553 lines
24 KiB
Python
553 lines
24 KiB
Python
import random
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from collections.abc import Mapping
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from encoding import EncodedNumber
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from util import invert, powmod, getprimeover
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from visualize import show_name_args
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DEFAULT_KEYSIZE = 1024 # 定义默认的二进制数长度
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@show_name_args
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def generate_paillier_keypair(
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private_keyring=None, n_length=DEFAULT_KEYSIZE
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): # 生成公钥和私钥的函数
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# 生成 Paillier 密钥对函数
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p = q = n = None # 初始化素数 p, q 和计算结果 n
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length = 0 # 初始化计算结果 n 的长度 (即用二进制表示 n 所需要的二进制位数)
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while length != n_length: # 循环直至计算结果 n 的长度达到指定长度 n_length
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p = getprimeover(n_length // 2) # 随机生成一个 (n_length//2) 长的素数 p
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q = p
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while q == p:
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# 确保 q 与 p 不相等
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q = getprimeover(n_length // 2) # 随机生成一个 (n_length//2) 长的素数 q
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n = p * q # 计算 n,即两个素数乘积
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length = n.bit_length() # 计算 n 的二进制长度
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# 创建公钥对象
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public_key = PaillierPublicKey(n)
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# 创建私钥对象
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private_key = PaillierPrivateKey(public_key, p, q)
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if private_keyring is not None: # 如果传入了私钥环对象,则将私钥添加到私钥环中
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private_keyring.add(private_key)
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return public_key, private_key # 返回公钥和私钥
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class PaillierPublicKey(object): # 定义公钥类
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def __init__(self, n):
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self.g = n + 1
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self.n = n # 公钥的模数
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self.nsquare = n * n # n的平方
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self.max_int = n // 3 - 1 # 公钥的一个属性（限制可加密/解密的最大整数值）
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def __repr__(self): # 用于打印出该类的对象
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public_key_hash = hex(hash(self))[2:]
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return "<PaillierPublicKey {}>".format(
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public_key_hash[:10]
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) # 返回表示对象的字符串
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def __eq__(self, other): # 用于比较两个对象是否相等,并返回比较结果
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return self.n == other.n
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def __hash__(self): # 用于返回n的Hash值
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return hash(self.n)
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def get_n_and_g(self): # 获取该公钥的 n 和 g 的值
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return self.n, self.g
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def raw_encrypt(
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self, plaintext, r_value=None
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): # 用于返回加密后的密文,其中r_value可给随机数赋值
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if not isinstance(plaintext, int): # 判断plaintext是否是整数
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raise TypeError("明文不是整数,而是: %s" % type(plaintext))
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if (
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self.n - self.max_int <= plaintext < self.n
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): # 对于非常大的明文,使用特殊的计算方法进行加密:
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neg_plaintext = self.n - plaintext # = abs(plaintext - nsquare)
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neg_ciphertext = (self.n * neg_plaintext + 1) % self.nsquare
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nude_ciphertext = invert(neg_ciphertext, self.nsquare)
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else: # 如果不是非常大的明文:
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nude_ciphertext = (
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self.n * plaintext + 1
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) % self.nsquare # (n + 1)^plaintext = n * plaintext + 1 mod n^2
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# 生成一个随机数,其值为r_value。如果r_value没有值,则r随机:
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r = r_value or self.get_random_lt_n()
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obfuscator = powmod(r, self.n, self.nsquare) # (r ^ n) mod n^2
