Multi-authority attribute-based encryption scheme for private blockchain over public blockchain

doi:10.11772/j.issn.1001-9081.2023121816

Abstract

Abstract:

Blockchain is an emerging data structure that combines distributed storage， consensus mechanisms， principles of cryptography， and other technologies. Aiming at the problem of data access control on public blockchain， a Multi-Authority Attribute-Based Encryption （MA-ABE） scheme for Private blockchain Over Public blockchain （POP） was proposed. Firstly， the private blockchain based on public blockchain was constructed， and a specific data privacy protection process was given. Secondly， a joint authority initialization algorithm and a joint key generation algorithm were designed. Finally， the static security of the proposed scheme was proved by using the Decisional Bilinear Diffie-Hellman （DBDH） assumption through simulating the challenge ciphertext and the user private key under the random oracle model. Experimental results show that the proposed scheme can resist collusion attacks under $n - 1$ parties of malicious authorities targeting the master key.

Key words: blockchain, Multi-Authority Attribute-Based Encryption (MA-ABE), joint algorithm, static security, collusion attack

摘要：

区块链是一种结合分布式存储、共识机制和密码学原理等技术的新兴数据结构。针对公有链上的数据访问控制问题，提出一种面向公有区块链上的私有区块链（POP）的多权威属性加密（MA-ABE）方案。首先，构建依托公有区块链的私有区块链，并给出具体的数据隐私保护流程；其次，设计联合权威初始化算法以及联合密钥生成算法；最后，在随机预言机模型下，通过模拟挑战密文和用户私钥，使用基于判定性双线性Diffie-Hellman （DBDH）的假设证明所提方案满足静态安全性。实验结果表明，在保证安全性的前提下，所提方案能够抵抗针对主密钥的 $n - 1$ 方恶意权威下的合谋攻击。

关键词: 区块链, 多权威属性加密, 联合算法, 静态安全性, 合谋攻击

CLC Number:

TN918.1

Keshuo SUN, Haiying GAO, Yang SONG. Multi-authority attribute-based encryption scheme for private blockchain over public blockchain[J]. Journal of Computer Applications, 2024, 44(12): 3699-3708.

孙科硕, 高海英, 宋杨. 面向公有区块链上的私有区块链的多权威属性加密方案[J]. 《计算机应用》唯一官方网站, 2024, 44(12): 3699-3708.

Figures/Tables 7

Tab.1 Summary of different MA-ABE schemes

方案	加密方案	访问结构	困难问题	中央权威	权威协调
文献［17］方案	基于密钥策略	（T，N）门限	BDH	有	不需要
文献［18］方案	基于密钥策略	（T，N）门限	BDH	无	需要
文献［19］方案	基于密钥策略	（T，N）门限	k-DDHI	无	需要
文献［20］方案	基于密文策略	单调布尔电路	子群判定假设	无	不需要
文献［21］方案	基于密文策略	LSSS矩阵	q-DPBDHE	无	不需要
文献［22］方案	基于密文策略	NC¹电路	CBDH	无	不需要

Fig. 1 Structure of blockchain

Fig. 2 Basic architecture of POP blockchain

Fig. 3 Data protection on private blockchain

Tab. 2 Description of symbols

符号	含义
$l$	集合 ${1,2, ⋯, l}$
$ρ : l → A U$	建立了矩阵的行标号 $l$ 同属性权威 $A U$ 的对应关系
$M i$	矩阵 $M$ 的第 $i$ 行
$M L$	由矩阵 $M$ 的第 $i$ 行组成的集合， $L = i i ∈ l$
$(M i) k$	矩阵 $M$ 的第 $i$ 行中前 $k$ 维组成的向量
$u ∈$ $U 1$ \ $U 2$	属性 $u$ 在集合 $U 1$ 但不在集合 $U 2$

Tab. 2 Description of symbols

符号	含义
$l$	集合 ${1,2, ⋯, l}$
$ρ : l → A U$	建立了矩阵的行标号 $l$ 同属性权威 $A U$ 的对应关系
$M i$	矩阵 $M$ 的第 $i$ 行
$M L$	由矩阵 $M$ 的第 $i$ 行组成的集合， $L = i i ∈ l$
$(M i) k$	矩阵 $M$ 的第 $i$ 行中前 $k$ 维组成的向量
$u ∈$ $U 1$ \ $U 2$	属性 $u$ 在集合 $U 1$ 但不在集合 $U 2$

Tab. 3 Comparison of storage size and feature among different schemes

方案	权威公钥规模	权威私钥规模	用户私钥规模	密文规模	抗合谋能力
文献［21］方案	$2 A U$	$2 A U$	$2 A U$	$4 l + 1$	0
文献［22］方案	$s m a x A U$	$s m a x A U$	$A U$	$(s m a x + 1) l + 1$	0
本文方案	$s m a x ∑ u ∈ A U A S u$	$s m a x ∑ u ∈ A U A S u$	$∑ u ∈ A U A S u$	$(s m a x + 1) l + 1$	$n - 1$

Tab. 3 Comparison of storage size and feature among different schemes

方案	权威公钥规模	权威私钥规模	用户私钥规模	密文规模	抗合谋能力
文献［21］方案	$2 A U$	$2 A U$	$2 A U$	$4 l + 1$	0
文献［22］方案	$s m a x A U$	$s m a x A U$	$A U$	$(s m a x + 1) l + 1$	0
本文方案	$s m a x ∑ u ∈ A U A S u$	$s m a x ∑ u ∈ A U A S u$	$∑ u ∈ A U A S u$	$(s m a x + 1) l + 1$	$n - 1$

Tab. 4 Comparison of computational complexity among different schemes

方案	密钥生成算法	加密算法	解密算法
文献［21］方案	$4 A U A 1$	$P + 4 l A 1 + 2 l + 1 A 2$	$3 A U D P + I$
文献［22］方案	$s m a x A U A 1$	$P + 4 s m a x l A 1 + 2 l + 1 A 2$	$s m a x A U D P + A U D + 1 I$
本文方案	$s m a x ∑ u ∈ A U A S u A 1$	$P + 4 s m a x l A 1 + 2 l + 1 A 2$	$s m a x A U D P + A U D + 1 I$

Tab. 4 Comparison of computational complexity among different schemes

方案	密钥生成算法	加密算法	解密算法
文献［21］方案	$4 A U A 1$	$P + 4 l A 1 + 2 l + 1 A 2$	$3 A U D P + I$
文献［22］方案	$s m a x A U A 1$	$P + 4 s m a x l A 1 + 2 l + 1 A 2$	$s m a x A U D P + A U D + 1 I$
本文方案	$s m a x ∑ u ∈ A U A S u A 1$	$P + 4 s m a x l A 1 + 2 l + 1 A 2$	$s m a x A U D P + A U D + 1 I$

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