Electronic voting scheme based on SM2 threshold blind signature

doi:10.11772/j.issn.1001-9081.2022121876

Abstract

Abstract:

An electronic voting scheme based on SM2 blind threshold signature was proposed to address the security and efficiency issues in the algorithm protocol layer of domestic electronic election system. Firstly，the SM2 threshold blind signature algorithm was constructed based on the SM2 signature algorithm，the methods of Shamir secret sharing， Random Secret Sharing （RSS）， secret sum， difference and product sharing， and Inversion Secret Sharing （ISS） were used to share the secret private key and random number in SM2 signature algorithm without changing the original signature process. At the same time，a blinding factor was introduced to blind the message to be signed， achieving the privacy protection of the message sender and effective sharing of sensitive information. Secondly，the algorithm security analysis results show that， the constructed blind signature algorithm has blindness， robustness，and non-forgeability under the random oracle model. Compared with the existing RSA （Rivest-Shamir-Adleman） and Elliptic Curve Digital Signature Algorithm （ECDSA） threshold blind signature algorithms，the constructed SM2 threshold blind signature algorithm has the advantages of low computational complexity and small computational cost， making it suitable for large-scale elections. Finally， a secure electronic voting protocol was designed based on the SM2 threshold blind signature algorithm. The analysis results show that the proposed protocol has properties such as non-forgeability， confidentiality， legality， and robustness. Furthermore， a single voting process can be completed in just 15.706 1 ms.

Key words: electronic voting, SM2 signature algorithm, threshold cryptography, non-forgeability, robustness

摘要：

针对提高国产化电子选举系统算法协议层的安全和效率问题，提出一种基于SM2门限盲签名电子选举方案。首先，基于SM2签名算法构造SM2门限盲签名算法，在不改变原有签名流程的前提下，采用Shamir秘密分享、随机秘密分享（RSS）、秘密和差、乘积分享、逆的秘密分享（ISS）等方法分享SM2签名算法中的秘密私钥和随机数，同时引入盲化因子对签名的消息进行盲化，实现签名过程中消息发送方的隐私保护及敏感信息的有效分享；其次，算法安全分析结果表明，在随机预言机模型下，所提的盲签名算法具有盲性、健壮性和不可伪造性，相较于现有的RSA（Rivest-Shamir-Adleman）、椭圆曲线数字签名算法（ECDSA）门限盲签名算法，所提的SM2门限盲签名算法具有计算复杂度低、通信开销较小的优势，适用于大规模选举；最后，基于SM2门限盲签名算法设计安全电子选举协议，分析结果表明，所提协议具有不可伪造性、保密性、合法性和鲁棒性，并且完成一次投票过程仅需15.706 1 ms。

关键词: 电子选举, SM2签名算法, 门限密码学, 不可伪造性, 健壮性

CLC Number:

TP309.7

Jintao RAO, Zhe CUI. Electronic voting scheme based on SM2 threshold blind signature[J]. Journal of Computer Applications, 2024, 44(2): 512-518.

饶金涛, 崔喆. 基于SM2门限盲签名电子选举方案[J]. 《计算机应用》唯一官方网站, 2024, 44(2): 512-518.

Figures/Tables 5

Tab. 1 Computation overhead of primary operations

符号	运算操作	长度/bit	计算开销/ms
$T M 0$	模乘运算	1 024	0.002 4
$T M 1$	模乘运算	256	0.000 7
$T P$	标量乘法的运算	256	0.861 0
$T I 0$	模逆运算	1 024	0.046 0
$T I 1$	模逆运算	256	0.010 0
$T A$	点加运算	256	0.003 0
$T Q$	模指数运算	1 024	2.500 0

Tab. 1 Computation overhead of primary operations

符号	运算操作	长度/bit	计算开销/ms
$T M 0$	模乘运算	1 024	0.002 4
$T M 1$	模乘运算	256	0.000 7
$T P$	标量乘法的运算	256	0.861 0
$T I 0$	模逆运算	1 024	0.046 0
$T I 1$	模逆运算	256	0.010 0
$T A$	点加运算	256	0.003 0
$T Q$	模指数运算	1 024	2.500 0

Tab. 2 Performance comparison of different schemes

方案	计算开销/ms	通信开销/bit
本文方案	$(2 m + 4) T P + (m + 1) T A + T I 1 ≈ 1.725 m + 3.457 0$	$m * 256 * 3 + (2 m + 1) * 512 + 512 ≈ 1 792 m + 1 024$
文献［10］方案	$2 m T Q + (m + 1) T M 0 + T I 0 ≈ 5.002 4 m + 0.048 4$	$m * 1 024 * 5 + m * 2 048 + 2 048 ≈ 7 168 m + 2 048$
文献［11］方案	$(m + 1) T Q ≈ 2.5 m + 2.5$	$m * 1 024 * 4 + m * 2 048 + 2 048 ≈ 6 144 m + 2 048$
文献［12］方案	$(2 m + 1) T M 0 + (m + 1) T Q ≈ 2.504 8 m + 2.502 4$	$m * 1 024 * 8 + m * 2 048 + 2 048 ≈ 10 240 m + 2 048$
文献［13］方案	$(2 m + 1) T Q + m T I 0 + T M 0 ≈ 5.046 m + 2.502 4$	$m * 1 024 * 6 + m * 2 048 + 2 048 ≈ 8 192 m + 2 048$

Tab. 2 Performance comparison of different schemes

方案	计算开销/ms	通信开销/bit
本文方案	$(2 m + 4) T P + (m + 1) T A + T I 1 ≈ 1.725 m + 3.457 0$	$m * 256 * 3 + (2 m + 1) * 512 + 512 ≈ 1 792 m + 1 024$
文献［10］方案	$2 m T Q + (m + 1) T M 0 + T I 0 ≈ 5.002 4 m + 0.048 4$	$m * 1 024 * 5 + m * 2 048 + 2 048 ≈ 7 168 m + 2 048$
文献［11］方案	$(m + 1) T Q ≈ 2.5 m + 2.5$	$m * 1 024 * 4 + m * 2 048 + 2 048 ≈ 6 144 m + 2 048$
文献［12］方案	$(2 m + 1) T M 0 + (m + 1) T Q ≈ 2.504 8 m + 2.502 4$	$m * 1 024 * 8 + m * 2 048 + 2 048 ≈ 10 240 m + 2 048$
文献［13］方案	$(2 m + 1) T Q + m T I 0 + T M 0 ≈ 5.046 m + 2.502 4$	$m * 1 024 * 6 + m * 2 048 + 2 048 ≈ 8 192 m + 2 048$

Fig.1 Comparison of relation between computation overhead and maximum threshold number among different schemes

Fig.2 Comparison of relation between communication overhead and maximum threshold number among different schemes

Fig.3 Overall architecture of proposed scheme

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