// Initialize Elligator 1 parameters given magic point s
func (el *el1param) init(ec *curve, s *big.Int) *el1param {
var two, invc, cm1, d nist.Int
el.ec = ec
el.s.Init(s, &ec.P)
// c = 2/s^2
two.Init64(2, &ec.P)
el.c.Mul(&el.s, &el.s).Div(&two, &el.c)
// r = c+1/c
invc.Inv(&el.c)
el.r.Add(&el.c, &invc)
// Precomputed values
el.r2m2.Mul(&el.r, &el.r).Sub(&el.r2m2, &two) // r^2-2
el.invc2.Mul(&invc, &invc) // 1/c^2
el.pp1d4.Add(&ec.P, one).Div(&el.pp1d4, big.NewInt(4)) // (p+1)/4
cm1.Sub(&el.c, &ec.one)
el.cm1s.Mul(&cm1, &el.s) // (c-1)s
el.m2.Init64(-2, &ec.P) // -2
// 2s(c-1)Chi(c)/r
chi(&el.c3x, &el.c)
el.c3x.Mul(&el.c3x, &two).Mul(&el.c3x, &el.s).Mul(&el.c3x, &cm1)
el.c3x.Div(&el.c3x, &el.r)
// Sanity check: d = -(c+1)^2/(c-1)^2
d.Add(&el.c, &ec.one).Div(&d, &cm1).Mul(&d, &d).Neg(&d)
if d.Cmp(&ec.d) != 0 {
panic("el1 init: d came out wrong")
}
return el
}