Showing papers presented at "International Conference on Cryptology in Africa in 2008"

Efficient Multiplication in \mathbb{F}_{3^{\ell m}}, m ≥ 1 and 5 ≤ ℓ ≤ 18

Abstract: Using a method based on Chinese Remainder Theorem for polynomial multiplication and suitable reductions, we obtain an efficient multiplication method for finite fields of characteristic 3. Large finite fields of characteristic 3 are important for pairing based cryptography [3]. For 5 ≤ l ≤ 18, we show that our method gives canonical multiplication formulae over \(\mathbb{F}_{3^{\ell m}}\) for any m ≥ 1 with the best multiplicative complexity improving the bounds in [6]. We give explicit formula in the case \(\mathbb{F}_{3^{6 \cdot 97}}\).