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SI-CP-ABE: an isogeny-based ciphertext-policy attribute-based encryption scheme

Xiwen Chen, Jinrong Chen, Xu Zheng, Zhou Zijian

Published Apr 1, 2026• 0 citations
OpenAlex

Abstract

Ciphertext-policy attribute-based encryption (CP-ABE) serves as a fundamental cryptographic primitive for fine-grained data access control. However, existing schemes, primarily based on bilinear maps or lattice hardness assumptions, generally suffer from large system parameters, key sizes, and ciphertext sizes, which severely restrict their deployment in resource-constrained scenarios. To address this challenge, a novel CP-ABE scheme based on supersingular elliptic curve isogeny (SI-CP-ABE) is proposed. This scheme integrates the action of isogeny ideal class group with linear secret sharing schemes, achieving efficient fine-grained access control in a post-quantum security setting. Regarding security, two new hardness assumptions—P+-CSSCDH and P+-CSSDDH—are proposed, based on which the scheme is rigorously proven to satisfy indistinguishability under chosen plaintext attack in the selective security model. To further enhance performance, an optimized scheme is designed based on SI-CP-ABE. Furthermore, based on the core algebraic structure of SI-CP-ABE, a post-quantum Naor-Reingold-type pseudo-random function with authentication capability is constructed, thereby enriching the building blocks for post-quantum cryptographic protocols.

