BFV-Blockchainvoting：支持BFV全同态加密的区块链电子投票系统

doi:10.11959/j.issn.1000-436x.2022172

通信学报 ›› 2022, Vol. 43 ›› Issue (9): 100-111.doi: 10.11959/j.issn.1000-436x.2022172

BFV-Blockchainvoting：支持BFV全同态加密的区块链电子投票系统

杨亚涛¹^,², 刘德莉¹, 刘培鹤², 曾萍¹^,², 肖嵩¹^,²

¹ 西安电子科技大学通信工程学院，陕西西安 710071
² 北京电子科技学院电子与通信工程系，北京 100070

修回日期:2022-06-06 出版日期:2022-09-25 发布日期:2022-09-01
作者简介:杨亚涛（1978- ），男，河南平顶山人，博士，北京电子科技学院教授、博士生导师，西安电子科技大学硕士生导师，主要研究方向为密码学与通信安全、全同态加密、密码协议和算法等
刘德莉（1998- ），女，山东德州人，西安电子科技大学硕士生，主要研究方向为区块链安全、安全协议与算法
刘培鹤（1972- ），男，黑龙江鹤岗人，北京电子科技学院工程师，主要研究方向为网络与通信安全、区块链安全
曾萍（1969- ），女，河南焦作人，博士，北京电子科技学院教授，主要研究方向为通信与网络安全、车联网安全、区块链安全等
肖嵩（1977- ），女，陕西西安人，博士，西安电子科技大学教授、博士生导师，主要研究方向为多媒体通信安全、通信与信息安全等
基金资助:
北京高校高精尖学科建设基金资助项目(3201023);“通信工程”“电子信息工程”国家级一流本科专业建设点基金资助项目;国家密码科学基金资助项目

BFV-Blockchainvoting: blockchain-based electronic voting systems with BFV full homomorphic encryption

Yatao YANG¹^,², Deli LIU¹, Peihe LIU², Ping ZENG¹^,², Song XIAO¹^,²

¹ School of Telecommunication Engineering, Xidian University, Xi’an 710071, China
² Department of Electronic and Communication Engineering, Beijing Electronics Science and Technology Institute, Beijing 100070, China

Revised:2022-06-06 Online:2022-09-25 Published:2022-09-01
Supported by:
Advanced and High Level Discipline Construction Fund of Universities in Beijing(3201023);The National First-class Under Graduate Dicipline Construction of “Communication Engineering” and “Electronic Information Engineering”;The National Cryptography Science Foundation of China

摘要/Abstract

摘要：

当前的电子投票系统大多依赖于中心服务器和可信第三方，这种系统架构增加了投票的安全隐患，甚至使投票可能失败。为了解决这一问题，将区块链技术应用于电子投票系统，使区块链代替可信第三方，提出了一种支持BFV全同态加密的区块链电子投票系统BFV-Blockchainvoting。首先，用一个公开透明的公告板记录选票信息，同时设计了智能合约来实现验证、自计票功能；其次，为进一步提高投票过程的安全可靠性，使用 SM2 签名算法对投票者的注册信息进行签名处理，再选择能够互相监督的双方共同监管选票，并使用 BFV 同态加密算法来隐藏计票数据。经过测试与分析，所提系统单张选票的计票时间平均为 1.69 ms。所提方案可以为投票过程中的不可操纵性、匿名性、可验证性、不可重用性、不可胁迫性和抗量子攻击等安全属性提供保障，适用于多种投票场合，并且可以满足大型投票场景下的高效率需求。

关键词: 电子投票, 区块链, 全同态加密, BFV同态加密, 智能合约

Abstract:

Current electronic voting systems mostly relied on central server and the trusted third party, this kind system architecture increases the security risks of voting, and even makes voting fail.In order to solve this issue, an electronic voting system BFV-blockchainvoting that supported BFV homomorphic encryption was proposed, and this system applied the blockchain technology to the electronic voting system to replace the trusted third party.Firstly, an open and transparent bulletin board was used to record the vote information, and an intelligent contract was used to realize the functions of verification and self counting.Secondly, in order to further improve the security and reliability of the voting process, the voter’s registration information was signed by SM2 signature algorithm, the ballot was managed by both parties that can supervise each other, and the counting data was encrypted by the BFV full homomorphic encryption algorithm.Finally, the evaluation of performance shows that it only costs 1.69 ms to complete one ballot in the proposed electronic voting system.This electronic voting scheme based on the BFV full homomorphic encryption and blockchain has better security attributes such as manipulation-resistance, anonymity, verifiability, double-voting resistance, coercion-resistance and resistance to quantum attacks.The scheme is suitable for a variety of voting scenarios and can meet the efficiency requirements in large voting scenarios.

Key words: electronic voting, blockchain, full homomorphic encryption, BFV homomorphic encryption, smart contract

中图分类号:

TP309

杨亚涛, 刘德莉, 刘培鹤, 曾萍, 肖嵩. BFV-Blockchainvoting：支持BFV全同态加密的区块链电子投票系统[J]. 通信学报, 2022, 43(9): 100-111.

