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6 Divisor functions

A divisor (class) is a pair of polynomials [u(x), v(x)] over GF(q) with \deg{v}<\deg{u}\le 2 so that they satisfy certain conditions related to the curve C. Therefore, every divisor (class) has a curve to associate with. G2HEC use a C++ class divisor to hold a divisor.

For cryptographic purposes, G2HEC does not support the existence of divisors associated with different curves in the same running process. It implements the associated genus 2 curve as a static data member of the divisor class. The client program only needs to set the curve once for a divisor, and it works for all divisors. A curve change for one divisor in a program will cause all divisors in the same program to switch to the new curve. This is another important convention of G2HEC.

We list some of the divisor class’s public member functions as follows.

divisor():

default constructor; sets u(x) = 1, v(x) = 0, and associated curve as y^2 = 0. A divisor is not valid by default.

divisor(const poly_tc& polyu, const poly_tc& polyv, const g2hcurve& curve):

constructor; set u(x) = polyu, v(x) = polyv, and associated curve to curve.

divisor(const divisor& div):

copy constructor.

void set_upoly(poly_tc& poly):

sets u(x) to poly for the divisor.

void set_vpoly(poly_tc& poly):

sets v(x) to poly for the divisor.

void set_curve(const g2hcurve& curve):

sets the associated curve to curve for divisor. The curve does not need to be a valid genus 2 curve.

void update():

This function checks and updates information related to the divisor. It must be called by a client program after any set_ routine is called. Otherwise error make occur when operations on divisor are performed.

const poly_tc& get_upoly():

returns u(x) of the divisor.

const poly_tc& get_vpoly():

returns v(x) of the divisor.

const g2hcurve& get_curve():

returns the associated curve of the divisor.

bool_t is_valid_divisor():

returns TRUE is the representation of the divisor is valid, FALSE otherwise.

bool_t is_unit():

tests if the divisor is the unit divisor [1, 0].

set_unit():

sets the divisor to the unit divisor [1, 0].

You can write divisor1 = divisor2 to assign the value of divisor2 to divisor1. divisor2 can be either valid or invalid.

You can do comparisons like divisor1 == divisor2 or divisor1 != divisor2 to test if two divisors are the same. Divisors do not need to be valid for such comparisons.

There is also a non-member function

that tests if two divisors a and b have the same associated curve. According to the way G2HEC implements the divisor class, this function always returns TRUE. Therefore this test is redundant.