PPT-COS 433: Cryptography

Princeton University Spring 2010 Boaz Barak Lecture 7 Chosen Plaintext Attack Block Ciphers Short Review of PRF construction 2 G f s x Snapshot after i invocations Short Review of PRF construction. cos eV RF RF RF RF RF RF RF RF RF RF eV eV cos cos cos cos RF RF RF RF RF eV eV eV RF RF RF RF RF RF RF eV eV cos cos cos 66 65 RF RF RF RF RF eV eV cos sin 66 65 5666 566 56 56 566 56 66 65 66 897 Special Topics in Cryptography Instructors Ran Canetti and Ron Rivest Lecture 25 PairingBased Cryptography May 5 2004 Scribe Ben Adida 1 Introduction The 64257eld of PairingBased Cryptography has exploded 4KEITHCONRADGeometrically,theeectofthesematricesispicturedbelow.Ontheleft,(cossinsincos)isacounterclockwiserotationbyanglearoundtheorigin.Ontheright,(cossinsincos)isare ectionacrosstheline Theabovecalculationalsoallowsustoobtain~J2,~J2=J2z+1 2(J+J+JJ+)=(jhcos)2+1 2q jh(1+cos)(jh(1cos)+h)q jh(1+cos)q jh(1cos)(jh(1+cos)+h)q jh(1cos)=j(j+1)h2:(25)3.3WaveFunctionsWe MCS320IntroductiontoSymbolicComputationSpring2007[diff(cos(t),t);#differentiationoftheformulacos(t)[diff(cos,t);#wrong![D(cos(t));#alsowrong[D(cos);#differentiationofthecosinefunctionThefollowingi WorksupportedbytheNationalScienceFoundationwhichof3formsatermcantake.Therstformis )sinh()cos( )sinh()sin(.(2)Thesecondformis kysinh(k )sinh()sin( )sin()cos()cos()cos( )sin()sin( 436F.C.J.Bertheetal.:Aquat.LivingResour.17,433 (dx0)2+(dy0)2=Z0d0q (1cos0)2+sin20=21 2Z0d0p 1cos0=23 2hp 1+cos0i0=4241s 1+cos 235:Thetotallengthofthependulumis`,thepartthatisstillstraightattimethaslength`,andsothecoordinatesoft Princeton University . Spring 2010. Boaz Barak. Please . stop me if you have questions!. 2. Cryptography. History of 2500- 4000 years.. Recurring theme: . (until 1970’s). Secret code invented. Typically claimed “unbreakable” by inventor. Symmetric Encryption. Key exchange . Public-Key Cryptography. Key exchange. Certification . Why Cryptography. General Security Goal. - . Confidentiality . (. fortrolig. ). - . End-point Authentication . Spring 2010. Boaz Barak. Lecture 7: . Chosen Plaintext Attack. Block . Ciphers. Short Review of PRF construction. 2. G. f. s. (x). Snapshot after . i. invocations.. Short Review of PRF construction. 1 nnrnrnnnnn2nnnnrrnnrnrrrnrnrrrnnr rnnrnrrnnrrrnrrnrrrrrn3rnnrnrrrrrrrnrrrrrrrrrrrnrrrrrrnnrrrrrnnrrrrnnrrrrrrrnrnrn--/012/334561/3748/7396-04-6410/4431/3/334/-0143410/412/30404634149463012146374-36- The . art and science of concealing the messages to introduce secrecy in . information security . is recognized as cryptography. .. The word ‘cryptography’ was coined by combining two Greek words, ‘Krypto’ . 4&+/&!73/!,4&!/&6('&.)J!=*,)4 (.)+-'&!V*6()!,/*(.(.9@!6-==&/!=&'()(.&!,/*(.(.9!/39/*=6@!*.'!73-/,4!J&*/!*F*J!/3,*,(3.6!F(,4(.!=(+(,*/J!4&*+,4)*/&!(.6,*++*,(3.6H!E4&!.-=V&/!37!,3-/6!J3-!*/&!*-,43/(Y&'!