diff --git a/README.md b/README.md
deleted file mode 100644
index 4bc6aba..0000000
--- a/README.md
+++ /dev/null
@@ -1,2 +0,0 @@
-# MathStudySystem
-
diff --git a/doc/README.md b/doc/README.md
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index 0000000..e69de29
diff --git a/requirements.txt b/requirements.txt
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--- /dev/null
+++ b/requirements.txt
@@ -0,0 +1 @@
+PyQt6==6.7.0
\ No newline at end of file
diff --git a/src/__pycache__/app.cpython-311.pyc b/src/__pycache__/app.cpython-311.pyc
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diff --git a/src/app.py b/src/app.py
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--- /dev/null
+++ b/src/app.py
@@ -0,0 +1,14 @@
+from PyQt6.QtWidgets import QApplication
+from src.ui.main_window import MainWindow
+
+
+def main() -> None:
+    """应用程序入口：创建 QApplication，显示主窗口，并进入事件循环。"""
+    app = QApplication([])
+    window = MainWindow()
+    window.show()
+    app.exec()
+
+
+if __name__ == "__main__":
+    main()
\ No newline at end of file
diff --git a/src/services/__init__.py b/src/services/__init__.py
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index 0000000..e69de29
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diff --git a/src/services/__pycache__/storage_service.cpython-311.pyc b/src/services/__pycache__/storage_service.cpython-311.pyc
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diff --git a/src/services/__pycache__/user_service.cpython-311.pyc b/src/services/__pycache__/user_service.cpython-311.pyc
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diff --git a/src/services/email_service.py b/src/services/email_service.py
new file mode 100644
index 0000000..2d05d0c
--- /dev/null
+++ b/src/services/email_service.py
@@ -0,0 +1,66 @@
+"""
+邮件服务模块：基于 SMTP 发送验证码邮件。支持 TLS/SSL。
+"""
+import smtplib
+import ssl
+from email.message import EmailMessage
+from typing import Dict
+
+from .storage_service import StorageService
+
+
+class EmailService:
+    """负责发送邮件验证码的服务类。"""
+
+    def __init__(self, storage: StorageService) -> None:
+        """初始化邮件服务，依赖存储服务获取 SMTP 配置。"""
+        self.storage = storage
+
+    def send_verification_code(self, to_email: str, code: str) -> bool:
+        """发送验证码到指定邮箱。
+
+        参数:
+            to_email: 收件人邮箱。
+            code: 验证码字符串。
+        返回:
+            True 表示发送成功，False 表示失败。
+        """
+        config = self.storage.load_config().get('smtp', {})
+        server = config.get('server', '')
+        port = int(config.get('port', 587))
+        username = config.get('username', '')
+        password = config.get('password', '')
+        use_tls = bool(config.get('use_tls', True))
+        use_ssl = bool(config.get('use_ssl', False))
+        sender_name = config.get('sender_name', 'Math Study App')
+
+        if not server or not username or not password:
+            return False
+
+        msg = EmailMessage()
+        msg['Subject'] = '数学学习软件注册验证码'
+        msg['From'] = f"{sender_name} <{username}>"
+        msg['To'] = to_email
+        msg.set_content(f"您的注册验证码为：{code}\n该验证码10分钟内有效。")
+
+        try:
+            if use_ssl:
+                context = ssl.create_default_context()
