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.

Journal of Eastern Europe Research in Business & EconomicsApr 8, 20260 citations

Lwe-Based Single Noisy Linear Equations for Public Key Over Integer Encryption

Mostefa Kara, Ahcène Bounceur, Abdelkader Laouid +3 more

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 as $2.45 \times 10^{-5}$ seconds, decryption time of $4.47 \times 10^{-5}$ seconds, and an integrity check time of $5.30 \times 10^{-5}$ seconds. 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.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 as$2.45 \times 10^{-5}$seconds, decryption time of$4.47 \times 10^{-5}$seconds, and an integrity check time of$5.30 \times 10^{-5}$seconds. 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.

IEEE PES Conference on Innovative Smart Grid Technologies - Middle East (ISGT Middle East)Nov 23, 20250 citations

Enhanced Provably Secure NTRU Encryption Based on Hard Learning over Rings

Wu Yan Fang, Zheng Huang, Wang Li Cheng +1 more

Since the presentation of NTRU public-key cryptosystem by Hoffstein, Pipher and Silverman, its favorable properties, such as easily created keys, high speed, excellent performance and conjectured resistance to quantum computers, have made it to be of great use. This paper proposes an enhanced scheme based on the hard learning with error over ring (R-LWE) problem to improve the security of the modified NTRUEncrypt presented by Stehle and Steinfled. We used part of the padding ideas of Fujisaki and Okamoto to obtain this scheme. It is semantically secure in strong sense of indistinguishability against adaptive chosen-ciphertext attacks in the random oracle model assuming the quantum hardness of standard worst-case problem over ideal lattices. It is also possible to arbitrarily decrease the error probability, and even to eliminate it completely. We gave the detailed analysis using the known results from classic works. Furthermore, this scheme owns many advantages such as the uniformity of public key, usual assumptions and the freedom for coding messages.Since the presentation of NTRU public-key cryptosystem by Hoffstein, Pipher and Silverman, its favorable properties, such as easily created keys, high speed, excellent performance and conjectured resistance to quantum computers, have made it to be of great use. This paper proposes an enhanced scheme based on the hard learning with error over ring (R-LWE) problem to improve the security of the modified NTRUEncrypt presented by Stehle and Steinfled. We used part of the padding ideas of Fujisaki and Okamoto to obtain this scheme. It is semantically secure in strong sense of indistinguishability against adaptive chosen-ciphertext attacks in the random oracle model assuming the quantum hardness of standard worst-case problem over ideal lattices. It is also possible to arbitrarily decrease the error probability, and even to eliminate it completely. We gave the detailed analysis using the known results from classic works. Furthermore, this scheme owns many advantages such as the uniformity of public key, usual assumptions and the freedom for coding messages.

Applied Mechanics and MaterialsNov 1, 20120 citations

Ring-LWE Identity-Based Encryption with Dynamic Revocation for Cloud Data Sharing

Gabriel Assamah, Alimatu Latiff Yussif, Benjamin Appiah +2 more

Cloud storage faces significant security and access control challenges due to reduced user oversight and the emerging threat of quantum computing to traditional cryptographic methods. Existing revocable Identity-Based Encryption (IBE) schemes are limited by their lack of post quantum security, inefficient revocation mechanisms that require re-encryption of data, and cumbersome key update procedures. We propose a post-quantum secure Ring-LWE IBE scheme with dynamic time-based revocation tailored for cloud environments. Our solution is built on the hardness of the Ring Learning with Errors (RLWE) problem to ensure quantum resistance and introduces a novel time-based revocation framework. In our approach, user access is bound to discrete periods and managed through a hierarchical binary tree structured over identities and time. This design eliminates the need to re-encrypt stored data upon user revocation. Instead, a trusted authority periodically distributes lightweight key updates exclusively to non-revoked users. Thanks to the binary tree structure, non-revoked users can compute updated decryption keys with only O (log Nₘₐₓ) overhead in both computation and communication, where Nₘₐₓ is the maximum number of users or periods. Revoked users, having no access to future updates, lose decryption capabilities. We provide formal security proofs showing the schemes resistance against adaptive identity and time-period-based attacks, grounded in the RLWE assumption. Overall, our scheme offers an effective combination of post-quantum security, efficient access control, and simplified key management, making it suitable for secure cloud data sharing in the quantum era.Cloud storage faces significant security and access control challenges due to reduced user oversight and the emerging threat of quantum computing to traditional cryptographic methods. Existing revocable Identity-Based Encryption (IBE) schemes are limited by their lack of post quantum security, inefficient revocation mechanisms that require re-encryption of data, and cumbersome key update procedures. We propose a post-quantum secure Ring-LWE IBE scheme with dynamic time-based revocation tailored for cloud environments. Our solution is built on the hardness of the Ring Learning with Errors (RLWE) problem to ensure quantum resistance and introduces a novel time-based revocation framework. In our approach, user access is bound to discrete periods and managed through a hierarchical binary tree structured over identities and time. This design eliminates the need to re-encrypt stored data upon user revocation. Instead, a trusted authority periodically distributes lightweight key updates exclusively to non-revoked users. Thanks to the binary tree structure, non-revoked users can compute updated decryption keys with only O (log Nₘₐₓ) overhead in both computation and communication, where Nₘₐₓ is the maximum number of users or periods. Revoked users, having no access to future updates, lose decryption capabilities. We provide formal security proofs showing the schemes resistance against adaptive identity and time-period-based attacks, grounded in the RLWE assumption. Overall, our scheme offers an effective combination of post-quantum security, efficient access control, and simplified key management, making it suitable for secure cloud data sharing in the quantum era.

