move gotd fork into repo. (#111)

- update to latest telegram layer
- remove some references to fields in tg.Entities that don't exist in
the schema
- originally added here:
https://github.com/beeper/td/commit/820929062a2ba0104397bc01235ab58a9cff780e
  - referenced here
-
https://github.com/mautrix/telegramgo/commit/124f0967ed195b5a380c9bd02e170ada9710dde3
-
https://github.com/mautrix/telegramgo/commit/4205047aab2e0639217148b5d125bfaab668bd8e

pkg/gotd/crypto/check_gp.go

@@ -0,0 +1,61 @@
+package crypto
+
+import (
+	"math/big"
+
+	"github.com/go-faster/errors"
+)
+
+// CheckGP checks whether g generates a cyclic subgroup of prime order (p-1)/2, i.e. is a quadratic residue mod p.
+// Also check that g is 2, 3, 4, 5, 6 or 7.
+//
+// This function is needed by some Telegram algorithms(Key generation, SRP 2FA).
+//
+// See https://core.telegram.org/mtproto/auth_key.
+//
+// See https://core.telegram.org/api/srp.
+func CheckGP(g int, p *big.Int) error {
+	// Since g is always equal to 2, 3, 4, 5, 6 or 7,
+	// this is easily done using quadratic reciprocity law, yielding a simple condition on p mod 4g -- namely,
+	var result bool
+	switch g {
+	case 2:
+		// p mod 8 = 7 for g = 2;
+		result = checkSubgroup(p, 8, 7)
+	case 3:
+		// p mod 3 = 2 for g = 3;
+		result = checkSubgroup(p, 3, 2)
+	case 4:
+		// no extra condition for g = 4
+		result = true
+	case 5:
+		// p mod 5 = 1 or 4 for g = 5;
+		result = checkSubgroup(p, 5, 1, 4)
+	case 6:
+		// p mod 24 = 19 or 23 for g = 6;
+		result = checkSubgroup(p, 24, 19, 23)
+	case 7:
+		// and p mod 7 = 3, 5 or 6 for g = 7.
+		result = checkSubgroup(p, 7, 3, 5, 6)
+	default:
+		return errors.Errorf("unexpected g = %d: g should be equal to 2, 3, 4, 5, 6 or 7", g)
+	}
+
+	if !result {
+		return errors.New("g should be a quadratic residue mod p")
+	}
+
+	return nil
+}
+
+func checkSubgroup(p *big.Int, divider int64, expected ...int64) bool {
+	rem := new(big.Int).Rem(p, big.NewInt(divider)).Int64()
+
+	for _, e := range expected {
+		if rem == e {
+			return true
+		}
+	}
+
+	return false
+}