用python实现Shamir-secret-share

概述采用galois的python库（https://github.com/mhostetter/galois ），快速写了一个在扩GF(2^m)上的[t,n]门限的Shamir-secret-sharing流程；document写的也很详细使用起来非常趁手。缺点就是效率略低一些。https://pypi.org/project/galois/#polynomial-construction 代码如下：i

采用 galois 的python库（https://github.com/mhostetter/galois ），快速写了一个在扩GF(2^m)上的 [t,n] 门限的Shamir-secret-sharing 流程；

document写的也很详细使用起来非常趁手。缺点就是效率略低一些。

https://pypi.org/project/galois/#polynomial-construction 

代码如下：

import numpy as npimport galois # Apply GF calculation implement Shamir Secret Share# system parameter# fIEld paramn = 10t = 6F_num = 2**8GF256 = galois.GF(F_num)def distribute_shares(s):    # Construct the polynomial and distribute the shares     #     print('The secret is :',s)    powers =[i for i in range(t-1,-1,-1)]    coeffs = [np.random.randint(F_num) for _ in range(t-1)]    # append the secret as intercept;    coeffs.append(s)    p = galois.poly.degrees(powers, coeffs, fIEld=GF256)    print('construct the polynomials:',p)    # randomly generate n points     secret_shares =[]    xp = np.random.choice(range(F_num),n,replace=False)    secret_shares = [str(xi)+'-'+str(int(p(xi).base)) for xi in xp]    return secret_sharesdef reconstruct_secret(collected_shares):    # reconstruct the secret with collected shares     if len(collected_shares) != t:        return np.nan    x = []    y = []    for item in collected_shares:        xi = int(item.split('-')[0])        yi = int(item.split('-')[1])        x.append(xi)        y.append(yi)    ss_0 = GF256(0)    for i in range(t):        item = GF256(y[i])        for j in range(t):            if i!=j:                item *= -1*GF256(x[j])/(GF256(x[i])-GF256(x[j]))        ss_0 += item    return int(ss_0.base)      # generate secret sharessecret_shares = distribute_shares(33)# collect random share collected_shares = np.random.choice(secret_shares,t,replace=False)print('Randomly selected t shares \'x-y\':')print(collected_shares)recon_secret = reconstruct_secret(collected_shares)print('Reconstructed secret:',recon_secret)

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