+                with smtplib.SMTP_SSL(server, port, context=context) as smtp:
+                    smtp.login(username, password)
+                    smtp.send_message(msg)
+            else:
+                with smtplib.SMTP(server, port) as smtp:
+                    if use_tls:
+                        smtp.starttls(context=ssl.create_default_context())
+                    smtp.login(username, password)
+                    smtp.send_message(msg)
+            return True
+        except Exception:
+            return False
+
+    def update_smtp_config(self, config: Dict) -> None:
+        """更新并保存 SMTP 配置。"""
+        data = self.storage.load_config()
+        data['smtp'] = config
+        self.storage.save_config(data)
\ No newline at end of file
diff --git a/src/services/question_service.py b/src/services/question_service.py
new file mode 100644
index 0000000..7265765
--- /dev/null
+++ b/src/services/question_service.py
@@ -0,0 +1,96 @@
+"""
+试题服务模块：按小学/初中/高中生成选择题试卷，并保证同一试卷题目不重复。
+"""
+import random
+from typing import List, Dict
+
+
+class QuestionService:
+    """负责生成不同年级难度的选择题。"""
+
+    def __init__(self) -> None:
+        """初始化题目服务。"""
+        random.seed()
+
+    def generate_questions(self, level: str, count: int) -> List[Dict]:
+        """生成指定年级与数量的题目列表。
+
+        参数:
+            level: 'primary'|'middle'|'high' 三选一。
+            count: 题目数量。
+        返回:
+            题目字典列表，每个字典包含 stem, options, answer_index。
+        """
+        generators = {
+            'primary': self._gen_primary,
+            'middle': self._gen_middle,
+            'high': self._gen_high,
+        }
+        gen = generators.get(level)
+        if not gen:
+            raise ValueError('无效的年级选项')
+        seen = set()
+        questions: List[Dict] = []
+        while len(questions) < count:
+            q = gen()
+            if q['stem'] in seen:
+                continue
+            seen.add(q['stem'])
+            questions.append(q)
+        return questions
+
+    def _gen_primary(self) -> Dict:
+        """生成一题小学难度的加减法选择题。"""
+        a = random.randint(1, 50)
+        b = random.randint(1, 50)
+        op = random.choice(['+', '-'])
+        if op == '+':
+            ans = a + b
+            stem = f"计算：{a} + {b} = ?"
+        else:
+            ans = a - b
+            stem = f"计算：{a} - {b} = ?"
+        options = self._make_options(ans)
+        return {'stem': stem, 'options': options, 'answer_index': options.index(str(ans))}
+
+    def _gen_middle(self) -> Dict:
+        """生成一题初中难度的一元一次方程选择题。"""
+        a = random.randint(2, 9)
+        b = random.randint(1, 20)
+        # ax + b = 0 => x = -b / a
+        x = -b / a
+        stem = f"解方程：{a}x + {b} = 0，x = ?"
+        options = self._make_options(x, float_mode=True)
+        correct = f"{x:.2f}"
+        return {'stem': stem, 'options': options, 'answer_index': options.index(correct)}
+
+    def _gen_high(self) -> Dict:
+        """生成一题高中难度的导数计算选择题：f(x)=ax^2+bx+c 在 x0 处的导数。"""
+        a = random.randint(1, 5)
+        b = random.randint(-5, 5)
+        c = random.randint(-10, 10)
+        x0 = random.randint(-5, 5)
+        # f'(x) = 2ax + b => f'(x0) = 2a*x0 + b
+        ans = 2 * a * x0 + b
+        stem = f"设 f(x)={a}x^2+{b}x+{c}，求 f'({x0}) = ?"
