Finite field multiplication combining AMNS and DFT approach for pairing cryptography
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چکیده
Pairings over ellitpic curve use fields Fpk with p ≥ 2 and 6 < k ≤ 32. In this paper we propose to represent elements in Fp 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 Fp. The DFT/FFT approach for multiplication in extension field Fpk is thus optimized. The resulting complexity of a multiplication in Fpk combining AMNS and DFT is about 50% less than the previously recommended approach [11].
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Finite Field Multiplication Combining AMNS and DFT Approach for Pairing Cryptography
Pairings over ellitpic curve use fields Fpk with p ≥ 2 and 6 < k ≤ 32. In this paper we propose to represent elements in Fp 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 Fp. The DFT/FFT approach for multiplication in extension field Fpk is thus optimized. The resulting complexity of a...
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