python 实现shamir秘密分割和秘密恢复及其加法同态性

秘密分割：

#The following function turns an integer into a number of shares given a modulus and a number of parties.
def share(value1, parties, prime, coefficients = None):
    # if value1 == float('inf'):
    #     print(value1)
    # print('分解的值：',value1)

    value = int(value1 * (10**10))
    shares = {}
    threshold = parties - 1  #比总数少两份碎片时即可还原秘密

    if coefficients is None:        # Random polynomial coefficients.
        polynomial = [value] + [randint(0,prime-1) for _ in range(1,threshold)]

    else:
        polynomial = [value] + coefficients
    # Compute each share such that shares[i] = f(i).
    for i in range(1, parties+1):
        shares[i] = polynomial[0]
        for j in range(1, len(polynomial)):
            shares[i] = (shares[i] + polynomial[j] * pow(i,j)) % prime
    return shares, polynomial

实现秘密的分发：

# 定义分发函数，把shares分给不同的用户
def distribution(shares,shares_index,sensorydata, a_li):
    list0 = np.arange(1,len(shares)+1)
    np.random.shuffle(list0)
    i = 0
    for index,item in enumerate(sensorydata):

        li1 = [a[0] for a in a_li[i]]
        tmp = [list0[index], shares[list0[index]]]
        if index != 0:
            write(tmp)
        if tmp[0] in li1:
            ind = li1.index(tmp[0])
            a_li[i][ind][1] +=  tmp[1] % prime
        else:
            a_li[i].append(tmp)

        i += 1
    for i in range(len(sensorydata)):
        a_li[i].sort()
        if i != 0 :
            write(a_li)

    return a_li

实现其加法同态性及秘密恢复：

def recover(a_li):
    sharelist=[]
    for index,item in enumerate(a_li):
        dic = {}
        final ={}
        for i in range(len(a_li[index])):
            dic[a_li[index][i][0]] = a_li[index][i][1] % prime

        sharelist.append(dic)
        df = pd.DataFrame(sharelist)
        result = df.apply(lambda x: x.sum() % prime,axis=0) # 按列相加

    # 将最终结果整合为一个合并之后的share
        for index,item in enumerate(result):
            final[index+1]=item

    recovered = interpolate(final, prime)
    return np.round(recovered/(10**10),7)