写一个基于RSA算法的数字签名的程序包含GUI界面

以下是一个基于Python语言实现的RSA数字签名程序，包含GUI界面：

import random
import hashlib
import tkinter as tk

# 生成质数
def is_prime(num):
    if num < 2:
        return False
    for i in range(2, int(num**0.5)+1):
        if num % i == 0:
            return False
    return True

def generate_prime():
    while True:
        num = random.randint(100, 1000)
        if is_prime(num):
            return num

# 扩展欧几里得算法求解模反元素
def extended_gcd(a, b):
    if b == 0:
        return a, 1, 0
    else:
        gcd, x, y = extended_gcd(b, a % b)
        return gcd, y, x - (a // b) * y

# 生成公钥和私钥
def generate_key_pair():
    # 随机生成两个质数p和q
    p = generate_prime()
    q = generate_prime()
    n = p * q
    phi_n = (p - 1) * (q - 1)

    # 选择一个与phi_n互质的整数e作为公钥
    while True:
        e = random.randint(2, phi_n-1)
        if extended_gcd(e, phi_n)[0] == 1:
            break

    # 计算e的模反元素d作为私钥
    gcd, d, _ = extended_gcd(e, phi_n)
    d = d % phi_n
    if d < 0:
        d += phi_n

    return (n, e), (n, d)

# 加密
def encrypt(m, public_key):
    n, e = public_key
    c = pow(m, e, n)
    return c

# 解密
def decrypt(c, private_key):
    n, d = private_key
    m = pow(c, d, n)
    return m

# 签名
def sign(message, private_key):
    n, d = private_key
    hash = hashlib.sha256(message.encode('utf-8')).hexdigest()
    h = int(hash, 16)
    signature = pow(h, d, n)
    return signature

# 验证签名
def verify(message, signature, public_key):
    n, e = public_key
    hash = hashlib.sha256(message.encode('utf-8')).hexdigest()
    h = int(hash, 16)
    h_new = pow(signature, e, n)
    return h == h_new

# GUI界面
class Application(tk.Frame):
    def __init__(self, master=None):
        super().__init__(master)
        self.master = master
        self.master.title('RSA数字签名')
        self.pack()
        self.create_widgets()

    def create_widgets(self):
        # 待签名消息
        self.message_label = tk.Label(self, text='待签名消息：')
        self.message_label.grid(row=0, column=0, padx=5, pady=5)
        self.message_entry = tk.Entry(self, width=40)
        self.message_entry.grid(row=0, column=1, padx=5, pady=5)

        # 生成密钥对
        self.generate_key_button = tk.Button(self, text='生成密钥对', command=self.generate_key)
        self.generate_key_button.grid(row=1, column=0, padx=5, pady=5)

        # 公钥
        self.public_key_label = tk.Label(self, text='公钥：')
        self.public_key_label.grid(row=2, column=0, padx=5, pady=5)
        self.public_key_text = tk.Text(self, height=3, width=40)
        self.public_key_text.grid(row=2, column=1, padx=5, pady=5)

        # 私钥
        self.private_key_label = tk.Label(self, text='私钥：')
        self.private_key_label.grid(row=3, column=0, padx=5, pady=5)
        self.private_key_text = tk.Text(self, height=3, width=40)
        self.private_key_text.grid(row=3, column=1, padx=5, pady=5)

        # 签名
        self.sign_button = tk.Button(self, text='签名', command=self.sign_message)
        self.sign_button.grid(row=4, column=0, padx=5, pady=5)
        self.signature_label = tk.Label(self, text='签名结果：')
        self.signature_label.grid(row=4, column=1, padx=5, pady=5)
        self.signature_text = tk.Text(self, height=3, width=40)
        self.signature_text.grid(row=5, column=1, padx=5, pady=5)

        # 验证签名
        self.verify_button = tk.Button(self, text='验证签名', command=self.verify_signature)
        self.verify_button.grid(row=6, column=0, padx=5, pady=5)
        self.is_valid_label = tk.Label(self, text='签名是否有效：')
        self.is_valid_label.grid(row=6, column=1, padx=5, pady=5)
        self.is_valid_text = tk.Text(self, height=1, width=10)
        self.is_valid_text.grid(row=7, column=1, padx=5, pady=5)

        # 退出
        self.quit_button = tk.Button(self, text='退出', command=self.master.quit)
        self.quit_button.grid(row=8, column=1, padx=5, pady=5)

    # 生成密钥对
    def generate_key(self):
        self.public_key, self.private_key = generate_key_pair()
        self.public_key_text.delete(1.0, tk.END)
        self.public_key_text.insert(tk.END, str(self.public_key))
        self.private_key_text.delete(1.0, tk.END)
        self.private_key_text.insert(tk.END, str(self.private_key))

    # 签名
    def sign_message(self):
        message = self.message_entry.get()
        if message:
            signature = sign(message, self.private_key)
            self.signature_text.delete(1.0, tk.END)
            self.signature_text.insert(tk.END, str(signature))

    # 验证签名
    def verify_signature(self):
        message = self.message_entry.get()
        signature = self.signature_text.get(1.0, tk.END)
        if message and signature:
            is_valid = verify(message, int(signature), self.public_key)
            self.is_valid_text.delete(1.0, tk.END)
            self.is_valid_text.insert(tk.END, str(is_valid))

# 启动GUI程序
if __name__ == '__main__':
    root = tk.Tk()
    app = Application(master=root)
    app.mainloop()

在程序中，首先定义了一些辅助函数，包括生成质数、扩展欧几里得算法求解模反元素等。然后，利用这些函数实现了RSA算法的核心功能，包括生成密钥对、加密、解密、签名和验证签名。最后，使用tkinter库创建了一个简单的GUI界面，包括待签名消息、生成密钥对、公钥和私钥、签名结果、验证签名和退出按钮。用户可以在GUI界面中输入待签名消息，点击“生成密钥对”按钮生成公钥和私钥，点击“签名”按钮进行签名，点击“验证签名”按钮验证签名是否有效。