密码分析学——Md4碰撞代码实现

——ECNU YZ

File: Md4.py

class Md4Orign:# ----- 这里忽略了一些规范化过程，采用小端序和无消息填充的方法，可自行通过重写get_m拓展...MAX_MARGIN = 0X100000000MAX_LEN = 32ERR_INPUT_MSG = '输入存在错误，请输入一个16进制的数组（0<=list[i]<2^512）'def __init__(self):self.FGH = [Md4Orign.F, Md4Orign.G, Md4Orign.H]self.PAD = [0x00000000, 0x5a827999, 0x6ed9eba1]self.m = [0x00000000 for i in range(16)]self.aa = 0x67452301self.bb = 0xefcdab89self.cc = 0x98badcfeself.dd = 0x10325476self.m_48 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,0, 4, 8, 12, 1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15,0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]self.s_48 = [3, 7, 11, 19, 3, 7, 11, 19, 3, 7, 11, 19, 3, 7, 11, 19,3, 5, 9, 13, 3, 5, 9, 13, 3, 5, 9, 13, 3, 5, 9, 13,3, 9, 11, 15, 3, 9, 11, 15, 3, 9, 11, 15, 3, 9, 11, 15]def phi(self, i, abcd, mk, s):return Md4Orign.left_s((abcd[0] + self.FGH[i](abcd[1], abcd[2], abcd[3]) + mk + self.PAD[i])% Md4Orign.MAX_MARGIN, s)def compute(self, m=None):self.get_m(m)abcd = [self.aa, self.bb, self.cc, self.dd]for i in range(48):abcd[-(i % 4)] = self.phi(int(i / 16), abcd[-(i % 4)::] + abcd[:-(i % 4):], self.m[self.m_48[i]],self.s_48[i])return "{:0>8x}{:0>8x}{:0>8x}{:0>8x}".format((abcd[0] + self.aa) % Md4Orign.MAX_MARGIN,(abcd[1] + self.bb) % Md4Orign.MAX_MARGIN,(abcd[2] + self.cc) % Md4Orign.MAX_MARGIN,(abcd[3] + self.dd) % Md4Orign.MAX_MARGIN)def get_m(self, m=None):self.m = m if m is not None and Md4Orign.m_valid(m) else self.m@staticmethoddef F(X, Y, Z):return (X & Y) | (~X & Z)@staticmethoddef G(X, Y, Z):return (X & Y) | (X & Z) | (Y & Z)@staticmethoddef H(X, Y, Z):return X ^ Y ^ Z@staticmethoddef left_s(val, s):s = s % Md4Orign.MAX_LENreturn val >> (Md4Orign.MAX_LEN - s) | ((val << s) % Md4Orign.MAX_MARGIN)@staticmethoddef right_s(val, s):s = s % Md4Orign.MAX_LENreturn val << (Md4Orign.MAX_LEN - s) | ((val >> s) % Md4Orign.MAX_MARGIN)@staticmethoddef m_valid(m):try:if len(m) != 16:print(Md4Orign.ERR_INPUT_MSG)return Falseelse:for mi in m:if type(mi) != int or not (0 <= mi < Md4Orign.MAX_MARGIN):print(Md4Orign.ERR_INPUT_MSG)return Falsereturn Trueexcept:print(Md4Orign.ERR_INPUT_MSG)return False

