth century where it played a crucial role in the outcome of both world wars. Completed in 1963, Kahn’s book coversthose aspects of the history which were mostsignificant(up to thattime) to the devel￾opment of the subject. The predominant practitioners of the art were those associated with the military, the diplomatic service and government in general. Cryptography was used as a tool to protect national secrets and strategies. The proliferation of computers and communicationssystemsin the 1960s brought with it a demand from the private sector for means to protect information in digital form and to provide security services. Beginning with the work ofFeistel at IBM in the early 1970s and culminating in 1977 with the adoption as a U.S. Federal Information Processing Standard for encrypting unclassified information, DES, the Data Encryption Standard, is the most well-known cryptographic mechanism in history. It remains the standard means for secur￾ing electronic commerce for many financial institutions around the world. The moststriking developmentin the history of cryptography came in 1976 when Diffie and Hellman published New Directionsin Cryptography. This paper introduced the revolu￾tionary concept of public-key cryptography and also provided a new an