import numpy as np def matrix_construct(policy_list): p_len = len(policy_list) list_and = [] for i in range(p_len): list_and.append(matrix_construct_and(policy_list[i])) return_value = matrix_construct_or(list_and[0], list_and[1]) for i in range(p_len - 2): return_value = matrix_construct_or(return_value, list_and[i + 2]) return return_value.astype(np.int_) # 计算与门元素生成的矩阵 def matrix_construct_and(list_and): length = len(list_and) # 若长度为2,则不进行计算，直接返回这个矩阵 two_item_array = np.array([[1, 1], [0, 1]]) # 虽然输入中已经确定了不可能为1,但还是放在这儿，以方便理解算法 if (length == 1): return np.array([[1]]) elif (length == 2): return two_item_array else: # 设定返回值 return_value = two_item_array # 每次循环都是一个大矩阵与单条目矩阵[[1]]进行计算 for i in range(length - 2): return_temp = np.empty([i + 3, i + 3]) # 生成c_a的过程 c_a = return_value[..., 0] c_a_temp = list(c_a) c_a_temp1 = list(c_a) c_a_temp.append(0) c_a_temp1.append(1) c_a = np.array(c_a_temp) c_a_b = np.array(c_a_temp1) # 生成r_a的过程 r_a = return_value[..., 1:] r_a = np.concatenate((r_a, np.zeros([1, (i + 1)]))) # 对各列进行赋值 return_temp[..., 0] = c_a return_temp[..., 1] = c_a_b return_temp[..., 2:] = r_a return_value = return_temp return return_value # 计算或门生成的矩阵 def matrix_construct_or(a, b): h_len_a = a.shape[0] h_len_b = b.shape[0] l_len_a = a.shape[1] l_len_b = b.shape[1] # 生成第一列 c_a = a[..., 0] c_b = b[..., 0] c_a_b = np.append(c_a, c_b) # 取得r_a和r_b r_a = a[..., 1:] r_b = b[..., 1:] # 生成要填充的零矩阵 r_a_add = np.zeros([h_len_b, l_len_a - 1]) r_b_add = np.zeros([h_len_a, l_len_b - 1]) # 对r_a进行填充 if l_len_a == 2: r_a = np.append(r_a, r_a_add) r_a = r_a.reshape(h_len_a + h_len_b, 1) else: r_a = np.concatenate((r_a, r_a_add)) # 对r_b进行填充 if l_len_b == 2: r_b = np.append(r_b_add, r_b) r_b = r_b.reshape(h_len_a + h_len_b, 1) else: r_b = np.concatenate((r_b_add, r_b)) # 联接r_a和r_b r_a_b = np.concatenate((r_a, r_b), axis=1) return_value = np.empty([h_len_a + h_len_b, l_len_a + l_len_b - 1]) return_value[..., 0] = c_a_b return_value[..., 1:] = r_a_b return return_value from gmpy2 import mpz, random_state, mpz_urandomb, mpz_random import random import sys rand = random_state(random.randrange(sys.maxsize)) bits = 128 # 建立Access对象 class Access(object): def __init__(self, policy_list, att_list): # 初始化后生成访问矩阵M self.m_matrix = matrix_construct(policy_list) # 访问列表要拉平，变成一个一维数组，方便后面操作 self.policy = [] for i in range(len(policy_list)): self.policy.extend(policy_list[i]) # 相当于用户属性组，即是policy_list中的一行 self.att = att_list # 秘密分享函数 def secretSharing(access, secret): # lambda向量，有的地方写成向量rho lambda_vector = [] # 生成随机向量v v_vector = [] v_vector.append(secret) count = 0 while (count < access.m_matrix.shape[1] - 1): v_vector.append(mpz_urandomb(rand, bits - 2)) count = count + 1 # 很简单，矩阵M与向量v相乘，得到lambda向量 lambda_vector = np.matmul(access.m_matrix, np.array(v_vector)) return lambda_vector def omegaReconstruct(access): # 得到向量Ma ma = np.array(get_ma(access.m_matrix, access.policy, access.att)) # Ma的转置 ma_trans = np.array(ma.T) ma_row = len(ma_trans) # 向量e=[1,0,0,.....] e_vector = [] e_vector.append(1) count = 0 while (count < ma_row - 1): e_vector.append(0) count += 1 # 求Ma的转置矩阵的伪逆矩阵 ma_trans_inv = np.linalg.pinv(ma_trans) # 计算得出omega向量 omega_temp = np.matmul(ma_trans_inv, np.array(e_vector)) omega_vector = [] for i in range(len(ma)): omega_vector.append(mpz(round(omega_temp[i]))) return omega_vector # 由矩阵M生成Ma的函数 def get_ma(m_matrix, policy, att): str_policy = '' for pp in policy: if pp < 10: str_policy += '000' + str(pp) elif pp >= 10 & pp < 100: str_policy += '00' + str(pp) elif pp >= 100 & pp < 1000: str_policy += '0' + str(pp) else: str_policy += str(pp) str_att = '' for aa in att: if aa < 10: str_att += '000' + str(aa) elif aa >= 10 & aa < 100: str_att += '00' + str(aa) elif aa >= 100 & aa < 1000: str_att += '0' + str(aa) else: str_att += str(aa) # 找对应用户属性组在矩阵M中对应的是哪几行 att_index = int((str_policy.find(str_att) + 1) / 4) att_len = len(att) ma = [] for i in range(att_len): ma.append(m_matrix[att_index + i]) return ma if __name__ == "__main__": policy_list = [[1, 3, 4, 6, 8, 9], [1, 3, 4, 6, 8, 9, 34, 56, 67]] att_list = np.array([1, 3, 4, 6, 8, 9], dtype=np.int_) ac = Access(policy_list, att_list) s = mpz(100) lam_vector = secretSharing(ac, s) omg_vector = omegaReconstruct(ac) print(omg_vector) s_un = np.inner(lam_vector[:6], omg_vector) print(s_un)