File: main.py

import struct
import timefrom MD4 import Md4Orign
import randomclass Md4Collision(Md4Orign):constraints1 = [[['=', 6]], [['0', 6], ['=', 7], ['=', 10]],[['1', 6], ['1', 7], ['0', 10], ['=', 25]],[['1', 6], ['0', 7], ['0', 10], ['0', 25]],[['1', 7], ['1', 10], ['0', 25], ['=', 13]],[['0', 13], ['=', 18], ['=', 19], ['=', 20], ['=', 21], ['1', 25]],[['=', 12], ['0', 13], ['=', 14], ['0', 18], ['0', 19], ['1', 20], ['0', 21]],[['1', 12], ['1', 13], ['0', 14], ['=', 16], ['0', 18], ['0', 19], ['0', 20], ['0', 21]],[['1', 12], ['1', 13], ['1', 14], ['0', 16], ['0', 18], ['0', 19], ['0', 20], ['=', 22], ['1', 21], ['=', 25]],[['1', 12], ['1', 13], ['1', 14], ['0', 16], ['0', 19], ['1', 20], ['1', 21], ['0', 22], ['1', 25], ['=', 29]],[['1', 16], ['0', 19], ['0', 20], ['0', 21], ['0', 22], ['0', 25], ['1', 29], ['=', 31]],[['0', 19], ['1', 20], ['1', 21], ['=', 22], ['1', 25], ['0', 29], ['0', 31]],[['0', 22], ['0', 25], ['=', 26], ['=', 28], ['1', 29], ['0', 31]],[['0', 22], ['0', 25], ['1', 26], ['1', 28], ['0', 29], ['1', 31]],[['=', 18], ['1', 22], ['1', 25], ['0', 26], ['0', 28], ['0', 29]],[['0', 18], ['=', 25], ['1', 26], ['1', 28], ['0', 29], ['=', 31]]]constraints2 = [[['=', 18, 2], ['1', 25], ['0', 26], ['1', 28], ['1', 31]],[['=', 18, 0], ['=', 25, 1], ['=', 26, 1], ['=', 28, 1], ['=', 31, 1]]]M_1 = 0x80000000M_2 = 0x70000000M_12 = -0x10000def modify_m(self, m):abcd = [self.aa, self.bb, self.cc, self.dd]# Round1for i in range(16):abcd[-(i % 4)], m[i] = self.one_step_modify(abcd[-(i % 4)::] + abcd[:-(i % 4):], m[i], self.s_48[i],Md4Collision.constraints1[i], Md4Collision.F)# Round2abcdi = self.get_abcdi(m, 3)# - a5abcd[0], m[0] = self.one_step_modify(abcd, m[0], 3, Md4Collision.constraints2[0], Md4Collision.G, abcd)abcdi[1][0] = Md4Collision.left_s((self.aa + self.F(self.bb, self.cc, self.dd) + m[0]) % Md4Orign.MAX_MARGIN, 3)self.mutiple_step_modify(abcdi, m, 0)# - d5abcd[3], m[4] = self.one_step_modify(abcd[3:]+abcd[:3], m[4], 5, Md4Collision.constraints2[1], Md4Collision.G,abcd)abcdi[2][0] = Md4Collision.left_s((abcdi[1][0] + self.F(abcdi[1][1], abcdi[1][2], abcdi[1][3]) + m[4])% Md4Orign.MAX_MARGIN, 3)self.mutiple_step_modify(abcdi, m, 1)return mdef find_collision(self):m1_o, m1, m2 = Md4Collision.get_random_m(), None, Noneh1, h2 = "h1", "h2"i = 1print('--------正在寻找Md4碰撞中---------')while h1 != h2:m1_o = Md4Collision.get_random_m()m1 = self.modify_m(m1_o)m2 = m1.copy()m2[1] = (m2[1] + Md4Collision.M_1) % Md4Collision.MAX_MARGINm2[2] = (m2[2] + Md4Collision.M_2) % Md4Collision.MAX_MARGINm2[12] = (m2[12] + Md4Collision.M_12) % Md4Collision.MAX_MARGINh1, h2 = self.compute(m1), self.compute(m2)i += 1print('总时长：%ds' % time.perf_counter(), '； 尝试次数：%d次' % i)print('m1:', "".join(["%x" % mi for mi in m1]))print('m2:', "".join(["%x" % mi