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/pq_test.go

@@ -0,0 +1,53 @@
+package crypto
+
+import (
+	"math/big"
+	"math/rand"
+	"testing"
+)
+
+func TestDecomposePQ(t *testing.T) {
+	for _, tt := range []struct {
+		pq, p, q *big.Int
+	}{
+		// Testing vectors taken from one of SplitPQ implementations.
+		// * https://github.com/sdidyk/mtproto/blob/cf2cb57ade6932a7e0854f2e3246492a2028d369/math_test.go
+		{big.NewInt(1724114033281923457), big.NewInt(1229739323), big.NewInt(1402015859)},
+		{big.NewInt(378221), big.NewInt(613), big.NewInt(617)},
+		{big.NewInt(15), big.NewInt(3), big.NewInt(5)},
+
+		// Testing vector taken from telegram docs.
+		// * https://core.telegram.org/mtproto/samples-auth_key#4-encrypted-data-generation
+		{big.NewInt(0x17ED48941A08F981), big.NewInt(0x494C553B), big.NewInt(0x53911073)},
+	} {
+		rnd := rand.New(rand.NewSource(239))
+		p, q, err := DecomposePQ(tt.pq, rnd)
+		if err != nil {
+			t.Fatal(err)
+		}
+		if tt.p.Cmp(p) != 0 || tt.q.Cmp(q) != 0 {
+			t.Errorf("PQ mismatch: %v %v, want %v %v", p, q, tt.p, tt.q)
+		}
+	}
+}
+
+func BenchmarkDecomposePQ(b *testing.B) {
+	// DecomposePQ is used as Proof of Work so it is not required to be
+	// very fast, leaving this benchmark here as a reference.
+	//
+	// This runs at ~300ms on Intel 8700k and allocates ~30mb, probably we
+	// can at least reduce allocations.
+	b.ReportAllocs()
+
+	pq := big.NewInt(0x17ED48941A08F981)
+	rnd := rand.New(rand.NewSource(239))
+	for i := 0; i < b.N; i++ {
+		p, q, err := DecomposePQ(pq, rnd)
+		if err != nil {
+			b.Fatal(err)
+		}
+		if p == nil || q == nil {
+			b.Fatal("nil")
+		}
+	}
+}