Indian Journal of Cryptography and Network SecurityNov 25, 20250 citations

Novel Identity-Based Hash Proof System with Compact Master Public Key from Lattices in the Standard Model

Qiqi Lai, Bo Yang, Zhe Xia +3 more

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.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.

International Journal of Foundations of Computer ScienceJun 1, 20191 citation

NIST’s Module-Lattice-Based Key-Encapsulation Mechanism and its security

Anna Jokiniemi

This thesis is an in-depth introduction to NIST's post-quantum Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM). We begin by introducing the problem at the core of ML-KEM, known as the Module Learning With Errors (MLWE) problem. In this problem, an adversary attempts to distinguish between samples selected from a specific distribution and samples from uniformly random samples. We also discuss the hardness of the MLWE problem, under the conjecture that certain lattice problems over modules are hard. ML-KEM utilizes a variant of the Fujisaki-Okamoto transformation, which employs a weakly secure Public-Key Encryption (PKE) scheme to construct a strongly secure key-encapsulation mechanism in the Random Oracle Model (ROM). We explain the working principle of the MLWE-based public-key encryption scheme and demonstrate how ML-KEM is constructed from it. Finally, we analyze the security of ML-KEM. We provide a tight security bound for IND-CCA security of ML-KEM in ROM, under the assumption that the underlying PKE is IND-CPA secure. Additionally, we present two security theorems in the Quantum Random Oracle Model (QROM). The first theorem establishes non-tightly IND-CCA security of ML-KEM in QROM if the MLWE problem is hard to solve. The second theorem assumes that the deterministic PKE is ciphertext-indistinguishable. Under this assumption, we derive a tighter bound for the IND-CCA security of ML-KEM in QROM.This thesis is an in-depth introduction to NIST's post-quantum Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM). We begin by introducing the problem at the core of ML-KEM, known as the Module Learning With Errors (MLWE) problem. In this problem, an adversary attempts to distinguish between samples selected from a specific distribution and samples from uniformly random samples. We also discuss the hardness of the MLWE problem, under the conjecture that certain lattice problems over modules are hard. ML-KEM utilizes a variant of the Fujisaki-Okamoto transformation, which employs a weakly secure Public-Key Encryption (PKE) scheme to construct a strongly secure key-encapsulation mechanism in the Random Oracle Model (ROM). We explain the working principle of the MLWE-based public-key encryption scheme and demonstrate how ML-KEM is constructed from it. Finally, we analyze the security of ML-KEM. We provide a tight security bound for IND-CCA security of ML-KEM in ROM, under the assumption that the underlying PKE is IND-CPA secure. Additionally, we present two security theorems in the Quantum Random Oracle Model (QROM). The first theorem establishes non-tightly IND-CCA security of ML-KEM in QROM if the MLWE problem is hard to solve. The second theorem assumes that the deterministic PKE is ciphertext-indistinguishable. Under this assumption, we derive a tighter bound for the IND-CCA security of ML-KEM in QROM.

Työväentutkimus VuosikirjaFeb 26, 20250 citations

2.45 \times 10^{-5}

seconds, decryption time of

4.47 \times 10^{-5}

seconds, and an integrity check time of

5.30 \times 10^{-5}

seconds. 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.