Eecient Arithmetic in Gf (2 N ) through Palindromic Representation
نویسندگان
چکیده
A representation of the eld GF (2 n) for various values of n is described, where the eld elements are palindromic polynomials, and the eld operations are polynomial addition and multiplication in the ring of polynomials modulo x 2n+1 ?1. This representation can be shown to be equivalent to a eld representation of Type-II optimal normal bases. As such, the suggested palindromic representation inherits the advantages of two commonly-used representations of nite elds, namely, the standard (polynomial) representation and the optimal normal basis representation. Modular polynomial multiplication is well suited for software implementations, whereas the optimal normal basis representation admits eecient hardware implementations. Also, the new representation allows for eecient implementation of eld inversion in both hardware and software.
منابع مشابه
Efficient Arithmetic in GF(2n) through Palindromic Representation
finite field representation, optimal normal basis, palindromic representation A representation of the field GF(2n) for various values of n is described, where the field elements are palindromic polynomials, and the field operations are polynomial addition and multiplication in the ring of polynomials modulo x2n+1–1. This representation can be shown to be equivalent to a field representation of ...
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