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return (nude_ciphertext * obfuscator) % self.nsquare # 返回加密后的密文
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def get_random_lt_n(self): # 返回一个1——n间的随机整数
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return random.SystemRandom().randrange(1, self.n)
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def encrypt(
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self, value, precision=None, r_value=None
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): # value表示要加密的值,precision是加密精度,r_value是随机数
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# 判断value是否是EncodedNumber类型,如果是则直接赋值给encoding；如果不是,则对value进行编码
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if isinstance(value, EncodedNumber):
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encoding = value
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else:
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encoding = EncodedNumber.encode(self, value, precision)
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return self.encrypt_encoded(encoding, r_value)
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def encrypt_encoded(
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self, encoding, r_value
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): # 将已编码的数值对象转换为加密后的数值对象,并可以选择进行混淆处理
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obfuscator = r_value or 1 # 为随机数r_value,没有则默认为1
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ciphertext = self.raw_encrypt(encoding.encoding, r_value=obfuscator)
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encrypted_number = EncryptedNumber(self, ciphertext, encoding.exponent)
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"""
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PS:默认生成情况下（不输入随机数r_value的情况下）:
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encrypt中的随机数r_value为:None
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raw_encrypt中的随机数为:1
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encrypt_encoded中的随机数为:None
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"""
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if r_value is None: # 结合上述注释,可知:密文混淆函数是会默认执行的
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encrypted_number.obfuscate() # 如果encrypt_encoded没有随机数r_value,则进行密文混淆处理obfuscate()
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return encrypted_number
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class PaillierPrivateKey(object): # 私钥
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def __init__(self, public_key, p, q):
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if not p * q == public_key.n: # 如果p * q 不等于 公钥的n,则说明出错
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raise ValueError("所给公钥与p,q不匹配！")
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if p == q: # p,q相同
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raise ValueError("p,q不能相同！")
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self.public_key = public_key
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# 给self的p q赋值:
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if q < p: # 默认是p 大于等于 q
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self.p = q
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self.q = p
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else:
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self.p = p
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self.q = q
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self.psquare = self.p * self.p
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self.qsquare = self.q * self.q
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self.p_inverse = invert(self.p, self.q) # 计算p mod q 的乘法逆元
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self.hp = self.h_function(self.p, self.psquare) # p mod p方
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self.hq = self.h_function(self.q, self.qsquare) # q mod q方
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def __repr__(self): # 用于打印出该类的对象
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pub_repr = repr(self.public_key)
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return "<PaillierPrivateKey for {}>".format(pub_repr)
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def decrypt(self, encrypted_number): # 解密密文,并返回明文
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# 执行下面这个语句前的类型为EncryptedNumber,执行完毕后类型为EncodedNumber（中间会变为int型的ciphertext）:
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encoded = self.decrypt_encoded(encrypted_number)
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return encoded.decode()
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def decrypt_encoded(
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self, encrypted_number, Encoding=None
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): # 用于解密密文并返回解密后的EncodedNumber类型
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# 检查输入信息是否是EncryptedNumber参数,如果不是:
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if not isinstance(encrypted_number, EncryptedNumber):
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raise TypeError(
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"参数应该是EncryptedNumber," " 参数不能为: %s" % type(encrypted_number)
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)
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if (