for mi in m2]))print(self.compute(m1), '(m1 结果) ==', self.compute(m2), '(m2 结果)')return m1, m2, h1, h2def one_step_modify(self, abcd, mi, si, constraintsi, f, abcd_normal=None):v = Md4Collision.left_s((abcd[0] + f(abcd[1], abcd[2], abcd[3]) + (self.PAD[1] if f == self.FGH[1] else 0) + mi)% Md4Orign.MAX_MARGIN, si)for c in constraintsi:if c[0] == '=':v ^= (v ^ (abcd[1] if len(c) < 3 else abcd_normal[c[2]])) & (2 ** c[1])elif c[0] == '0':v &= ~(2 ** c[1])elif c[0] == '1':v |= 2 ** c[1]return v, (Md4Collision.right_s(v, si) - abcd[0] - f(abcd[1], abcd[2], abcd[3]) -(self.PAD[1] if f == self.FGH[1] else 0)) % Md4Collision.MAX_MARGINdef mutiple_step_modify(self, abcd_i, m, i):  # i=0 / i=1for j in range(1, 5):m[self.m_48[i * 4 + j]] = \(Md4Collision.right_s(abcd_i[i + 1 + (1 if j >= 4 else 0)][-j], self.s_48[i * 4 + j]) -abcd_i[i + (1 if j >= 4 else 0)][-j] - Md4Collision.F(abcd_i[i + 1][-j + 1],abcd_i[i + (1 if j >= 2 else 0)][-j + 2],abcd_i[i + (1 if j >= 3 else 0)][-j + 3])) % Md4Collision.MAX_MARGINdef get_abcdi(self, m, ii):abcd = [self.aa, self.bb, self.cc, self.dd]abcd_i = [abcd.copy()]for i in range(ii * 4):abcd[-(i % 4)] = self.phi(int(i / 16), abcd[-(i % 4)::] + abcd[:-(i % 4):], m[self.m_48[i]],self.s_48[i])if i % 4 == 3:abcd_i.append(abcd.copy())return abcd_i@staticmethoddef Endian(b):return [struct.unpack('<I', ''.join(b[i:i + 4]))[0] for i in range(0, len(b), 4)]@staticmethoddef get_random_m():return [random.randint(0, Md4Collision.MAX_MARGIN - 1) for i in range(16)]def md4ValidPre(md4):m1 = [0x4d7a9c83, 0x56cb927a, 0xb9d5a578, 0x57a7a5ee, 0xde748a3c, 0xdcc366b3, 0xb683a020, 0x3b2a5d9f,0xc69d71b3, 0xf9e99198, 0xd79f805e, 0xa63bb2e8, 0x45dd8e31, 0x97e31fe5, 0x2794bf08, 0xb9e8c3e9]m2 = [0x4d7a9c83, 0xd6cb927a, 0x29d5a578, 0x57a7a5ee, 0xde748a3c, 0xdcc366b3, 0xb683a020, 0x3b2a5d9f,0xc69d71b3, 0xf9e99198, 0xd79f805e, 0xa63bb2e8, 0x45dc8e31, 0x97e31fe5, 0x2794bf08, 0xb9e8c3e9]print('m1:', ["0x%x" % mi for mi in m1])print('m2:', ["0x%x" % mi for mi in m2])print(md4.compute(m1), '(m1 result) ==', md4.compute(m2), '(m2 result)')def test(md4):m1 = [0x4d7a9c83, 0x56cb927a, 0xb9d5a578, 0x57a7a5ee, 0xde748a3c, 0xdcc366b3, 0xb683a020, 0x3b2a5d9f,0xc69d71b3, 0xf9e99198, 0xd79f805e, 0xa63bb2e8, 0x45dd8e31, 0x97e31fe5, 0x2794bf08, 0xb9e8c3e9]print('m1:', ["0x%x" % mi for mi in m1])m2 = m1.copy()m2[1] = (m2[1] + Md4Collision.M_1) % Md4Collision.MAX_MARGINm2[2] = (m2[2] + Md4Collision.M_2) % Md4Collision.MAX_MARGINm2[12] = (m2[12] + Md4Collision.M_12) % Md4Collision.MAX_MARGINprint(md4.compute(m1) == md4.compute(m2))print(md4.compute(m1), '(m1 result) ==', md4.compute(m2), '(m2 result)')if __name__ == '__main__':md4_collision = Md4Collision()md4_collision.find_collision()

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