基于编码的多接收方广义签密方案

doi:10.11959/j.issn.1000-436x.2020002

摘要/Abstract

摘要：

为解决具有多个接收方时的消息安全传输问题，设计了一种基于编码的多接收方广义签密方案。首先，设计了一个能够满足IND-CCA2安全的多次加密McEliece方案；然后，与CFS签名方案相结合设计了基于编码的多接收方签密与广义签密方案。安全性分析表明，该多接收方广义签密方案在机密性方面能够满足IND-CCA2安全，在不可伪造性方面能够满足EUF-CMA安全。与其他类似多接收方签密方案相比，所提方案不包含指数运算、双线性对运算等操作，具有较高的计算效率和抗量子计算的优势。与先签名后加密的方式相比，所提方案私钥数据量更少，效率更高。

关键词: 编码密码, 签密, 广义签密, 多接收方加密

Abstract:

In order to solve the problem of secure transmission of messages with multiple receivers,a code-based generalized signcryption scheme with multi-receiver was designed.Firstly,a multi-encrypted McEliece scheme that can meet the security of IND-CCA2 was designed.Combined with the CFS signature scheme,the multi-receiver signcryption and generalized signcryption scheme based on code were designed.The security analysis shows that the multi-receiver generalized signcryption scheme can meet the security of IND-CCA2 in terms of confidentiality and can meet EUF-CMA security in terms of unforgeability.Compared with other similar multi-receiver signcryption schemes,the proposed scheme does not include exponential,bilinear pairing operations,etc.,and has high computational efficiency and the advantage of anti-quantum computing.Compared with the method of signing-then-encrypting method,the proposed scheme has the smaller private key and higher efficiency.

Key words: code-based encryption, signcryption, generalized signcryption, multi-receiver encryption

中图分类号:

TP309.7

韩益亮,王众. 基于编码的多接收方广义签密方案[J]. 通信学报, 2020, 41(1): 53-65.

Yiliang HAN,Zhong WANG. Code-based generalized signcryption scheme with multi-receiver[J]. Journal on Communications, 2020, 41(1): 53-65.