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self.public_key != encrypted_number.public_key
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): # 如果公钥与加密数字的公钥不一致
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raise ValueError("加密信息不能被不同的公钥进行加密！")
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if Encoding is None: # 将Encoding设置为未赋值的EncodedNumber变量
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Encoding = EncodedNumber
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"""提取 encrypted_number 中的 ciphertext
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这里是禁用安全模式,
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所以是直接提取ciphertext,
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随后调用raw_decrypt函数对ciphertext进行处理:"""
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encoded = self.raw_decrypt(encrypted_number.ciphertext(be_secure=False))
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return Encoding(self.public_key, encoded, encrypted_number.exponent)
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def raw_decrypt(self, ciphertext): # 对密文进行原始解密
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if not isinstance(ciphertext, int): # 如果所给的密文不是int型
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raise TypeError("密文应该是int型, 而不是: %s" % type(ciphertext))
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# 将解密结果存放在p和q中,并将p q进行合并:
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decrypt_to_p = (
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self.l_function(powmod(ciphertext, self.p - 1, self.psquare), self.p)
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* self.hp
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% self.p
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)
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decrypt_to_q = (
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self.l_function(powmod(ciphertext, self.q - 1, self.qsquare), self.q)
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* self.hq
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% self.q
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)
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return self.crt(decrypt_to_p, decrypt_to_q)
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def h_function(self, x, xsquare): # 计算并返回h函数值[用于中国剩余定理]
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return invert(self.l_function(powmod(self.public_key.g, x - 1, xsquare), x), x)
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def l_function(self, mju, p): # 计算并返回l值（算L(μ) ）
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return (mju - 1) // p
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def crt(self, mp, mq): # 实现中国剩余定理(Chinese remainder theorem)
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u = (mq - mp) * self.p_inverse % self.q
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return mp + (u * self.p)
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def __eq__(self, other): # 判断两个对象的 q 与 p 是否相等
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return self.p == other.p and self.q == other.q
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def __hash__(self): # 计算 p 与 q 元组的哈希值
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return hash((self.p, self.q))
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class PaillierPrivateKeyring(Mapping): # 私钥环类,并继承了Mapping类
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def __init__(self, private_keys=None): # 初始化私钥环对象（私钥环列表）
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if private_keys is None:
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private_keys = []
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# 将私钥和公钥进行组合,并存储在私钥环中:
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public_keys = [k.public_key for k in private_keys]
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self.__keyring = dict(zip(public_keys, private_keys))
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def __getitem__(self, key): # 通过公钥,来查找私钥环中对应的私钥
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return self.__keyring[key]
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def __len__(self): # 存储的私钥数量
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return len(self.__keyring)
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def __iter__(self): # 遍历私钥环中的公钥
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return iter(self.__keyring)
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def __delitem__(self, public_key): # 删除与公钥对应的私钥
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del self.__keyring[public_key]
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def add(self, private_key): # 向私钥环中添加私钥
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if not isinstance(private_key, PaillierPrivateKey): # 对要添加的私钥进行判断
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raise TypeError(
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"私钥应该是PaillierPrivateKey类型, " "而不是 %s" % type(private_key)
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)
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self.__keyring[private_key.public_key] = (
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private_key # 将该公钥和对用的私钥一块儿加入到私钥环中
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)
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def decrypt(self, encrypted_number): # 对密文进行解密
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relevant_private_key = self.__keyring[
