These are the proceedings of WAIFI 2008, the second workshop on the Arithmeticof Finite Fields, that was held in Siena, Italy, July 6-9, 2008. The firstworkshop, WAIFI 2007, which was held in Madrid (Spain), was received quiteenthusiastically by mathematicians, computer scientists, engineers and physicistswho are performing research on finite field arithmetic. We believe that there isa need for a workshop series bridging the gap between the mathematical theoryof finite fields and their hardware/software implementations and technical applications.We hope that the WAIFI workshop series, which from now on will beheld on even years, will help to fill this gap.There were 34 submissions to WAIFI 2008, of which the Program Committeeselected 16 for presentation. Each submission was reviewed by at least threereviewers. Our thanks go to the Program Committee members for their manycontributions and hard work.We are also grateful to the external reviewers listedbelow for their expertise and assistance in the deliberations. In addition to thecontributions appearing in these proceedings, the workshop program includedan invited lecture given by Amin Shokrollahi

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