+        options = self._make_options(ans)
+        return {'stem': stem, 'options': options, 'answer_index': options.index(str(ans))}
+
+    def _make_options(self, answer, float_mode: bool = False) -> List[str]:
+        """根据正确答案生成 4 个选项（包含正确答案与3个干扰项）。"""
+        opts = set()
+        if float_mode:
+            correct = f"{answer:.2f}"
+            opts.add(correct)
+            while len(opts) < 4:
+                delta = random.uniform(-5, 5)
+                opts.add(f"{answer + delta:.2f}")
+        else:
+            correct = str(answer)
+            opts.add(correct)
+            while len(opts) < 4:
+                delta = random.randint(-10, 10)
+                opts.add(str(answer + delta))
+        options = list(opts)
+        random.shuffle(options)
+        return options
\ No newline at end of file
diff --git a/src/services/storage_service.py b/src/services/storage_service.py
new file mode 100644
index 0000000..7c41bd4
--- /dev/null
+++ b/src/services/storage_service.py
@@ -0,0 +1,85 @@
+"""
+存储服务模块：使用 JSON 文件持久化数据（不使用数据库）。
+提供用户数据与配置数据的读写接口。
+"""
+import json
+import os
+from typing import Dict, Any, List
+
+
+class StorageService:
+    """使用 JSON 文件进行数据持久化的服务类。"""
+
+    def __init__(self) -> None:
+        """初始化存储路径并确保必要文件存在。"""
+        base_dir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
+        self.storage_dir = os.path.join(base_dir, 'storage')
+        self.users_file = os.path.join(self.storage_dir, 'users.json')
+        self.config_file = os.path.join(self.storage_dir, 'config.json')
+        self._ensure_files()
+
+    def _ensure_files(self) -> None:
+        """确保存储目录与文件存在，如不存在则创建。"""
+        os.makedirs(self.storage_dir, exist_ok=True)
+        if not os.path.exists(self.users_file):
+            with open(self.users_file, 'w', encoding='utf-8') as f:
+                json.dump({'users': []}, f, ensure_ascii=False, indent=2)
+        if not os.path.exists(self.config_file):
+            with open(self.config_file, 'w', encoding='utf-8') as f:
+                json.dump({
+                    'smtp': {
+                        'server': '',
+                        'port': 587,
+                        'username': '',
+                        'password': '',
+                        'use_tls': True,
+                        'use_ssl': False,
+                        'sender_name': 'Math Study App'
+                    }
+                }, f, ensure_ascii=False, indent=2)
+
+    def load_users(self) -> Dict[str, List[Dict[str, Any]]]:
+        """读取用户列表数据。返回字典 {'users': [...]}。"""
+        with open(self.users_file, 'r', encoding='utf-8') as f:
+            return json.load(f)
+
+    def save_users(self, data: Dict[str, List[Dict[str, Any]]]) -> None:
+        """写入用户列表数据到文件。"""
+        with open(self.users_file, 'w', encoding='utf-8') as f:
+            json.dump(data, f, ensure_ascii=False, indent=2)
+
+    def load_config(self) -> Dict[str, Any]:
+        """读取配置数据（包含 SMTP 配置）。"""
+        with open(self.config_file, 'r', encoding='utf-8') as f:
+            return json.load(f)
+
+    def save_config(self, data: Dict[str, Any]) -> None:
+        """写入配置数据到文件。"""
+        with open(self.config_file, 'w', encoding='utf-8') as f:
+            json.dump(data, f, ensure_ascii=False, indent=2)
+
+    def get_user(self, email: str) -> Dict[str, Any] | None:
+        """根据邮箱获取用户字典，不存在返回 None。"""
+        users = self.load_users().get('users', [])
+        for u in users:
+            if u.get('email') == email:
+                return u
+        return None
+