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encrypted_number.public_key
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] # 在私钥环中获取对应的私钥
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return relevant_private_key.decrypt(encrypted_number) # 返回加密结果
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class EncryptedNumber(object): # 浮点数或整数的Pailier加密
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"""
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1. D(E(a) * E(b)) = a + b
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2. D(E(a)**b) = a * b
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"""
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def __init__(self, public_key, ciphertext, exponent=0):
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self.public_key = public_key
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self.__ciphertext = ciphertext # 密文
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self.exponent = exponent # 用于表示指数
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self.__is_obfuscated = False # 用于表示数据是否被混淆
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if isinstance(self.ciphertext, EncryptedNumber): # 如果密文是EncryptedNumber
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raise TypeError("密文必须是int型")
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if not isinstance(
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self.public_key, PaillierPublicKey
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): # 如果公钥不是PaillierPublicKey
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raise TypeError("公钥必须是PaillierPublicKey")
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def __add__(
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self, other
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): # 运算符重载,重载为EncryptedNumber与(EncryptedNumber/整数/浮点数)的加法
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if isinstance(other, EncryptedNumber):
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return self._add_encrypted(other)
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elif isinstance(other, EncodedNumber):
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return self._add_encoded(other)
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else:
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return self._add_scalar(other)
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def __radd__(self, other): # 反加,处理整数/浮点数与EncryptedNumber之间的加法
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return self.__add__(other)
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def __mul__(self, other): # 运算符重载,重载为EncryptedNumber与(整数/浮点数)的乘法
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# 判断other对象是否是EncryptedNumber,如果是:
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if isinstance(other, EncryptedNumber):
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raise NotImplementedError(
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"EncryptedNumber 与 EncryptedNumber 之间不能相乘！"
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)
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if isinstance(other, EncodedNumber):
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encoding = other
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else:
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encoding = EncodedNumber.encode(self.public_key, other)
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product = self._raw_mul(encoding.encoding) # 重新更新乘积
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exponent = self.exponent + encoding.exponent # 重新更新指数
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return EncryptedNumber(self.public_key, product, exponent)
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def __rmul__(self, other): # 反乘,处理整数/浮点数与EncryptedNumber之间的乘法
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return self.__mul__(other)
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def __sub__(
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self, other
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): # 运算符重载,重载为EncryptedNumber与(EncryptedNumber/整数/浮点数)的减法
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return self + (other * -1)
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def __rsub__(self, other): # 处理整数/浮点数与EncryptedNumber之间的减法
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return other + (self * -1)
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def __truediv__(
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self, scalar
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): # 运算符重载,重载为EncryptedNumber与(EncryptedNumber/整数/浮点数)的除法
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return self.__mul__(1 / scalar)
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def __invert__(self): # 运算符重载~（对 数 的取反）
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return self * (-1)
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# def __pow__(self, exponent): # 运算符重载 ** （对密文的幂函数）
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# if not isinstance(exponent, int): # 如果输入有问题
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# print("指数应输入 整数 标量！")
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# else:
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# result = self
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# for i in [1, exponent]:
