Title :
Bit-Parallel Polynomial Basis Multiplier for New Classes of Finite Fields
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Windsor, Windsor, ON
Abstract :
In this paper, three small classes of finite fields GF(2m) are found for which low complexity bit-parallel multipliers are proposed. The proposed multipliers have lower complexities compared to those based on the irreducible pentanomials. It is also shown that there does not always exist an irreducible all-one polynomial, equally-spaced polynomial, or trinomial for the new classes of fields.
Keywords :
circuit complexity; digital arithmetic; multiplying circuits; bit-parallel polynomial basis multiplier; equally-spaced polynomial; finite fields; irreducible all-one polynomial; irreducible pentanomial; low complexity bit-parallel multiplier; Application software; Arithmetic; Computer architecture; Electrostatic precipitators; Elliptic curve cryptography; Galois fields; Hardware; Polynomials; Very large scale integration; Finite fields arithmetic; hardware architecture; irreducible polynomial.; polynomial basis;
Journal_Title :
Computers, IEEE Transactions on
