# Pairing-Friendly Elliptic Curves of Prime Order

@inproceedings{Barreto2005PairingFriendlyEC, title={Pairing-Friendly Elliptic Curves of Prime Order}, author={Paulo Barreto and Michael Naehrig}, booktitle={Selected Areas in Cryptography}, year={2005} }

Previously known techniques to construct pairing-friendly curves of prime or near-prime order are restricted to embedding degree $k \leqslant 6 $. More general methods produce curves over ${\mathbb F}_{p}$ where the bit length of p is often twice as large as that of the order r of the subgroup with embedding degree k; the best published results achieve ρ ≡ log(p)/log(r) ~ 5/4. In this paper we make the first step towards surpassing these limitations by describing a method to construct elliptic…

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## 935 Citations

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