4 research outputs found
Factoring Polynomials for Constructing Pairing-friendly Elliptic Curves
In this paper we present a new method to construct a polynomial
which will make
reducible. We construct a finite separable extension of
, denoted as . By primitive
element theorem, there exists a primitive element such that . We represent
the primitive -th root of unity by and get a
polynomial from the representation. The
resulting will make factorable
Polynomials for Ate Pairing and Pairing
The irreducible factor of and are often used in constructing pairing-friendly curves. and
are selected to be the Miller
loop control polynomial in Ate pairing and
pairing. In this paper we show that when or the minimal prime
which divides is larger than , some and can not
be used as curve generation parameters if we want
pairing to be efficient. We also show that the Miller loop length
can not reach the bound when
we use the factorization of to generate
elliptic curves