bn

 Barreto-Naehrig curves

 

p(t) = 36t 4 + 36t 3 + 24t 2 + 6t + 1,

r(t) = 36t 4 + 36t 3 + 18t 2 + 6t + 1, 

tr(t) = 6t 2 + 1,

 

func main() {
   p := 6 * 66410 + 1
   r := 6 * 66310 + 1
   d := 1
   for i := 1; i < 0xfffffffff; i++{
      d *= p
      d = d % r
      //fmt.Println(d)
      if d == 1 {
         fmt.Println(i)
         return
      }
   }
}

func zmain() {
   //u, _ := new(big.Int).SetString("6518589491078791937", 10)
   for j := 1; j < 0xfffffff; j++{
      u := big.NewInt(int64(j))
      u2 := new(big.Int).Mul(u, u)
      u3 := new(big.Int).Mul(u2, u)
      u4 := new(big.Int).Mul(u3, u)
      p := new(big.Int).Mul(u4, big.NewInt(36))
      p.Add(p, new(big.Int).Mul(u3, big.NewInt(36)))
      p.Add(p, new(big.Int).Mul(u, big.NewInt(6)))
      p.Add(p, big.NewInt(1))
      r := new(big.Int).Set(p)
      p.Add(p, new(big.Int).Mul(u2, big.NewInt(24)))
      r.Add(r, new(big.Int).Mul(u2, big.NewInt(18)))
      //fmt.Println(p)
      //fmt.Println(r)
      for i := 1; i < 0xfffffffff; i++{
         d := new(big.Int).Exp(p, new(big.Int).SetUint64(uint64(i)), r)
         if d.Cmp(new(big.Int).SetUint64(1)) == 0 {
            if i == 12 {
               break
            }
            fmt.Println(j)
            fmt.Println(i)
         }
      }
   }
}