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Lecture notes in computer science

Fine-Grained Non-interactive Key-Exchange Without Idealized Assumptions

Yuyu Wang, Chuanjie Su, Jiaxin Pan

Published Jan 1, 2024• 0 citations
Publisher
DOI
10.1007/978-3-031-68379-4_8

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Attribute-based authenticated key exchange (AB-AKE) is a useful primitive that allows a group of users to establish a shared secret key and at the same time enables fine-grained access control. A straightforward approach to design an AB-AKE protocol is to extend a key exchange protocol using an attribute-based authentication technique. However, insider security is a challenge security issue for AB-AKE in the multi-party setting and cannot be solved using the straightforward approach. In addtion, many existing key exchange protocols for the multi-party setting (e.g., the well-known Burmester-Desmedt protocol) require multiple broadcast rounds to complete the protocol. In this paper, we propose a novel one-round attribute-based key exchange (OAKE) protocol in the multi-party setting. We define the formal security models, including session key security, insider security and user privacy, for OAKE, and prove the security of the proposed protocol under some standard assumptions in the random oracle model.
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.