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#elligator2:
# curve a*x^2+y^2==1+d*x^2*y^2
# input r0
# n is any non-square
#
elligator2(p,a,d, n, r0, X,Y,Z,T) mod(p) {
r = n*r0*r0;
D = (d*r+a-d)*(d*r-a*r-d);
N = (r+1)*(a-2*d);
ND = N*D;
if(ND == 0) {
c = 1;
e = 0;
} else {
e = msqrt(ND, p);
if(e != 0) {
c = 1;
e = 1/e;
} else {
c = -1;
e = n*r0*misqrt(n*ND, p);
}
}
s = c*N*e;
t = -c*N*(r-1)*((a-2*d)*e)^2-1;
X = 2*s*t;
Y = (1-a*s*s)*(1+a*s*s);
Z = (1+a*s*s)*t;
T = (2*s)*(1-a*s*s);
}
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