+    def upsert_user(self, user: Dict[str, Any]) -> None:
+        """插入或更新用户字典，并立即持久化。"""
+        data = self.load_users()
+        users = data.get('users', [])
+        found = False
+        for i, u in enumerate(users):
+            if u.get('email') == user.get('email'):
+                users[i] = user
+                found = True
+                break
+        if not found:
+            users.append(user)
+        self.save_users({'users': users})
+
+    def user_exists(self, email: str) -> bool:
+        """判断指定邮箱的用户是否存在。"""
+        return self.get_user(email) is not None
\ No newline at end of file
diff --git a/src/services/user_service.py b/src/services/user_service.py
new file mode 100644
index 0000000..2006ff6
--- /dev/null
+++ b/src/services/user_service.py
@@ -0,0 +1,123 @@
+"""
+用户服务模块：处理注册、验证码、设置密码、登录与修改密码逻辑。
+"""
+import time
+from typing import Any, Dict
+
+from ..utils.security_utils import (
+    validate_email,
+    validate_password_strength,
+    generate_verification_code,
+    hash_password,
+    verify_password,
+)
+from .storage_service import StorageService
+from .email_service import EmailService
+
+
+class UserService:
+    """封装用户相关业务逻辑的服务类。"""
+
+    def __init__(self, storage: StorageService, email_service: EmailService) -> None:
+        """初始化用户服务，注入存储与邮件服务。"""
+        self.storage = storage
+        self.email_service = email_service
+
+    def request_registration(self, email: str) -> tuple[bool, str]:
+        """发起注册请求：校验邮箱，生成验证码并发送邮件。
+
+        参数:
+            email: 用户邮箱。
+        返回:
+            (success, message) 二元组，表示结果与提示信息。
+        """
+        if not validate_email(email):
+            return False, '邮箱格式不正确'
+        existing = self.storage.get_user(email)
+        if existing and existing.get('verified'):
+            return False, '该邮箱已注册'
+        code = generate_verification_code()
+        salt, code_hash = hash_password(code)
+        user = existing or {'email': email}
+        user.update({
+            'verified': False,
+            'code_salt': salt.hex(),
+            'code_hash': code_hash.hex(),
+            'code_time': int(time.time()),
+            'password_salt': '',
+            'password_hash': '',
+            'created_at': user.get('created_at') or int(time.time())
+        })
+        self.storage.upsert_user(user)
+        sent = self.email_service.send_verification_code(email, code)
+        if not sent:
+            return False, '验证码发送失败，请检查SMTP设置'
+        return True, '验证码已发送，请查收邮箱'
+
+    def verify_code(self, email: str, code: str) -> tuple[bool, str]:
+        """校验验证码并标记邮箱已验证。
+
+        参数:
+            email: 用户邮箱。
+            code: 用户输入的验证码。
+        返回:
+            (success, message)。
+        """
+        user = self.storage.get_user(email)
+        if not user:
+            return False, '用户不存在，请先注册'
+        # 10 分钟有效期
+        if int(time.time()) - int(user.get('code_time', 0)) > 600:
+            return False, '验证码已过期，请重新获取'
+        salt_hex = user.get('code_salt', '')
+        hash_hex = user.get('code_hash', '')
+        if not salt_hex or not hash_hex:
+            return False, '未找到验证码信息'
+        salt = bytes.fromhex(salt_hex)
+        hash_bytes = bytes.fromhex(hash_hex)
+        if not verify_password(code, salt, hash_bytes):
+            return False, '验证码不正确'
+        user['verified'] = True
+        # 清除验证码信息
+        user['code_salt'] = ''
+        user['code_hash'] = ''
+        self.storage.upsert_user(user)
+        return True, '邮箱验证成功，请设置密码'
+
+    def set_password(self, email: str, password: str, confirm: str) -> tuple[bool, str]:
+        """设置或重置密码：校验强度、确认一致并持久化哈希。"""
+        if password != confirm:
+            return False, '两次输入的密码不一致'
+        if not validate_password_strength(password):
+            return False, '密码需为6-10位且包含大小写字母与数字'
+        user = self.storage.get_user(email)
+        if not user or not user.get('verified'):
+            return False, '邮箱未验证或用户不存在'
+        salt, pwd_hash = hash_password(password)
+        user['password_salt'] = salt.hex()
+        user['password_hash'] = pwd_hash.hex()
+        self.storage.upsert_user(user)
+        return True, '密码设置成功'
+
+    def login(self, email: str, password: str) -> tuple[bool, str]:
+        """登录：校验邮箱存在与密码匹配。"""
+        user = self.storage.get_user(email)
+        if not user or not user.get('password_hash'):
+            return False, '用户不存在或未设置密码'
+        salt_hex = user.get('password_salt', '')
+        hash_hex = user.get('password_hash', '')
+        ok = verify_password(password, bytes.fromhex(salt_hex), bytes.fromhex(hash_hex))
+        if not ok:
+            return False, '密码不正确'
+        return True, '登录成功'
+
+    def change_password(self, email: str, old_password: str, new_password: str, confirm: str) -> tuple[bool, str]:
+        """修改密码：校验原密码正确并设置新密码。"""
+        user = self.storage.get_user(email)
+        if not user:
+            return False, '用户不存在'
+        salt_hex = user.get('password_salt', '')
+        hash_hex = user.get('password_hash', '')
+        if not verify_password(old_password, bytes.fromhex(salt_hex), bytes.fromhex(hash_hex)):
+            return False, '原密码不正确'
+        return self.set_password(email, new_password, confirm)
\ No newline at end of file
diff --git a/src/storage/config.json b/src/storage/config.json
new file mode 100644
index 0000000..e358e09
--- /dev/null
+++ b/src/storage/config.json
@@ -0,0 +1,11 @@
+{
+  "smtp": {
+    "server": "",
+    "port": 587,
+    "username": "",
+    "password": "",
+    "use_tls": true,
+    "use_ssl": false,
+    "sender_name": "Math Study App"
+  }
+}
\ No newline at end of file
diff --git a/src/storage/users.json b/src/storage/users.json
new file mode 100644
index 0000000..4ef6c8c
--- /dev/null
+++ b/src/storage/users.json
@@ -0,0 +1,3 @@
+{
+  "users": []
+}
\ No newline at end of file
diff --git a/src/ui/__init__.py b/src/ui/__init__.py
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index 0000000..e69de29
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diff --git a/src/ui/__pycache__/main_window.cpython-311.pyc b/src/ui/__pycache__/main_window.cpython-311.pyc
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diff --git a/src/ui/main_window.py b/src/ui/main_window.py
new file mode 100644
index 0000000..1888ab6
--- /dev/null
+++ b/src/ui/main_window.py
@@ -0,0 +1,141 @@
+from PyQt6.QtWidgets import (
+    QMainWindow, QWidget, QStackedWidget, QVBoxLayout, QHBoxLayout,
+    QLabel, QLineEdit, QPushButton, QMessageBox, QCheckBox
+)
+from PyQt6.QtCore import Qt
+
+from src.services.storage_service import StorageService
+from src.services.email_service import EmailService
+from src.services.user_service import UserService
+from src.services.question_service import QuestionService
+
+
+class MainWindow(QMainWindow):
+    """应用主窗口：组织各个页面并承载业务服务。"""
+
+    def __init__(self) -> None:
+        """初始化主窗口并构建基础页面。"""
+        super().__init__()
+        self.setWindowTitle("数学学习软件")
+        self.setFixedSize(900, 600)
+
+        # 业务服务初始化
+        self.storage_service = StorageService()
+        self.email_service = EmailService(self.storage_service)