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# result *= self
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# return result
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# # 原本的幂运算 ** ；return self.value ** exponent
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def ciphertext(self, be_secure=True): # 用于混淆密文,并返回混淆后的密文
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"""
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EncryptedNumber类的一个方法ciphertext,用于返回该对象的密文。
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在Paillier加密中,为了提高计算性能,加法和乘法操作进行了简化,
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避免对每个加法和乘法结果进行随机数的加密操作。
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这样会使得内部计算快速,但会暴露一部分信息。
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此外,为了保证安全,如果需要与其他人共享密文,应该使用be_secure=True。
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这样,如果密文还没有被混淆,会调用obfuscate方法对其进行混淆操作。
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"""
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if be_secure and not self.__is_obfuscated: # 如果密文没有被混淆,则进行混淆操作
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self.obfuscate()
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return self.__ciphertext
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def decrease_exponent_to(
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self, new_exp
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): # 返回一个指数较低但大小相同的数（即返回一个同值的,但指数较低的EncryptedNumber）
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if new_exp > self.exponent:
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raise ValueError(
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"新指数值 %i 应比原指数 %i 小！ " % (new_exp, self.exponent)
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)
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multiplied = self * pow(
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EncodedNumber.BASE, self.exponent - new_exp
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) # 降指数后的乘积
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multiplied.exponent = new_exp # 降指数后的新指数
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return multiplied
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def obfuscate(self): # 混淆密文
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r = self.public_key.get_random_lt_n() # 生成一个(1——n)间的随机数r,不 ＞＝ r
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r_pow_n = powmod(
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r, self.public_key.n, self.public_key.nsquare
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) # (r ^ n) mod n^2
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self.__ciphertext = (
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self.__ciphertext * r_pow_n % self.public_key.nsquare
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) # 对原密文进行处理
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self.__is_obfuscated = True # 用于判断密文是否被混淆
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def _add_scalar(self, scalar): # 执行EncodedNumber与标量(整型/浮点型)相加的操作
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encoded = EncodedNumber.encode(
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self.public_key, scalar, max_exponent=self.exponent
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)
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return self._add_encoded(encoded)
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def _add_encoded(self, encoded): # 对EncodedNumber与标量encoded加法编码
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# 返回 E(a + b)
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if self.public_key != encoded.public_key: # 如果公钥与编码公钥不相同
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raise ValueError("不能使用不同的公钥,对数字进行编码！")
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a, b = self, encoded
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# 对指数处理（使指数相同）:
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if a.exponent > b.exponent:
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a = self.decrease_exponent_to(b.exponent)
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elif a.exponent < b.exponent:
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b = b.decrease_exponent_to(a.exponent)
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encrypted_scalar = a.public_key.raw_encrypt(
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b.encoding, 1
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) # 用公钥加密b.encoding后的标量
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sum_ciphertext = a._raw_add(
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a.ciphertext(False), encrypted_scalar
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) # 进行相加操作
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return EncryptedNumber(a.public_key, sum_ciphertext, a.exponent)
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def _add_encrypted(self, other): # 对EncodedNumber与EncodedNumber加法加密
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if self.public_key != other.public_key:
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raise ValueError("不能使用不同的公钥,对数字进行加密！")
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# 对指数处理（使指数相同）:
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a, b = self, other
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if a.exponent > b.exponent:
