This book constitutes the refereed proceedings of the First International Workshop on the Arithmetic of Finite Fields, WAIFI 2007, held in Madrid, Spain in June 2007. It covers structures in finite fields, efficient implementation and architectures, efficient finite field arithmetic, classification and construction of mappings over finite fields, curve algebra, cryptography, codes, and discrete structures.

Thesearetheproceedingsofthe7thWorkshoponCryptographic Hardwareand EmbeddedSystems(CHES2005)heldinEdinburgh, ScotlandfromAugust29to September1,2005.TheCHESworkshophasbeensponsoredbytheInternational Association for Cryptologic Research (IACR) for the last two years. We received a total of 108 paper submissions for CHES 2005. The doub- blindreviewprocessinvolveda27-memberprogramcommittee anda largen- ber of external sub-referees. The review process concluded with a two week d- cussion process which resulted in 32 papers being selected for presentation. We are grateful to the program committee members and the external sub-referees for carrying out such an enormous task. Unfortunately, there were many strong papers that could not be included in the program due to a lack of space. We would like to thank all our colleagues who submitted papers to CHES 2005. In addition to regular presentations, there were three excellent invited talks given by Ross Anderson (University of Cambridge) on "What Identity Systems Can and Cannot Do," by Thomas Wille (Philips Semiconductors Inc) on "- curity of Identi?cation Products: How to Manage," and by Jim Ward (Trusted Computing Groupand IBM)on"TrustedComputing inEmbedded Systems."It also included a rump session, chaired by Christof Paar, featuring informal talks on recent results.