Cryptology ePrint Archive: Report 2005/139

Scaling security in pairing-based protocols

Michael Scott

Abstract: In number theoretic cryptography there is always the problem of scaling-up security to a higher level. This usually means increasing the size of the modulus, from, say 1024 bits to 2048 bits. In pairing-based cryptography however another option is available, keeping the modulus constant and increasing instead the embedding degree. This has a big potential advantage in smart-card and embedded applications -- security can be scaled up while continuing to use the same sized calculations. For example a cryptographic co-processor which does 512-bit modular multiplications can be directly re-used in the higher security setting. Here we investigate the scaling-up issue in the context of prime characteristic non-supersingular elliptic curves. We also confirm the observation that at higher levels of security a slightly modified Weil pairing becomes more efficient than the Tate pairing.

Category / Keywords: public-key cryptography / Pairing-based cryptosystems

Date: received 10 May 2005, last revised 24 Feb 2006

Contact author: mike at computing dcu ie

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Note: Updated and corrected

Version: 20060224:101158 (All versions of this report)

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