Chapter

Algorithmic Number Theory

Volume 4076 of the series Lecture Notes in Computer Science pp 480-494

High Security Pairing-Based Cryptography Revisited

  • R. GrangerAffiliated withDept. Computer Science, University of Bristol
  • , D. PageAffiliated withDept. Computer Science, University of Bristol
  • , N. P. SmartAffiliated withDept. Computer Science, University of Bristol

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Abstract

The security and performance of pairing based cryptography has provoked a large volume of research, in part because of the exciting new cryptographic schemes that it underpins. We re-examine how one should implement pairings over ordinary elliptic curves for various practical levels of security. We conclude, contrary to prior work, that the Tate pairing is more efficient than the Weil pairing for all such security levels. This is achieved by using efficient exponentiation techniques in the cyclotomic subgroup backed by efficient squaring routines within the same subgroup.