These are the proceedings of WAIFI 2010, the Third International Workshop on theArithmeticofFiniteFields, heldinIstanbul, Turkey, duringJune27-30,2010. The ?rst workshop, WAIFI 2007, was held in Madrid, Spain, and then WAIFI 2008 was held in Siena, Italy. In 2008, the workshop series was made biannual and it is now being held every even year, bringing together mathematicians, computer scientists, engineers and physicists who are doing research on various aspects of ?nite ?eld arithmetic. This year the workshop received 33 submissions, each of which was reviewed by at least three reviewerswho were either members of the ProgramCommittee of the workshop or external reviewers chosen by the members. Once the review phase was over, the Program Committee had online discussions over a period of several days. In the end, a total of 15 papers representing both theoretical and practical aspects of ?nite ?eld arithmetic were accepted for presentation. These accepted papers are part of these proceedings. In addition to the presentations of these papers, we were fortunate to have three invited talks given by P. Vijay Kumar, Alfred Menezes andHenning Stichtenoth. Thepapers, whichthe invited talks were based on, are also part of the proceedings. We are very grateful to the members of the Program Committee for their dedication, professionalism and careful work with the review and selection p- cess. We also sincerely thank the external reviewers who contributed with their special expertise to review papers for this wor