Finite Field Multiplication Combining AMNS and DFT Approach for Pairing Cryptography

@inproceedings{Mrabet2009FiniteFM,
  title={Finite Field Multiplication Combining AMNS and DFT Approach for Pairing Cryptography},
  author={Nadia El Mrabet and Christophe N{\`e}gre},
  booktitle={ACISP},
  year={2009}
}
Pairings over elliptic curves use fields $\mathbb{F}_{p^k}$ with p *** 2160 and 6 < k ≤ 32. In this paper we propose to represent elements in $\mathbb{F}_p$ with AMNS sytem of [1]. For well chosen AMNS we get roots of unity with sparse representation. The multiplication by these roots are thus really efficient in $\mathbb{F}_p$. The DFT/FFT approach for multiplication in extension field $F_{p^k}$ is thus optimized. The resulting complexity of a multiplication in $\mathbb{F}_{p^k}$ combining… 
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