基于随机线性分组码的秘密分享在电子投票中的应用

针对电子投票的大规模秘密分享的应用要求，提高在大量设备间的秘密分享的效率，本文提出基于随机线性分组码的秘密分享，并将其应用于电子投票中。首先，构造随机线性分组码的校验矩阵，使得秘密恢复的译码方程组的系数矩阵有极高的列满秩概率，可以保证正确译码恢复秘密；然后，由校验矩阵生成编码矩阵，并用编码矩阵对投票信息向量编码，将码字中部分元素作为秘密份额分享给其他设备，但不泄漏投票信息向量；最后，各个设备将接收到的份额返回给源设备，并用从其他设备收到的返回份额译码恢复投票信息向量。基于随机线性分组码的秘密分享可在秘密恢复的同时发现恢复结果及份额错误。本文对不同数据大小和参与方数量的秘密分享、恢复速度与数据冗余量进行实验。实验结果表明，与传统的秘密分享方法相比，基于随机线性分组码的秘密分享方法具有较高的分享与恢复速度和较低的数据冗余量。基于随机线性分组码的秘密分享方法是一种高效的秘密分享方法，能够有效解决大规模电子投票的隐私保护、投票记录防篡改、存储安全等关键信息安全问题。

Application of Secret Sharing Based on Random Linear Block Code in Electronic Voting

To meet the application requirements of large-scale secret sharing for electronic voting and improve the efficiency of secret sharing among a large number of devices, a secret sharing scheme based on random linear block code was proposed and applied to electronic voting. First, a parity-check matrix of random linear block code was constructed, which gives the coefficient matrix of the decoding equation set an extremely high probability of full rank, and ensures correct decoding of the secret. The encoding matrix was then generated from the parity-check matrix, and the voting information was encoded. Part of code word elements of the voting information were distributed to other equipment as shares without revealing the original information. Finally, the received shares were sentback by equipment to the source and the voting information with the shares received from others for restoration was decoded. The secret sharing based on random linear block code can discover the restored secret and shares error while restoring the secret. In this paper, the secret sharing speed, recovery speed and data redundancy volume under different data sizes of secret and the number of sharing participants were tested. Experiments showed that the proposed scheme has higher sharing and restoration efficiency, and lower data redundancy than traditional schemes. The proposed secret sharing based on random linear block code provides an efficient secret sharing scheme, which can effectively solve the key security problems such as privacy protection, voting record tamper-proof and storage security of large-scale electronic voting.