International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Efficient Algorithms for Pairing-Based Cryptosystems

Paulo S.L.M. Barreto
Hae Y. Kim
Ben Lynn
Michael Scott
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Abstract: We describe fast new algorithms to implement recent cryptosystems based on the Tate pairing. In particular, our techniques improve pairing evaluation speed by a factor of about 55 compared to previously known methods in characteristic 3, and attain performance comparable to that of RSA in larger characteristics. We also propose faster algorithms for scalar multiplication in characteristic 3 and square root extraction over $\GF{p^m}$, the latter technique being also useful in contexts other than that of pairing-based cryptography.
  title={Efficient Algorithms for Pairing-Based Cryptosystems},
  booktitle={IACR Eprint archive},
  keywords={implementation/elliptic curve cryptosystem, Tate pairing, pairing-based cryptosystem},
  note={Accepted for Crypto'2002 11909 received 10 Jan 2002, last revised 10 Aug 2002},
  author={Paulo S.L.M. Barreto and Hae Y. Kim and Ben Lynn and Michael Scott},