# negate r when n > (p-1)/2decaf_neg(p, n, r) { mod(p) m = -r; r = n > (p-1)>>1 ? m : r;}# field F_p# curve a*x**2+y**2==1+d*x**2*y**2# input X,Y,Z,T (extended coordinates)decaf_encode(p,a,d, X,Y,Z,T, s) mod(p) { r = misqrt((a-d)*(Z+Y)*(Z-Y), p); u = (a-d)*r; decaf_neg(p, -2*u*Z, r); s = u*(r*(a*Z*X-d*Y*T)+Y)/a; decaf_neg(p, s, s);}# field F_p# curve a*x**2+y**2==1+d*x**2*y**2# input s# output in extended coordinatesdecaf_decode(p,a,d, s, ok,X,Y,Z,T) { if(s > (p-1)>>1){ ok = 0; } else mod(p) { ss = s^2; Z = 1+a*ss; u = Z^2 - 4*d*ss; v = u*ss; if(v == 0) ok = 1; else { ok = msqrt(v, p); if(ok != 0){ v = 1/ok; ok = 1; } } if(ok != 0) { decaf_neg(p, u*v, v); w = v * s * (2-Z); if(s == 0) w = w + 1; X = 2*s; Y = w * Z; T = w * X; } }}
# negate r when n > (p-1)/2
decaf_neg(p, n, r) {
mod(p) m = -r;
r = n > (p-1)>>1 ? m : r;
}
# field F_p
# curve a*x**2+y**2==1+d*x**2*y**2
# input X,Y,Z,T (extended coordinates)
decaf_encode(p,a,d, X,Y,Z,T, s) mod(p) {
r = misqrt((a-d)*(Z+Y)*(Z-Y), p);
u = (a-d)*r;
decaf_neg(p, -2*u*Z, r);
s = u*(r*(a*Z*X-d*Y*T)+Y)/a;
decaf_neg(p, s, s);
}
# field F_p
# curve a*x**2+y**2==1+d*x**2*y**2
# input s
# output in extended coordinates
decaf_decode(p,a,d, s, ok,X,Y,Z,T) {
if(s > (p-1)>>1){
ok = 0;
} else mod(p) {
ss = s^2;
Z = 1+a*ss;
u = Z^2 - 4*d*ss;
v = u*ss;
if(v == 0)
ok = 1;
else {
ok = msqrt(v, p);
if(ok != 0){
v = 1/ok;
ok = 1;
}
}
if(ok != 0) {
decaf_neg(p, u*v, v);
w = v * s * (2-Z);
if(s == 0)
w = w + 1;
X = 2*s;
Y = w * Z;
T = w * X;
}
}
}