ThetafunctionsandapplicationsincryptographyFonctionsthêtaetapplicationsencryptographieThèsed’informatique1DamienRobert1Caramelteam,NancyUniversités,CNRS,INRIANancyGrandEst21/07/2010(Nancy)Outline1 Public-keycryptography2 Abelianvarieties3 Thetafunctions4 Pairings5 Isogenies6 PerspectivesDamienRobert (Caramel,LORIA) Thetafunctionsandcryptography 21/07/2010(Nancy) 2/40Public-keycryptographyOutline1 Public-keycryptography2 Abelianvarieties3 Thetafunctions4 Pairings5 Isogenies6 PerspectivesDamienRobert (Caramel,LORIA) Thetafunctionsandcryptography 21/07/2010(Nancy) 3/40Public-keycryptography Public-keysystemsA briefhistoryofpublic-keycryptographySecret-keycryptography:Vigenère(1553),Onetimepad(1917),AES(NIST,2001).Public-keycryptography:Diffie–Hellmankeyexchange(1976).RSA(1978):multiplication/factorisation.∗ElGamal:exponentiation/discretelogarithminG =F .qECC/HECC(1985):discretelogarithminG = A(F ).qLattices,NTRU(1996),IdealLattices(2006):perturbatealatticepoint/ClosestVectorProblem,BoundedDistanceDecoding.Polynomialsystems,HFE(1996):evaluatingpolynomials/findingroots.Coding-basedcryptography,McEliece(1978):Matrix.vector/decodingalinearcode.⇒ Encryption,Signature(+PseudoRandomNumberGenerator,ZeroKnowledge).Pairing-basedcryptography(2000–2001).Homomorphiccryptography(2009).DamienRobert (Caramel,LORIA) Thetafunctionsandcryptography 21/07/2010(Nancy) 4/40Public-keycryptography Public-keysystemsRSA versus(H)ECCSecurityRSA ...