Algebraic complexities and algebraic curves over finite fields
Journal of Complexity
Optimal algorithms for multiplication in certain finite fields using elliptic curves
SIAM Journal on Computing
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Rational Points on Curves over Finite Fields: Theory and Applications
Rational Points on Curves over Finite Fields: Theory and Applications
Hardware Implementation of Finite Fields of Characteristic Three
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
A Generalized Method for Constructing Subquadratic Complexity GF(2^k) Multipliers
IEEE Transactions on Computers
On the Bounds of the Bilinear Complexity of Multiplication in Some Finite Fields
Applicable Algebra in Engineering, Communication and Computing
Five, Six, and Seven-Term Karatsuba-Like Formulae
IEEE Transactions on Computers
Theoretical Computer Science
Comments on "Five, Six, and Seven-Term Karatsuba-Like Formulae"
IEEE Transactions on Computers
Improved Asymptotic Bounds for Codes Using Distinguished Divisors of Global Function Fields
SIAM Journal on Discrete Mathematics
Improved Polynomial Multiplication Formulas over $IF₂$ Using Chinese Remainder Theorem
IEEE Transactions on Computers
Algebraic Function Fields and Codes
Algebraic Function Fields and Codes
Efficient multiplication in F3lm, m ≥ 1 and 5 ≤ l ≤ 18
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Constructions of algebraic-geometry codes
IEEE Transactions on Information Theory
Curves with Many Points and Multiplication Complexity in Any Extension of Fq
Finite Fields and Their Applications
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
On the tensor rank of multiplication in any extension of F2
Journal of Complexity
Multiplication of polynomials modulo xn
Theoretical Computer Science
Bilinear complexity of algebras and the Chudnovsky-Chudnovsky interpolation method
Journal of Complexity
Finding optimal formulae for bilinear maps
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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We present a method for multiplication in finite fields which gives multiplication algorithms with improved or best known bilinear complexities for certain finite fields. Our method generalizes some earlier methods and combines them with the recently introduced complexity notion M@^"q(@?), which denotes the minimum number of multiplications needed in F"q in order to obtain the coefficients of the product of two arbitrary @?-term polynomials modulo x^@? in F"q[x]. We study our method for the finite fields F"q"^"n, where 2@?n@?18 and q=2,3,4 and we improve or reach the currently best known bilinear complexities. We also give some applications in cryptography.