Various scholars view Deuteronomy 4:32-40 as the climax of Moses' first speech. While passage has received considerable attention on literary-critical front and in terms its theology, structure not much scholarly attention, possibly because seems quite simple (Deut 4:32-35, 36-39, 40). The question, however, that been adequately addressed is: why does Deut 4:36-39 repeat 4:32-35 part what can b...

In this paper we describe an efficient implementation of the Tate and Ate pairings using Barreto-Naehrig pairing-friendly curves, on both a standard PC and on a 32-bit smartcard. First we introduce a subfamily of such curves with a particularly simple representation. Next we consider the issues that arise in the efficient implemention of field arithmetic in Fp12 , which is crucial to good perfo...