feat: playable arcade — rooms, identity, client, deployment

Round length is now bounded: the multiplier follows a hyperbolic curve
diverging at 60s, replacing an exponential one where a 275x crash point
produced a two-and-a-half minute round.

Fixes seed reveal, which silently failed every round because pgx cannot
encode a fixed-size byte array as bytea.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

pkg/identity/identity_test.go

@@ -0,0 +1,86 @@
+package identity_test
+
+import (
+	"crypto/ed25519"
+	"crypto/rand"
+	"encoding/hex"
+	"errors"
+	"testing"
+
+	"github.com/drjones/quantum-arcade/pkg/identity"
+)
+
+func newKey(t *testing.T) (string, ed25519.PrivateKey) {
+	t.Helper()
+	pub, priv, err := ed25519.GenerateKey(rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+	return hex.EncodeToString(pub), priv
+}
+
+func TestValidSignatureAuthenticates(t *testing.T) {
+	a := identity.NewAuthenticator()
+	pubHex, priv := newKey(t)
+
+	nonceHex, err := a.Challenge(pubHex)
+	if err != nil {
+		t.Fatal(err)
+	}
+	nonce, _ := hex.DecodeString(nonceHex)
+	sig := ed25519.Sign(priv, nonce)
+
+	if err := a.Verify(pubHex, hex.EncodeToString(sig)); err != nil {
+		t.Fatalf("valid signature rejected: %v", err)
+	}
+}
+
+func TestWrongKeyCannotAuthenticate(t *testing.T) {
+	a := identity.NewAuthenticator()
+	pubHex, _ := newKey(t)
+	_, otherPriv := newKey(t)
+
+	nonceHex, _ := a.Challenge(pubHex)
+	nonce, _ := hex.DecodeString(nonceHex)
+	sig := ed25519.Sign(otherPriv, nonce)
+
+	if err := a.Verify(pubHex, hex.EncodeToString(sig)); !errors.Is(err, identity.ErrBadSignature) {
+		t.Fatalf("got %v, want ErrBadSignature", err)
+	}
+}
+
+// A captured signature must not work twice.
+func TestChallengeIsSingleUse(t *testing.T) {
+	a := identity.NewAuthenticator()
+	pubHex, priv := newKey(t)
+
+	nonceHex, _ := a.Challenge(pubHex)
+	nonce, _ := hex.DecodeString(nonceHex)
+	sigHex := hex.EncodeToString(ed25519.Sign(priv, nonce))
+
+	if err := a.Verify(pubHex, sigHex); err != nil {
+		t.Fatal(err)
+	}
+	if err := a.Verify(pubHex, sigHex); !errors.Is(err, identity.ErrUnknownChallenge) {
+		t.Fatalf("replay succeeded or gave %v, want ErrUnknownChallenge", err)
+	}
+}
+
+func TestMalformedKeyRejected(t *testing.T) {
+	a := identity.NewAuthenticator()
+	if _, err := a.Challenge("not-hex"); !errors.Is(err, identity.ErrBadPublicKey) {
+		t.Fatalf("got %v, want ErrBadPublicKey", err)
+	}
+	if _, err := a.Challenge("aabb"); !errors.Is(err, identity.ErrBadPublicKey) {
+		t.Fatalf("short key: got %v, want ErrBadPublicKey", err)
+	}
+}
+
+func TestVerifyWithoutChallengeFails(t *testing.T) {
+	a := identity.NewAuthenticator()
+	pubHex, priv := newKey(t)
+	sig := ed25519.Sign(priv, []byte("anything"))
+	if err := a.Verify(pubHex, hex.EncodeToString(sig)); !errors.Is(err, identity.ErrUnknownChallenge) {
+		t.Fatalf("got %v, want ErrUnknownChallenge", err)
+	}
+}