Abstract
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 AMNS and DFT is about 50% less than the previously recommended approach [2].
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El Mrabet, N., Negre, C. (2009). Finite Field Multiplication Combining AMNS and DFT Approach for Pairing Cryptography. In: Boyd, C., González Nieto, J. (eds) Information Security and Privacy. ACISP 2009. Lecture Notes in Computer Science, vol 5594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02620-1_29
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DOI: https://doi.org/10.1007/978-3-642-02620-1_29
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