[Resource Topic] 2006/144: Implementing Cryptographic Pairings on Smartcards

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Implementing Cryptographic Pairings on Smartcards

Authors: Michael Scott, Neil Costigan, Wesam Abdulwahab


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 Hi{P}er{S}mart\texttrademark , an instantiation of the MIPS-32 based Smart{MIPS}\texttrademark architecture. Three types of pairing are considered, first the standard Tate pairing on a nonsupersingular curve E(\F_p), second the Ate pairing, also on a nonsupersingular curve E(\F_p), and finally the \eta_T pairing on a supersingular curve
E(\F_{2^m}). 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.

ePrint: https://eprint.iacr.org/2006/144

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