+        self.user_service = UserService(self.storage_service, self.email_service)
+        self.question_service = QuestionService()
+
+        # 页面容器
+        self.stack = QStackedWidget()
+        self.setCentralWidget(self.stack)
+
+        # 先构建最基础的两个页面：登录与SMTP设置
+        self._build_login_page()
+        self._build_smtp_page()
+
+        # 默认显示登录页
+        self.stack.setCurrentIndex(0)
+
+    def _build_login_page(self) -> None:
+        """构建登录页面：邮箱+密码+登录按钮。"""
+        page = QWidget()
+        layout = QVBoxLayout(page)
+        layout.setAlignment(Qt.AlignmentFlag.AlignTop)
+
+        title = QLabel("登录")
+        title.setAlignment(Qt.AlignmentFlag.AlignCenter)
+        title.setStyleSheet("font-size: 22px; font-weight: bold; margin: 16px 0;")
+        layout.addWidget(title)
+
+        self.login_email = QLineEdit()
+        self.login_email.setPlaceholderText("请输入邮箱")
+        layout.addWidget(self.login_email)
+
+        self.login_password = QLineEdit()
+        self.login_password.setPlaceholderText("请输入密码")
+        self.login_password.setEchoMode(QLineEdit.EchoMode.Password)
+        layout.addWidget(self.login_password)
+
+        btn_row = QHBoxLayout()
+        self.btn_login = QPushButton("登录")
+        self.btn_to_smtp = QPushButton("SMTP设置")
+        btn_row.addWidget(self.btn_login)
+        btn_row.addWidget(self.btn_to_smtp)
+        layout.addLayout(btn_row)
+
+        self.btn_login.clicked.connect(self._on_login)
+        self.btn_to_smtp.clicked.connect(lambda: self.stack.setCurrentIndex(1))
+
+        self.stack.addWidget(page)
+
+    def _on_login(self) -> None:
+        """处理登录逻辑：校验输入并调用用户服务。"""
+        email = (self.login_email.text() or "").strip()
+        password = self.login_password.text() or ""
+        if not email or not password:
+            QMessageBox.warning(self, "提示", "邮箱与密码均不能为空")
+            return
+        ok, msg = self.user_service.login(email, password)
+        if ok:
+            QMessageBox.information(self, "提示", "登录成功")
+        else:
+            QMessageBox.warning(self, "提示", msg or "登录失败")
+
+    def _build_smtp_page(self) -> None:
+        """构建 SMTP 设置页面：服务器、端口、账号、授权码、TLS/SSL、发件人名。"""
+        page = QWidget()
+        layout = QVBoxLayout(page)
+        layout.setAlignment(Qt.AlignmentFlag.AlignTop)
+
+        title = QLabel("SMTP 设置")
+        title.setAlignment(Qt.AlignmentFlag.AlignCenter)
+        title.setStyleSheet("font-size: 22px; font-weight: bold; margin: 16px 0;")
+        layout.addWidget(title)
+
+        self.smtp_server = QLineEdit(); self.smtp_server.setPlaceholderText("服务器，例如 smtp.qq.com")
+        self.smtp_port = QLineEdit(); self.smtp_port.setPlaceholderText("端口，通常 465 或 587")
+        self.smtp_user = QLineEdit(); self.smtp_user.setPlaceholderText("邮箱账号，例如 123456@qq.com")
+        self.smtp_pass = QLineEdit(); self.smtp_pass.setPlaceholderText("邮箱授权码/应用密码")
+        self.smtp_pass.setEchoMode(QLineEdit.EchoMode.Password)
+        self.smtp_tls = QCheckBox("启用 TLS")
+        self.smtp_ssl = QCheckBox("启用 SSL")
+        self.smtp_sender = QLineEdit(); self.smtp_sender.setPlaceholderText("发件人显示名称，可选")
+
+        layout.addWidget(self.smtp_server)
+        layout.addWidget(self.smtp_port)
+        layout.addWidget(self.smtp_user)
+        layout.addWidget(self.smtp_pass)
+        layout.addWidget(self.smtp_tls)
+        layout.addWidget(self.smtp_ssl)
+        layout.addWidget(self.smtp_sender)
+
+        btn_row = QHBoxLayout()
+        self.btn_save_smtp = QPushButton("保存设置")
+        self.btn_back_login = QPushButton("返回登录")
