Cours.Frey

Mathematical Backgroundof Public Key CryptographyGerhard FreyUniversity of Duisburg-EssenInstitute for ExperimentalMathematicsfrey@exp-math.uni-essen.deG.A.T.ICIRM -May 12-16, 200311 Data security and ArithmeticProblem:¡¡!A open B"C(A;m;B) 7! (B;m;A)The transfer of the message has to be“secure”.This has (at least) 3 aspects:2†Reliability (engineers)†Correctness(codingtheory,engineersand mathematicians)†Authenticity,privateness(cryptogra-phy,mathematicians,computerscien-tists, engineers)Solutionshavetobesimple,efficientandcheap!3There was a basic decision some sixtyyears ago:Messages are stored and transmitted asnumbers.This makes it possible to applyArithmeticto data security.4Weshallconcentratetothethirdaspectwhich usesENCRYPTIONprovided bycryptography.This is, in the true sense of the word, aclassic discipline:We find it in Mesopotamia and Caesarused it.5Encryption Devices6The devices shown are examples forsymmetric procedures:There is a common secret amongst thepartners which enables them to de- andencrypt.In principle they are used till today, inrefined versions.The new standard is called AES.Typicallythehistoricalexamplesarein-volving secret services and military andtheinformationisexchangedamongstacommunity in which each member is tobe trusted.7This has changed dramatically becau-seofelectroniccommunicationinpublicnetworks.So data security has become a publicchallenge.Therearemillionsofpartnersin nets ...