Add baseline unit tests and fix home server normalization

test/crypto_service_test.dart

@@ -0,0 +1,42 @@
+import 'package:chat_server/src/auth/crypto_service.dart';
+import 'package:test/test.dart';
+
+void main() {
+  group('AuthService password hashing', () {
+    test('hash + verify works', () {
+      const password = 'pass1234';
+      final hash = AuthService.hashPassword(password);
+
+      expect(hash, isNotEmpty);
+      expect(AuthService.verifyPassword(password, hash), isTrue);
+      expect(AuthService.verifyPassword('wrong-password', hash), isFalse);
+    });
+  });
+
+  group('CryptoService signing', () {
+    test('signatures verify with matching keypair', () {
+      final keyPair = CryptoService.generateKeyPair();
+      const payload = 'alice@localhost:9870:1700000000';
+
+      final signature = CryptoService.sign(payload, keyPair.privateKey);
+      final ok = CryptoService.verify(payload, signature, keyPair.publicKey);
+
+      expect(ok, isTrue);
+    });
+
+    test('signature fails for modified payload', () {
+      final keyPair = CryptoService.generateKeyPair();
+      const payload = 'payload-a';
+      const tamperedPayload = 'payload-b';
+
+      final signature = CryptoService.sign(payload, keyPair.privateKey);
+      final ok = CryptoService.verify(
+        tamperedPayload,
+        signature,
+        keyPair.publicKey,
+      );
+
+      expect(ok, isFalse);
+    });
+  });
+}