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/* Finds random point of order n on curve e of order o.
* @returns [[P.x, P.y], n, h]
* @param e curve
* @param o curve order
* @param n desired point order
*/
find_point(e, o, n) = {
local(h, P);
h = o\n;
until(ellmul(e, P, n),
P = random(e);
);
return([P, n, h]);
}
/* Finds random points of orders given by vector p.
* @returns vector of points in format [[P.x, P.y], n, h]
* @param e curve
* @param o curve order
* @param p vector of point orders
*/
find_points(e, o, p) = {
return(vector(length(p),X,find_point(e, o, p[X])));
}
/*####################################################################*/
maxprime_order(e, o) = {
if(isprime(o),
return(o);
,
return(vecmax(factor(o)));
);
}
minprime_order(e, o) = {
if(isprime(o),
return(o);
,
return(factor(o)[1,1]);
);
}
max_order(e, o) = {
return(o);
}
/* Finds a random point of order given by f(o).
* @returns [[P.x, P.y], n, h]
* with P being the point with order f(o).
* @param e curve
* @param o curve order
* @param f function returning the point order, \in maxprime_order,
* minprime_order, max_order
*/
get_point(e, o, f) = {
return(find_point(e, o, f(o)));
}
/*####################################################################*/
prime_orders(e, o) = {
local(f);
if(isprime(o),
return([o]);;
,
f = factor(o);
return(vector(length(f),X,f[X,1]));
);
}
/* Finds random points of orders given by f(o).
* @returns vector of points in format [[P.x, P.y], n, h]
* @param e curve
* @param o curve order
* @param f function returning a vector of point orders
*/
get_points(e, o, f) = {
return(find_points(e, o, f(o)));
}
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