Abstract
Pairings on elliptic curves usually take as input a point in a subgroup G 1 of an elliptic curve group \(E({\mathbb{F}}_p)\) and a point in a subgroup G 2 of \(E'({\mathbb{F}}_{p^d})\) for some twist E′ of E. In this paper we consider the problem of hashing to G 2 when the group G 2 has prime order. The naive approach requires multiplication in the group \(E'({\mathbb{F}}_{p^d})\) by a large cofactor. Our main result is to describe a fast method to compute this cofactor multiplication; our method exploits an efficiently computable homomorphism.
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Scott, M., Benger, N., Charlemagne, M., Dominguez Perez, L.J., Kachisa, E.J. (2009). Fast Hashing to G 2 on Pairing-Friendly Curves. In: Shacham, H., Waters, B. (eds) Pairing-Based Cryptography – Pairing 2009. Pairing 2009. Lecture Notes in Computer Science, vol 5671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03298-1_8
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DOI: https://doi.org/10.1007/978-3-642-03298-1_8
Publisher Name: Springer, Berlin, Heidelberg
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