https://hal-lirmm.ccsd.cnrs.fr/lirmm-00181362Bajard, Jean-ClaudeJean-ClaudeBajardARITH - Arithmétique informatique - LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier - UM - Université de Montpellier - CNRS - Centre National de la Recherche ScientifiqueEl Mrabet, NadiaNadiaEl MrabetARITH - Arithmétique informatique - LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier - UM - Université de Montpellier - CNRS - Centre National de la Recherche ScientifiquePairing in Cryptography: an Arithmetic Point of ViewHAL CCSD2007computer arithmeticarithmeticprime finite fieldarithmetic operatorelliptic curve cryptographypairingimplementation[INFO.INFO-CR] Computer Science [cs]/Cryptography and Security [cs.CR][INFO.INFO-AO] Computer Science [cs]/Computer ArithmeticEl Mrabet, NadiaFranklin T. Luk2007-10-23 15:43:442022-09-06 17:01:022007-11-09 19:20:08enConference papershttps://hal-lirmm.ccsd.cnrs.fr/lirmm-00181362/document10.1117/12.733789application/pdf1The pairing is a mathematical notion wich appeared in cryptography during the 80'. At the beginning, it was used to build attacks on cryptosystems, transferring the discrete logarithm problem on elliptic curves, to a discrete logarithm problem on ﬁnite ﬁelds, the ﬁrst was the MOV36 attack in 1993. Now, pairings are used to construct some cryptographic protocols: Diﬃe Hellman tripartite, identity based encryption, or short signature. The main two pairings usually used are the Tate and Weil pairings. They use distortions and rationnal functions, and their complexities depends of the curve and the ﬁeld involved. This study deals with two particular papers: one due to N. Koblitz and A. Menezes27 published in 2005, and a second one written by R Granger, D. Page and N. Smart24 in 2006. These two papers compare Tate and Weil pairings, but they diﬀer in their conclusions. We consider the diﬀerent arithmetic tricks used, trying to precise each point, in a way to avoid any ambiguity. Thus, the arithmetics proposed take into account the features of the ﬁelds and the curves used. We clarify the complexity of the possible implementations. We compare the diﬀerent approaches, in order to clarify the conclusions of the previous papers.