import hashlib
import secrets
from mnemonic import Mnemonic # 仅用于标准的助记词转换

class SentinelKeyEngine:
    def __init__(self):
        self.mnemo = Mnemonic("english")

    def generate_vault_keys(self):
        """
        1. 生成原始 12 助记词 (Master Key)
        """
        words = self.mnemo.generate(strength=128)
        entropy = self.mnemo.to_entropy(words)
        return words, entropy

    def split_to_shares(self, entropy):
        """
        2. SSS (3,2) 门限分片逻辑
        公式: f(x) = S + a*x (直线方程，S为秘密，a为随机斜率)
        我们将秘密 S 分成 3 份，任选 2 份即可恢复
        """
        # 将熵转换为大整数
        secret_int = int.from_bytes(entropy, 'big')
        
        # 生成一个随机系数 a (安全性需与秘密强度一致)
        # 这里使用 secrets 保证加密级随机
        a = int.from_bytes(secrets.token_bytes(16), 'big')
        
        # 定义 3 个点: x=1, x=2, x=3
        # Share = (x, f(x))
        def f(x): return secret_int + a * x
        
        share1 = (1, f(1)) # 手机分片
        share2 = (2, f(2)) # 云端分片
        share3 = (3, f(3)) # 传承卡分片
        
        return [share1, share2, share3]

    def recover_from_shares(self, share_a, share_b):
        """
        3. 恢复逻辑：拉格朗日插值还原
        已知 (x1, y1) 和 (x2, y2)，求 f(0) 即秘密 S
        公式: S = (x2*y1 - x1*y2) / (x2 - x1)
        """
        x1, y1 = share_a
        x2, y2 = share_b
        
        # 还原常数项 S
        secret_int = (x2 * y1 - x1 * y2) // (x2 - x1)
        
        # 转回字节并生成助记词
        recovered_entropy = secret_int.to_bytes(16, 'big')
        return self.mnemo.to_mnemonic(recovered_entropy)
if __name__ == "__main__":
    # --- Sentinel 协议业务流程模拟 ---

    engine = SentinelKeyEngine()

    # [生前]：初始化金库
    master_words, entropy = engine.generate_vault_keys()
    print(f"【1. 生成原始助记词】: {master_words}")

    shares = engine.split_to_shares(entropy)
    print(f"【2. SSS 分片完成】:")
    print(f"   - 分片1 (手机安全区): {shares[0]}")
    print(f"   - 分片2 (Sentinel云): {shares[1]}")
    print(f"   - 分片3 (传承卡单词): {shares[2]}")

    print("-" * 50)

    # [死后/传承]：模拟用户失联，触发被动验证
    # 假设继承人拿着卡片 (Share 3)，向服务器请求分片 (Share 2)
    successor_share = shares[2]
    server_share = shares[1]

    # 执行恢复
    recovered_words = engine.recover_from_shares(shares[0], shares[1])
    print(f"【1. 手机+云     : {recovered_words}")

    recovered_words = engine.recover_from_shares(shares[0], shares[2])
    print(f"【2. 手机+传承卡 : {recovered_words}")

    recovered_words = engine.recover_from_shares(shares[1], shares[2])
    print(f"【3. 云+传承卡   : {recovered_words}")

    # 校验一致性
    assert recovered_words == master_words
    print("\n结果：恢复出的助记词与原始完全一致。")


    with open("words.txt", "w") as f:
        f.write("%s\n"%master_words)