Yatao YANG, Deli LIU, Peihe LIU, Ping ZENG, Song XIAO. BFV-Blockchainvoting: blockchain-based electronic voting systems with BFV full homomorphic encryption[J]. Journal on Communications, 2022, 43(9): 100-111.

图/表 10

表1

系统关键参数及含义"

参数	含义
$V_{i}, i \in [1, n]$	投票者
A	管理员
M	主持人
$C_{k}, k \in [1, m]$	候选人
$b_{i}, i \in [1, n]$	选票
xa	管理员的私钥
PA	管理员的公钥
xv	投票者的私钥
PV	投票者的公钥
(r,s)	SM2签名值
ki	SM4加密密钥
sk	BFV私钥
pk	BFV公钥
rlk	BFV计算密钥

表1

图1

表2

表3

图2

表4

BFV同态加密算法在本文方案中各个阶段的具体应用"

BFV流程	具体应用
私钥sk生成	随机生成的一个系数为-1、0或1的多项式
公钥pk生成	$pk = ([- a sk + e]_{p}, a)$ ，其中，a为在密文空间中随机生成的一个多项式，其系数模为 p；e为噪声多项式，是在
	离散高斯分布中随机选取的一组小系数，e在此处只用一次，用完后丢弃
计算密钥rlk生成	$rlk = [({[- (a_{i} sk + e_{i}) + T^{i} {sk}^{2}]}_{p}, a_{i})], i \in [0, 1, \dots, l]$ ，其中，T 为分解模数， $l = ⌊ \log_{T} (p) ⌋$ ，a_i、e_i的生成方式
	与公钥生成阶段该多项式的生成方式相同
选票加密(密文为cm )	$c_{m} = ({[{pk}_{0} u + e_{1} + \frac{q m}{t}]}_{p}, {[{pk}_{1} u + e_{2}]}_{p})$ ，其中，m 为明文，本文方案中投票者的选票b_i 中对某个候选人的
	cand_k 即需要加密的明文；u为系数为-1、0或1的多项式；t为远小于系数模 p的整数；e₁、e₂取自相同的高斯
	离散分布；u、e₁、e₂只在加密过程中使用，使用完后丢弃；pk为BFV的公钥， ${pk}_{0} = pk [0]$ ， ${pk}_{1} = pk [1]$
	$Add (c_{i m}, c_{j m}, rlk) = ({ct}_{i} [0] + {ct}_{j} [0], {ct}_{i} [1] + {ct}_{j} [1])$ ，其中， $Add (c_{i m}, c_{j m}, rlk)$ 表示将投票者v_i和v _j对候选人cand _m
计票(BFV密文相加运算)	的投票情况密文相加的结果， ${ct}_{i} [0]$ 和 ${ct}_{i} [1]$ 分别表示明文m_i 加密后得到的两位密文， ${ct}_{j} [0]$ 和 ${ct}_{j} [1]$ 分别表示明
	文m_j加密后得到的两位密文
BFV解密	$m^{'} = {[\frac{t {[c_{0} + c_{1} s]}_{p}}{p}]}_{t}$ ，其中， $c_{0} = c_{m} [0]$ ， $c_{1} = c_{m} [1]$ ，m′为BFV解密后的计票结果

表4

图3

图4

图5

表5

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结构名称	结构类型	存储数据
BlockID	int64	`json:"blockID"`
Timestamp	int64	`json:"timestamp"`
Transactions	string	`json:"transactions"`
Hash	[]transactionStruct	`json:"hash"`
PrevHash	string	`json:"prevhash"`
Difficulty	string	`json:"difficulty"`
Nonce	int	`json:"nonce"`

方法	功能
TimeSetup()	设置各阶段时间
KeyGenerator()	生成BFV算法公私钥
VaildID()	验证投票者身份是否合法
isVoted()	判断投票者是否重复投票
TallyElection()	计票
DecryptVote()	广播选票结果

方案	区块链技术	同态加密算法	多方安全监管	抗量子攻击	抗胁迫性	不可操纵性	匿名性	可验证性	计票时间/ms
文献[22]	√	Pallier	×	×	√	√	√	√	—
文献[29]	√	Pallier	×	×	×	√	√	√	813
文献[30]	×	Pallier	×	×	×	×	√	√	39.94
文献[31]	×	GSW	×	√	×	√	√	√	—
文献[11]	×	BFV	×	√	×	√	√	√	1.87
文献[20]	√	—	×	×	×	√	√	√	150
文献[25]	√	—	×	×	×	√	√	√	2.5
本文方案	√	BFV	√	√	√	√	√	√	1.69

BFV-Blockchainvoting：支持BFV全同态加密的区块链电子投票系统

BFV-Blockchainvoting: blockchain-based electronic voting systems with BFV full homomorphic encryption

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图/表 10

参考文献 31

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