lastupdated:2013/10/31Asimple,shortandlightIntroductiontoEllipticCurveCryptographyWrittenbyFlorianRienhardtpeanut.@.bitnuts.deAbstractThisisaverybasicandsimplifiedintroductionintoellipticcurvecryptogra-phy.Itriedtokeepthingsassimpleaspossible.Therearenomathematicalproofsorsomething.Thewhitepaperhopefullygivesyouanicestartintothefieldof ellipticcurvecryptographywithout fearingyoutohell byusingheavyweightedproofs,definitionsandcrypticacronymsasusuallyseenonthistopic.
iTableofContents1Somebasicsaboutellipticcurves....................................................................................11.1ExampleofanellipticcureovertheFieldF23..........................................................21.2AddingdistinctpointsPandQ...................................................................................31.3DoublingthepointP.....................................................................................................32Ellipticcurvediscretelogarithm......................................................................................32.1ExampleoftheEllipticcurvediscretelogarithmproblem.....................................32.2An“AliceandBob”-example(Diffie-HellmaninECC)..........................................43Brainpoolexamplecurvedomainparameterspecification.........................................54ECCinOpenSSL.................................................................................................................64.1BrainpoolCurvesinOpenSSL.....................................................................................65Furtherreading....................................................................................................................8