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

Abstract

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

CLC Number:

TP309

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.

Figures/Tables 10

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

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

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

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