Implementing Cryptographic Pairings on Smartcards

Pairings on elliptic curves are fast coming of age as cryptographic primitives for deployment in new security applications, particularly 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 HiPerSmart, an instantiation of the MIPS-32 based SmartMIPS architecture. Three types of pairing are considered, first the standard Tate pairing on a nonsupersingular curve E(Fp), second the Ate pairing, also on a nonsupersingular curve E(Fp), and finally the ηT pairing on a supersingular curve E(F2m). We demonstrate that pairings can be calculated as efficiently as classic cryptographic primitives on this architecture, with a calculation time of as little as 0.15 seconds.