feat : new auth in chicken

packages/chicken/lib/presentation/widget/captcha/logic.dart

@@ -0,0 +1,34 @@
+import 'dart:math';
+
+import 'package:flutter/material.dart';
+import 'package:rasadyar_core/core.dart';
+
+class CaptchaWidgetLogic extends GetxController with StateMixin<String> {
+  TextEditingController textController = TextEditingController();
+  RxnString captchaKey = RxnString();
+  GlobalKey<FormState> formKey = GlobalKey<FormState>();
+
+  final Random random = Random();
+
+  @override
+  void onInit() {
+    super.onInit();
+
+    getCaptcha();
+  }
+
+  @override
+  void onClose() {
+    textController.clear();
+    textController.dispose();
+    super.onClose();
+  }
+
+  Future<void> getCaptcha() async {
+    change(null, status: RxStatus.loading());
+    textController.clear();
+    await Future.delayed(Duration(milliseconds: 500));
+    captchaKey.value = (random.nextInt(900_000) + 100_000).toString();
+    change(captchaKey.value, status: RxStatus.success());
+  }
+}