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Ciphertext-policy attribute-based encryption (CP-ABE) serves as a fundamental cryptographic primitive for fine-grained data access control. However, existing schemes, primarily based on bilinear maps or lattice hardness assumptions, generally suffer from large system parameters, key sizes, and ciphertext sizes, which severely restrict their deployment in resource-constrained scenarios. To address this challenge, a novel CP-ABE scheme based on supersingular elliptic curve isogeny (SI-CP-ABE) is proposed. This scheme integrates the action of isogeny ideal class group with linear secret sharing schemes, achieving efficient fine-grained access control in a post-quantum security setting. Regarding security, two new hardness assumptions—P+-CSSCDH and P+-CSSDDH—are proposed, based on which the scheme is rigorously proven to satisfy indistinguishability under chosen plaintext attack in the selective security model. To further enhance performance, an optimized scheme is designed based on SI-CP-ABE. Furthermore, based on the core algebraic structure of SI-CP-ABE, a post-quantum Naor-Reingold-type pseudo-random function with authentication capability is constructed, thereby enriching the building blocks for post-quantum cryptographic protocols.
Ciphertext policy attribute-based encryption (CP-ABE) is a promising cryptographic technology that provides fine-grained access control as well as data confidentiality. It enables one sender to encrypt the data for more receivers, and to specify a policy on who can decrypt the ciphertext using his/her attributes alone. However, most existing ABE schemes are constructed on bilinear maps and they cannot resist quantum attacks. In this paper, we propose a multi-authority CP-ABE (MA-CPABE) scheme on ideal lattices which is still secure in post-quantum era. On one hand, multiple attribute authorities are required when user's attributes cannot be managed by a central authority. On the other hand, compared with generic lattice, the ideal lattice has extra algebraic structure and can be used to construct more efficient cryptographic applications. By adding some virtual attributes for each authority, our scheme can support flexible threshold access policy. Security analysis shows that the proposed scheme is secure against chosen plaintext attack (CPA) in the standard model under the ring learning with errors (R-LWE) assumption.
Lattice-based Attribute-based encryption is a well-known cryptographic mechanism that can resist quantum attacks and has the ability of fine-grained access control, and it has a wide range of application scenarios in current Internet of Thing (IoT) era. However, lack of efficiency and existing the problem of large ciphertext expansion rate are the main disadvantages impede the applications of this mechanism. Thus, we propose an efficient and practical ciphertext policy attribute-based encryption (CP-ABE) scheme from lattices in the paper. In this scheme, to make the secret key reusable, we adjust access tree and propose a basic access tree structure, which can be converted from disjunctive normal form, and combine it with a light post-quantum scheme of Kyber. In addition, the compression method and plaintext expansion method are introduced to optimize the scheme. Our CP-ABE scheme is secure against chosen plaintext attack under the hardness of module learning with errors problem. We implement our scheme and compare it with three recent related schemes in terms of security, function and communication cost. Experiments and comparisons show that our CP-ABE scheme has advantages in high encryption efficiency, small matrix dimension, small key sizes, and low ciphertext expansion rate, which has some merit in practice.
In Ciphertext Policy Attribute-Based Encryption (CP-ABE) system, a set of attributes is associated with the private keys of each user. Also, the ciphertext is attached with a policy which is defined over that set of attributes. A user can decrypt the ciphertext if the ciphertext’s policy is satisfied by the attributes associated hith her private key. Traditional CP-ABE schemes, based on number theoretic problems, rely on a trustworthy central authority. But in many distributed applications it is expected that such authorities should be decentralized to avoid the risks of single-point failure. While the number theory-based hardness problems are prone to quantum attacks, lattice-based hardness problems can resist such attacks. In this paper, we construct a Decentralized Ciphertext-Policy Attribute-Based Encryption (DCP-ABE) scheme. Under this scheme, any participating entity can act as an authority by creating a public key. The athority utilizes the users’ attributes to generate the private keys for them. Any user can encrypt data in terms of any monotone access structure over attributes issued from any chosen set of authorities. Hence the protocol does not depend on any central authority. We utilize Learning With Errors over Rings (R-LWE) as the underlying hardness assumption for te protocol. The proposed post-quantum protocol achieves security under selective-set model whereby adversaries are allowed to corrupt any authority only statically through adaptive key queries.
The advent of quantum computing poses a significant threat to traditional cryptographic algorithms, including RSA, Diffie-Hellman, and Elliptic Curve Cryptography, due to the capabilities of quantum algorithms like Shor’s algorithm. Post-quantum cryptography (PQC) has emerged to address these challenges, with lattice-based cryptography (LBC) being a prominent candidate. LBC, underpinned by hard mathematical problems like Learning with Errors (LWE) and Ring-LWE (RLWE), offers robust security against quantum and classical adversaries. In parallel, Ciphertext-Policy Attribute-Based Encryption (CPABE) has become a critical tool for enabling fine-grained access control in data-sharing scenarios, such as secure cloud storage and IoT. While existing CP-ABE implementations rely on bilinear pairings vulnerable to quantum attacks, lattice-based CPABE schemes provide a quantum-resistant alternative. Despite their potential, these schemes face challenges in computational efficiency, collusion resistance, and implementation correctness. Our contributions include a detailed mathematical breakdown of one of the state-of-the-art (SOTA) lattice-based CP-ABE schemes and a novel correctness proof for the same scheme.
The recent promising results on the hardness of lattice problems have inspired the construction of several Attribute-based Encryption (ABE) schemes from the quantum resistant perspective. However, these schemes are insufficient enough for supporting real-world applications due to inherent quadratic overhead problem in the use of Learning With Error (LWE). To solve this problem, this paper proposed a Ciphertext-Policy Attribute-Based Encryption (CP-ABE) scheme from a more lightweight ideal lattice classes- Ring-Learning with Errors (Ring-LWE), that further called as CP-ABER-LWEscheme. Compared to existing R-LWE based ABE scheme, the proposed CP-ABER-LWEis capable to handle a monotone access structure and enjoys collusion resistance properties. We exploited Linear Secret Scheme (LSSS) to express a monotone access structure. For resist to collusion attack, we applied the private key randomization technique to blind the user's private key. The proposed scheme CP-ABER-LWEis further proven to be secure under the Decision Ring-LWEd,q,χproblem in the selective set model.
As the internet becomes prevalent, plenty of sensitive data is being transferred in open networks environment. It is worth concerning how to achieve efficient data transfer in a privacy-preserving manner. Although attribute-based encryption (ABE) can achieve fine-grained access control over encrypted data, it still could not work for restricting unauthorised user to access. In this paper, we introduce a new cryptographic primitive called attribute-based encryption supporting data filtration (ABE-SDF), and formalise the security mode by incorporating the advantages into previous ABE. Finally, we present an efficient construction of the scheme over post-quantum assumptions our scheme is believed to be quantum-resistant owing to the special property of lattices. Based on the LWE assumption, we prove that the proposed scheme has the indistinguishability against selective chosen plaintext attacks and the authentication information security.