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参考文献 33

[1]	SHOR P W . Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer[J]. SIAM Journal on Computing, 1997,26(5): 1484-1509.
[2]	BERNSTEIN D J , BUCHMANN J , DAHMEN E . Post quantum cryptography[C]// Springer, 2009: 73-80.
[3]	郭秋玲, 向宏, 蔡斌 ,等. 基于多变量公钥密码体制的门限环签名方案[J]. 密码学报, 2018,5(2): 140-150.
	GUO Q L , XIANG H , CAI B ,et al. Threshold ring signature scheme based on multivariate public key cryptosystems[J]. Journal of Cryptologic Research, 2018,5(2): 140-150.
[4]	汤海婷, 汪学明 . 一种基于格的属性多重加密方案[J]. 计算机工程, 2018,44(2): 193-196.
	TANG H T , WANG X M . An attribute multiple encryption scheme based on lattices[J]. Computer Engineering, 2018,44(2): 193-196.
[5]	徐权佐, 蔡庆军 . 一种基于编码的公钥密码体制的参数选择研究[J]. 信息网络安全, 2014(10): 54-58.
	XU Q Z , CAI Q J . Research on parameter selection of a code-based public-key cryptosystem[J]. Netinfo Security, 2014(10): 54-58.
[6]	张焕国, 管海明, 王后珍 . 量子计算的挑战与思考[J]. 云南民族大学学报(自然科学版), 2011,20(5): 388-395.
	ZHANG H G , GUAN H M , WANG H Z . The challenge of quantum computing to information security and our countermeasures[J]. Journal of Yunnan University of Nationalities(Natural Sciences Edition), 2011,20(5): 388-395.
[7]	YAN S Y . Quantum attacks on public-key cryptosystems[M]. Berlin: SpringerPress, 2013.
[8]	MCELIECE R J . A public-key cryptosystem based on algebraic coding theory[J]. The Deep Space Network Progress Report, 1978,4244: 114-116.
[9]	NIEDERREITER H . Knapsack-type cryptosystems and algebraic coding theory[J]. Problems Control Inform Theory, 1986,15(2): 159-166.
[10]	COURTOIS N T , FINIASZ M , SENDRIER N . How to achieve a McEliece-based digital signature scheme[C]// Advances in CryptologyASIACRYPT 2001. 2001: 157-174.
[11]	MATHEW K P , VASANT S , RANGAN C P . A provably secure signature and signcryption scheme using the hardness assumptions in coding theory[C]// Information Security and Cryptology—ICISC 2013. Springer International Publishing, 2013: 342-362.
[12]	GABORIT P , . Shorter keys for code based cryptography[C]// The International Workshop on Coding and Cryptography (WCC 2005). Bergen,Norway, 2005: 81-90.
[13]	MONICO C , ROSENTHAL J , SHOKROLLAHI A . Using low density parity check codes in the McEliece cryptosystem[C]// IEEE International Symposium on Information Theory. IEEE, 2000:215.
[14]	OTMANI A , TILLICH J P , DALLOT L . Cryptanalysis of two McEliece cryptosystems based on quasi-cyclic codes[J]. Mathematics in Computer Science, 2010,3(2): 129-140.
[15]	LONDAHL C , JOHANSSON T . A new version of McEliece PKC based on convolutional codes[C]// International Conference on Information and Communications Security. Springer, 2012: 461-470.
[16]	BALDI M . QC-LDPC code-based cryptography[M]. Berlin: SpringerPress, 2014.
[17]	李梦东, 孙玉情, 韦依儿 ,等. 改进的基于奇偶校验码的 McEliece变型方案[J]. 计算机应用研究, 2019(11): 1-7.
	LI M D , SUN Y Q , WEI Y E ,et al. Improved McEliece variant scheme based on parity-check codes[J]. Application Research of Computers, 2019(11): 1-7.
[18]	DENEUVILLE J C , GABORIT P ， ZéMOR G . Ouroboros:a simple,secure and efficient key exchange protocol based on coding theory[C]// International Workshop on Post-quantum Cryptography. Springer, 2017: 18-34.
[19]	BALDI M , BARENGHI A , CHIARALUCE F ,et al. LEDAkem:a post-quantum key encapsulation mechanism based on QC-LDPC codes[C]// International Conference on Post-Quantum Cryptography. Springer, 2018: 3-24.
[20]	EATON E , LEQUESNE M , PARENT A ,et al. QC-MDPC:a timing attack and a CCA2 KEM[C]// International Conference on PostQuantum Cryptography. Springer, 2018: 47-76.
[21]	ZHENG Y , . Digital signcryption or how to achieve cost (signature ＆encryption) cost(signature)+cost(encryption)[C]// Annual International Cryptology Conference. Springer, 1997: 165-179.
[22]	韩益亮, 杨晓元 . ECDSA 可公开验证广义签密[J]. 计算机学报, 2006,29(11): 105-114.
	HAN Y L , YANG X Y . New ECDSA-verifiable generalized signcryption[J]. Chinese Journal of Computers, 2006,29(11): 105-114.
[23]	AL-RIYAMI S S , PATERSON K G . Certificateless public key cryptograph[C]// International Conference on the Theory and Application of Cryptology and Information Security. Springer, 2003: 452-473.
[24]	BARBOSA M , FARSHIM P . Certificateless signcryption[C]// The ACM Symposium on Information,Computer and Communications Security. ACM, 2008: 369-372.
[25]	SELVI S S D , VIVEK S S , SHUKLA D ,et al. Efficient and provably secure certificateless multi-receiver signcryption[C]// International Conference on Provable Security. Springer, 2008: 52-67.
[26]	李慧贤, 陈绪宝, 庞辽军 ,等. 基于多变量公钥密码体制的无证书多接收者签密体制[J]. 计算机学报, 2012,35(9): 93-101.
	LI H X , CHEN X B , PANG L J ,et al. Certificateless multi-receiver signcryption scheme based on multivariate public key cryptography[J]. Chinese Journal of Computers, 2012,35(9): 93-101.
[27]	YUNG M . Practical signcryption[M]. Springer Science ＆ Business Media, 2010.
[28]	屈娟, 李艳平, 李丽 . 普适计算中匿名跨域认证协议的分析与改进[J]. 信息网络安全, 2018(1): 73-79.
	QU J , LI Y P , LI L . Cryptanalysis and security enhancement of an efficient secure authentication scheme with user anonymity for roaming user in ubiquitous networks[J]. Netinfo Security, 2018(1): 73-79.
[29]	周彦伟, 杨波, 张文政 . 普适计算环境下的安全访问模型[J]. 电子学报, 2017,45(4): 959-965.
	ZHOU Y W , YANG B , ZHANG W Z . Security access model in pervasive computing environment[J]. Acta Electronica Sinica, 2017,45(4): 959-965.
[30]	HAN Y , GUI X . Adaptive secure multicast in wireless networks[J]. International Journal of Communication Systems, 2009,22(9): 1213-1239.
[31]	韩益亮, 蓝锦佳, 杨晓元 . 基于 LRPC 码和多变量的签密方案[J]. 密码学报, 2016,3(1): 56-66.
	HAN Y L , LAN J J , YANG X Y . A signcryption scheme based on LRPC and multivariate cryptosystem[J]. Journal of Cryptologic Research, 2016,3(1): 56-66.
[32]	LI P C , HE M X , LI X ,et al. Efficient and provably secure certificateles signcryption from bilinear pairings[J]. Journal of Computational Information Systems, 2010,6(11): 3643-3650.
[33]	朱辉, 李晖, 王育民 . 不使用双线性对的无证书签密方案[J]. 计算机研究与发展, 2010,47(9): 1587-1594.
	ZHU H , LI H , WANG Y M . Certificateless signcryption scheme without bilinear pairing[J]. Journal of Computer Research and Development, 2010,47(9): 1587-1594.

方案	(n,k)维码字	公钥量/B	明文量/bit	密文量/bit	信息率
Goppa-M方案	(1 024,524)	67 072	524	1 024	0.51
(QC-LDPC)-M方案	(16 128,12 096)	6 048	12 096	16 128	0.75
多次加密-M方案	(16 128,12 096)	6 048	12 096	b16 128	0.75

方案	公钥/B	私钥/KB	明文量/bit	密文量/bit
CFS签名方案	6 048	33 742.4	12 096	16 128
多次加密-M方案	6 048	49 618.4	12 096	16 128 b
签名加密方案	12 096	83 360.8	12 096	16 128(b+2)
本文广义签密方案	12 096	51 608.8	12 096	16 128(b+2)

方案	指数运算	双线性对运算	Hash函数运算
Li等^[32]方案	? +1	2	2?+2
朱辉等^[33]方案	3?+4	0	3?+3
Selvi等^[25]方案	2?+2	2	? +7
本文广义签密方案	0	0	?+11