Cryptology ePrint Archive: Report 2006/144

Implementing Cryptographic Pairings on Smartcards

Michael Scott and Neil Costigan and Wesam Abdulwahab

Abstract: 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.

Category / Keywords: implementation / Elliptic curves, pairing-based cryptosystems, Fast implementations

Date: received 12 Apr 2006, last revised 4 May 2006

Contact author: mike at computing dcu ie

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Version: 20060504:095002 (All versions of this report)

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