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a = self.decrease_exponent_to(b.exponent)
|
||
elif a.exponent < b.exponent:
|
||
b = b.decrease_exponent_to(a.exponent)
|
||
|
||
sum_ciphertext = a._raw_add(a.ciphertext(False), b.ciphertext(False))
|
||
return EncryptedNumber(a.public_key, sum_ciphertext, a.exponent)
|
||
|
||
def _raw_add(self, e_a, e_b): # 对加密后的a,b直接进行相加,并返回未加密的结果
|
||
return e_a * e_b % self.public_key.nsquare
|
||
|
||
def _raw_mul(self, plaintext): # 对密文进行乘法运算,并返回未加密的结果
|
||
# 检查乘数是否为int型:
|
||
if not isinstance(plaintext, int):
|
||
raise TypeError("期望密文应该是int型, 而不是 %s" % type(plaintext))
|
||
|
||
# 如果乘数是负数,或乘数比公钥的模（n）大:
|
||
if plaintext < 0 or plaintext >= self.public_key.n:
|
||
raise ValueError("超出可计算范围: %i" % plaintext)
|
||
|
||
if self.public_key.n - self.public_key.max_int <= plaintext:
|
||
# 如果数据很大,则先反置一下再进行运算:
|
||
neg_c = invert(self.ciphertext(False), self.public_key.nsquare)
|
||
neg_scalar = self.public_key.n - plaintext
|
||
return powmod(neg_c, neg_scalar, self.public_key.nsquare)
|
||
else:
|
||
return powmod(self.ciphertext(False), plaintext, self.public_key.nsquare)
|
||
|
||
def increment(self): # 定义自增运算
|
||
return self + 1
|
||
|
||
def decrement(self): # 定义自减运算
|
||
return self + 1
|
||
|
||
def cal_sum(self, *args):
|
||
result = 0 # 将初始值设置为0
|
||
for i in args:
|
||
if not isinstance(i, (int, float, EncryptedNumber)):
|
||
raise TypeError(
|
||
"期望密文应该是int/float/EncryptedNumber型, 而不是 %s" % type(i)
|
||
)
|
||
if isinstance(
|
||
i, int or float
|
||
): # 如果是 int 或 float 明文型,则先将明文加密在进行运算
|
||
result += self.public_key.encrypt(i)
|
||
else:
|
||
result += i # 第一次循环:标量与密文相加；后面的循环,密文与密文相加
|
||
return result
|
||
|
||
def average(self, *args): # 定义求平均值
|
||
total_sum = self.cal_sum(
|
||
*args
|
||
) # 计算总和total是<__main__.EncryptedNumber object at 0x000002AB74FB9850>
|
||
|
||
# # 如果总数超过了可计算范围
|
||
# if total_sum > 91000:
|
||
# raise ValueError('超出可计算范围: %i' % total_sum)
|
||
|
||
count = 0 # 定义count,用来统计参数的个数
|
||
for _ in args:
|
||
count += 1 # count++
|
||
return total_sum / count
|
||
|
||
def weighted_average(self, *args): # 定义加权平均 def weighted_average(*args):
|
||
"""PS:
|
||
args[0]: <__main__.EncryptedNumber object at 0x000001F7C1B6A610>
|
||
args[1]: 第一个参数
|
||
args[2]: 给第一个参数设置的权值
|
||
。。。。。。
|
||
"""
|
||
total_weight = sum(
|
||
args[2::2]
|
||
) # 计算权值的总和(使用切片操作从参数列表中取出索引为参数权值的元素)
|
||
if total_weight != 1:
|
||
raise TypeError("加权平均算法的权值设置错误！请重新设置！")
|
||
else:
|
||
# 计算加权和,其中: for i in range(0, len(args), 2) 表示以2为步长,从0递增,直到 i >= len(args)时:
|
||
result = sum(args[i] * args[i + 1] for i in range(1, len(args), 2))
|
||
return result
|
||
|
||
def reset(self): # 定义复位（置0运算）
|
||
zero = self.public_key.encrypt(0) # 用公钥对0进行加密
|
||
return zero
|
||
|
||
def calculate_variance(self, *args): # 定义求方差
|
||
mean = self.average(*args) # 均值
|
||
count = 0 # 定义count,用来统计参数的个数
|
||
for _ in args:
|
||
count += 1 # count++
|
||
variance = sum((x - mean) ** 2 for x in args) / (count - 1)
|
||
return variance
|
||
|
||
# def IsZero(self): # 判断该数是否为0
|
||
# ZERO = self
|
||
# zero = ZERO.public_key.encrypt(0) # 用公钥对0进行加密
|
||
# flag = False # 用于判断该数是否为0(默认不为0)
|
||
#
|
||
# if self == zero:
|
||
# flag = True
|
||
# return flag
|
||
|
||
# def POW(self, num): # 定义幂运算
|
||
# if not isinstance(num, int): # 如果输入有问题
|
||
# print("指数应输入 整数 标量！")
|
||
# else:
|
||
# result = self
|
||
# print(num)
|
||
# for i in [1, num]:
|
||
# result *= self
|
||
# return result
|
||
|
||
|
||
# def get_certificate(public_key):
|
||
# # 获得公钥的PEM编码的二进制形式
|
||
# public_bytes = public_key.public_bytes(
|
||
# encoding=serialization.Encoding.PEM, format=serialization.PublicFormat.SubjectPublicKeyInfo)
|
||
#
|
||
# # 获得数字证书
|
||
# cert = (public_bytes, hashlib.sha256(public_bytes).hexdigest()) # 元祖类型
|
||
# return cert
|
||
|
||
|
||
if __name__ == "__main__": # 主函数
|
||
Public_Key, Private_Key = generate_paillier_keypair() # 随机生成1024长的公钥和私钥
|
||
x = 90000.23
|
||
y = 90
|
||
z = 0.5
|
||
x_encrypted = Public_Key.encrypt(x) # 加密后的x
|
||
y_encrypted = Public_Key.encrypt(y) # 加密后的y
|
||
z_encrypted = Public_Key.encrypt(z) # 加密后的z
|
||
t_encrypted = (
|
||
x_encrypted + y_encrypted * 0.5
|
||
) # 在x,y保密的情况下计算t,得到加密后的t(t_encrypted)
|
||
|
||
# x_encrypted = x_encrypted.increment() # 自增
|
||
# y_encrypted = y_encrypted.decrement() # 自减
|
||
|
||
# print(x_encrypted != y_encrypted) # 不相等
|
||
# print(x_encrypted == y_encrypted) # 相等
|
||
|
||
# print(Private_Key.decrypt(~x_encrypted) ) # 取反
|
||
|
||
# total = x_encrypted.cal_sum(x_encrypted, y_encrypted, 0.5) # 求和函数
|
||
# print("密文之和为:", Private_Key.decrypt(total))
|
||
|
||
# avg = x_encrypted.average(y_encrypted, z_encrypted, z_encrypted) # 求平均值函数
|
||
# print("密文的平均值为:", Private_Key.decrypt(avg) ) # 只能对0~90090.73的数进行除法运算（除不尽）
|
||
|
||
# weight_average = x_encrypted.weighted_average(x_encrypted, 0.1, y_encrypted, 0.3, z_encrypted, 0.6) # 加权平均函数
|
||
# print("加权平均结果为:", Private_Key.decrypt(weight_average))
|
||
|
||
# variance = x_encrypted.calculate_variance(x_encrypted, y_encrypted) #求方差
|
||
# print("方差为:", Private_Key.decrypt(variance))
|
||
|
||
# z_encrypted = z_encrypted.reset() # 复位函数
|
||
# print("z复位后的结果为:", Private_Key.decrypt(z_encrypted) )
|
||
|
||
# print(x_encrypted ** x) # 相当于print(x_encrypted.POW(2) )
|
||
# print(x_encrypted > y_encrypted)
|
||
|
||
# print(type(Public_Key))
|
||
# print(Public_Key)
|
||
|
||
print(f"x + y * 0.5的结果是:{Private_Key.decrypt(t_encrypted)}") # 打印出t
|
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