Five, Six, and Seven-Term Karatsuba-Like Formulae
IEEE Transactions on Computers
Comments on "Five, Six, and Seven-Term Karatsuba-Like Formulae"
IEEE Transactions on Computers
Improved Polynomial Multiplication Formulas over $IF₂$ Using Chinese Remainder Theorem
IEEE Transactions on Computers
Explicit formulas for efficient multiplication in F36m
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
Efficient hardware for the tate pairing calculation in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
On multiplication in finite fields
Journal of Complexity
Compact hardware for computing the tate pairing over 128-bit-security supersingular curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Multiplication of polynomials modulo xn
Theoretical Computer Science
Finding optimal formulae for bilinear maps
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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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 F3lm for any m ≤ 1 with the best multiplicative complexity improving the bounds in [6]. We give explicit formula in the case F36.97.