Refinement of Miller’s Algorithm Over Edwards Curves
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Edwards gave a new form of elliptic curves in , and these curves were introduced to cryptography by Bernstein and Lange in . The Edwards curves enjoy faster addition and doubling operations, so they are very attractive for elliptic curve cryptography.
In 2006, Blake, Murty and Xu proposed three refinements to Millers algorithm for computing Weil/Tate pairings over Weierstraß curves. In this paper we extend their method to Edwards curve and propose a faster algorithm for computing pairings with Edwards coordinates, which comes from the analysis of divisors of rational functions.
KeywordsCryptography bilinear pairing Miller algorithm twisted Edwards curve
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- 3.Menezes, A.J., Okamoto, T., Vanstone, S.A.: Reducing Elliptic Curve Logarithms to Logarithms in a Finite Field. IEEE Transactions on Information Theory (1993)Google Scholar
- 14.Aréne, C., Lange, T., Naehrig, M., Ritzenthaler, C.: Faster Pairing Computation. Cryptology ePrint Archive, Report 2009/155 (2009)Google Scholar