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Pairings on elliptic curves are fast coming of age as crypto- graphic primitives for deployment in new security applications, partic- ularly in the context of implementations of Identity-Based Encryption (IBE). In this paper we describe the implementation of various pairings on a contemporary 32-bit smart-card, the Philips HiPerSmartTM, an instantiation of the MIPS-32 based SmartMIPSTM architecture. Three types of pairing are considered, flrst the standard Tate pairing on a non- supersingular curve E(Fp), second the Ate pairing, also on a nonsuper- singular curve E(Fp), and flnally the ·T pairing on a supersingular curve E(F2m). We demonstrate that pairings can be calculated as e-ciently as classic cryptographic primitives on this architecture, with a calculation time of as little as 0.15 seconds.
Cryptographic Hardware and Embedded Systems - CHES 2006, 8th International Workshop, Yokohama, Japan, October 10-13, 2006, Proceedings; 01/2006