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Journal of Eastern Europe Research in Business & Economics

Hierarchical Identity-Based Encryption over q-Ary Lattices in the Random Oracle Model

Weronika SUMERA, Mariusz Jurkiewicz

Published Apr 8, 2026• 0 citations
Publisher

Abstract

This paper investigates a Hierarchical Identity Based Encryption () scheme, with emphasis on the construction of D. Cash, D. Hofheinz, E. Kiltz, and Ch. Peikert. The scheme is founded on -ary lattices and its security relies on the hardness of the Learning With Errors () problem, which is regarded as resistant to all known quantum algorithms. We propose a modified variant of the original design and provide a formal security analysis in the random oracle model, confirming that the modification preserves its theoretical guarantees. The central contribution of the study, however, lies in the implementation. We evaluate the scheme with respect to correctness, execution time, and computational overhead, offering a concrete assessment of its efficiency and scalability. The results show that the modified scheme combines post-quantum security with practical performance, making it a compelling candidate for applications that require hierarchical key management in a quantum aware environment.

DOI
10.5171/2025.4629125

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This paper investigates a Hierarchical Identity Based Encryption () scheme, with emphasis on the construction of D. Cash, D. Hofheinz, E. Kiltz, and Ch. Peikert. The scheme is founded on -ary lattices and its security relies on the hardness of the Learning With Errors () problem, which is regarded as resistant to all known quantum algorithms. We propose a modified variant of the original design and provide a formal security analysis in the random oracle model, confirming that the modification preserves its theoretical guarantees. The central contribution of the study, however, lies in the implementation. We evaluate the scheme with respect to correctness, execution time, and computational overhead, offering a concrete assessment of its efficiency and scalability. The results show that the modified scheme combines post-quantum security with practical performance, making it a compelling candidate for applications that require hierarchical key management in a quantum aware environment.
This paper investigates a Hierarchical Identity Based Encryption () scheme, with emphasis on the construction of D. Cash, D. Hofheinz, E. Kiltz, and Ch. Peikert. The scheme is founded on -ary lattices and its security relies on the hardness of the Learning With Errors () problem, which is regarded as resistant to all known quantum algorithms. We propose a modified variant of the original design and provide a formal security analysis in the random oracle model, confirming that the modification preserves its theoretical guarantees. The central contribution of the study, however, lies in the implementation. We evaluate the scheme with respect to correctness, execution time, and computational overhead, offering a concrete assessment of its efficiency and scalability. The results show that the modified scheme combines post-quantum security with practical performance, making it a compelling candidate for applications that require hierarchical key management in a quantum aware environment.
In this work, we introduce a novel post-quantum public key encryption scheme over integers, leveraging a hybrid approach that combines large random numbers with the Learning With Errors (LWE) system. The scheme addresses the security challenges posed by quantum computing advancements, aiming to provide a robust solution resistant to quantum-based attacks. By using the unknown random number hardness assumption with enhancements to the traditional LWE framework and operating directly on integers, this approach ensures a high level of cryptographic security while maintaining computational efficiency. Extensive theoretical and experimental analyses demonstrate that the proposed encryption system achieves state-of-the-art performance: encryption execution time as low as2.45×10−52.45 \times 10^{-5}2.45×10−5seconds, decryption time of4.47×10−54.47 \times 10^{-5}4.47×10−5seconds, and an integrity check time of5.30×10−55.30 \times 10^{-5}5.30×10−5seconds. Moreover, the ciphertext size is reduced to only 1330 bits while maintaining a 256 -bit security level, representing a significant reduction in storage requirements compared to conventional lattice-based approaches. These results confirm that our scheme not only provides strong quantum-resistant security guarantees but also delivers excellent efficiency and scalability, making it a viable candidate for secure communications in bandwidth-limited and resource-constrained environments in the quantum era.
As the progress of quantum computers, it is desired to propose many more efficient cryptographic constructions with post-quantum security. In the literatures, almost all cryptographic schemes and protocols can be explained and constructed modularly from certain cryptographic primitives, among which an Identity-Based Hash Proof System (IB-HPS) is one of the most basic and important primitives. Therefore, we can utilize IB-HPSs with post-quantum security to present several types of post-quantum secure schemes and protocols. Up until now, all known IB-HPSs with post-quantum security are instantiated based on latticed-based assumptions. However, all these lattice-based IB-HPSs are either in the random oracle model or not efficient enough in the standard model. Hence, it should be of great significance to construct more efficient IB-HPSs from lattices in the standard model. In this paper, we propose a new smooth IB-HPS with anonymity based on the Learning with Errors (LWE) assumption in the standard model. This new construction is mainly inspired by a classical identity-based encryption scheme based on LWE due to Agreawal et al. in Eurocrypt 2010. And our innovation is to employ the algorithm SampleGaussian introduced by Gentry et al. and the property of random lattice to simulate the identity secret key with respect to the challenge identity. Compared with other existing IB-HPSs in the standard model, our master public key is quite compact. As a result, our construction has much lower overheads on computation and storage.
Lattice-based hierarchical identity-based signature (HIBS) schemes are receiving significant attention due to provable security reductions and potential security for quantum computers. However, most of the existing HIBS schemes based on lattices are less efficient for practical applications. To make lattice-based HIBS schemes become more practical, this paper presents an efficient HIBS scheme from lattices. Both the secret key size and the signature length of our proposal are much shorter than those of other lattice-based HIBS proposals. Our scheme is proven to be strongly unforgeable against adaptive identity attacks in the random oracle model. The security of the construction relies on the standard short integer solution (SIS) assumption.
Signcryption is a public-key cryptographic primitive which combines the functions of public-key encryption and digital signature into a single logical step at low computational and communication costs. While multi-receiver signcryption is suited for a situation where a sender wants to send a signcrypted message to multiple receivers in a confidential and authenticated way. Due to this attractive property, recently, multi-receiver signcryption plays an important role in some practical applications such as virtual conference as well as authenticated mail transferring. In this paper, we present an efficient multi-receiver identity-based signcryption (MIBSC) scheme from lattice assumption which is believed to resist quantum computer attacks. The proposed scheme is provably secure in the random oracle model, which has the indistinguishability against chosen ciphertext attacks under the hardness of learning with errors (LWE), and existentially unforgeability against chosen message attacks under the small integer solution assumption (SIS). Moreover, we also compare our MIBSC scheme with existing schemes from performance efficiency and security, the result shows that our proposed scheme is more efficient and more secure. In particular, our scheme can be properly applied in the post-quantum communication environments.