+        btn_row.addWidget(self.btn_save_smtp)
+        btn_row.addWidget(self.btn_back_login)
+        layout.addLayout(btn_row)
+
+        self.btn_save_smtp.clicked.connect(self._on_save_smtp)
+        self.btn_back_login.clicked.connect(lambda: self.stack.setCurrentIndex(0))
+
+        self.stack.addWidget(page)
+
+    def _on_save_smtp(self) -> None:
+        """保存 SMTP 配置到本地 JSON，以支持验证码发送。"""
+        try:
+            port_val = int(self.smtp_port.text().strip() or '587')
+        except ValueError:
+            QMessageBox.warning(self, '提示', '端口必须为数字')
+            return
+        config = {
+            'server': self.smtp_server.text().strip(),
+            'port': port_val,
+            'username': self.smtp_user.text().strip(),
+            'password': self.smtp_pass.text(),
+            'use_tls': self.smtp_tls.isChecked(),
+            'use_ssl': self.smtp_ssl.isChecked(),
+            'sender_name': self.smtp_sender.text().strip() or 'Math Study App',
+        }
+        self.email_service.update_smtp_config(config)
+        QMessageBox.information(self, '提示', 'SMTP设置已保存')
\ No newline at end of file
diff --git a/src/utils/__init__.py b/src/utils/__init__.py
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index 0000000..e69de29
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diff --git a/src/utils/security_utils.py b/src/utils/security_utils.py
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--- /dev/null
+++ b/src/utils/security_utils.py
@@ -0,0 +1,79 @@
+"""
+安全工具模块：提供邮箱校验、密码强度校验、验证码生成、密码哈希与校验。
+遵循 Google Python 风格指南，所有函数均提供中文函数级注释。
+"""
+import re
+import secrets
+import string
+import hashlib
+from typing import Tuple
+
+
+def validate_email(email: str) -> bool:
+    """验证邮箱格式是否正确。
+
+    参数:
+        email: 待验证的邮箱字符串。
+    返回:
+        True 表示格式合法，False 表示格式不合法。
+    """
+    pattern = r"^[A-Za-z0-9._%+-]+@[A-Za-z0-9.-]+\.[A-Za-z]{2,}$"
+    return re.match(pattern, email) is not None
+
+
+def validate_password_strength(password: str) -> bool:
+    """验证密码是否满足强度要求：6-10位，必须包含大小写字母和数字。
+
+    参数:
+        password: 待验证的密码字符串。
+    返回:
+        True 表示满足要求，False 表示不满足。
+    """
+    if not (6 <= len(password) <= 10):
+        return False
+    has_upper = any(c.isupper() for c in password)
+    has_lower = any(c.islower() for c in password)
+    has_digit = any(c.isdigit() for c in password)
+    return has_upper and has_lower and has_digit
+
+
+def generate_verification_code(length: int = 6) -> str:
+    """生成数字验证码字符串。
+
+    参数:
+        length: 验证码长度，默认为 6。
+    返回:
+        由数字组成的验证码字符串。
+    """
+    return ''.join(secrets.choice(string.digits) for _ in range(length))
+
+
+def hash_password(password: str, salt: bytes | None = None) -> Tuple[bytes, bytes]:
+    """对密码进行 PBKDF2 哈希。
+
+    参数:
+        password: 原始密码。
+        salt: 可选的盐值；若未提供则自动生成。
+    返回:
+        (salt, pwd_hash) 二元组，其中 salt 为随机盐，pwd_hash 为哈希值。
+    """
+    if salt is None:
+        salt = secrets.token_bytes(16)
+    pwd_hash = hashlib.pbkdf2_hmac(
+        'sha256', password.encode('utf-8'), salt, 100_000
+    )
+    return salt, pwd_hash
+
+
+def verify_password(password: str, salt: bytes, pwd_hash: bytes) -> bool:
+    """校验密码是否与存储的哈希匹配。
+
+    参数:
+        password: 用户输入的密码。
+        salt: 存储的盐值。
+        pwd_hash: 存储的密码哈希。
+    返回:
+        True 表示匹配，False 表示不匹配。
+    """
+    calc_hash = hashlib.pbkdf2_hmac('sha256', password.encode('utf-8'), salt, 100_000)
+    return secrets.compare_digest(calc_hash, pwd_hash)
\ No newline at end of file
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