Multi-party Collaborative SM4 Encryption/Decryption Scheme in Key Management Service

doi:10.3969/j.issn.1671-1122.2021.08.003

Abstract

Abstract:

With the increasing demand for cryptograph localization and key protection, the composite application of commercial cryptographic algorithm and key security management has become one of the focuses of experts and scholars. In order to solve the problem of easy key disclosure in encryption/decryption scheme, this paper proposes a secure and efficient multi-party collaborative SM4 encryption/decryption scheme for key management service (KMS) system. The scheme uses the Beaver’s triple, which can be calculated predicatively and once, to construct a secure two-party multiplication and addition converter to ensure multi-party S-box collaborative computing, so as to realize the secure and efficient multi-party collaborative SM4 encryption/decryption and effectively reduce the computation and communication costs in the process of online interaction. Security analysis shows that the proposed scheme is secure under the malicious model and the other performance analysis details the computation and communication costs of the proposed scheme, which show that the proposed scheme is efficient and suitable for KMS system.

Key words: key management service, SM4, multi-party collaborate, Beaver’s triple

CLC Number:

TP309

YANG Yi, HE Debiao, WEN Yihong, LUO Min. Multi-party Collaborative SM4 Encryption/Decryption Scheme in Key Management Service[J]. Netinfo Security, 2021, 21(8): 17-25.

Figures/Tables 4

符号	定义
$\tau $	协同加/解密参与方个数
$i$	当前轮数,$i\in \{0,\cdots,31\}$
$j$	当前执行的S盒序号,$j\in \{0,\cdots,3\}$
${{P}_{\alpha }}$	协同加/解密参与方,$\alpha \in \{1,\cdots,\tau \}$
${{P}_{\beta }}$	协同加/解密参与方,$\beta \in \{1,\cdots,\tau \}$
$A$	域为2的8阶可逆矩阵,$A=\left( \begin{matrix} 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 \\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 \\ 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 \\ 1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 \\ 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 \\ \end{matrix} \right)$
$f$	函数,输入为二进制数,输出为向量,即$f\text{(}a\text{)=}\mathbf{a}$
$C$	域为$GF({{2}^{8}})$的向量,$\mathbf{C}=(1,1,0,0,1,0,1,1)$
C_j	每轮单个S盒中使用的向量
$FK$,$CK$	128 bit系统参数,$FK=\ (F{{K}_{0}},F{{K}_{1}},F{{K}_{2}},F{{K}_{3}})$,$CK=\ (C{{K}_{0}},C{{K}_{1}},C{{K}_{2}},C{{K}_{3}})$
$\text{mod}\ M(x)$	模不可约多项式,$M\left( x \right)=\ {{x}^{8}}+{{x}^{7}}+{{x}^{6}}+{{x}^{5}}+{{x}^{4}}+{{x}^{3}}+{{x}^{2}}+1$
L	线性变换,$L(B)=B\oplus (B<<<2)\oplus (B<<<10)\oplus $ $(B<<<18)\oplus (B<<<24)$
L′	线性变换,$L´(B)=B\oplus (B<<<13)\oplus (B<<<23)$
$key$	128 bit加/解密密钥
$M$	128 bit消息
${{M}^{\alpha }}$	${{P}_{\alpha }}$拥有的部分消息
$ke{{y}^{\alpha }}$	${{P}_{\alpha }}$拥有的部分加/解密密钥
${{(a_{i}^{\alpha })}_{j}}$	${{P}_{\alpha }}$的S盒输入
${{(\mathbf{b}_{i}^{\alpha })}_{j}}$	${{P}_{\alpha }}$选择的随机向量,${{(\mathbf{b}_{i}^{\alpha })}_{j}}\in GF({{2}^{8}})$
$l_{i}^{\alpha }$	${{P}_{\alpha }}$的S盒输出
$r{{k}_{i}}$	32 bit轮密钥,$i\in \{0,\cdots,31\}$
$r{{k}_{i}}^{\alpha }$	${{P}_{\alpha }}$拥有的部分轮密钥
$EN$	128 bit密文
$E{{N}^{\alpha }}$	${{P}_{\alpha }}$产生的部分密文
$\pi _{mul}^{prive}$	一种基于安全两方计算的乘加转换器

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参与方数量/个安全模型	2	15	45
半诚实模型	2.234	17.483	66.696
恶意模型	2.256	17.537	67.015

参与方数量/个安全模型	2	15	45
半诚实模型	32	3360	31680
恶意模型	64	3600	32400