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Cryptography
Special Issues
Advances in Post-Quantum Cryptography
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Advances in Post-Quantum Cryptography

A special issue of Cryptography (ISSN 2410-387X).

Deadline for manuscript submissions: 20 December 2026 | Viewed by 7788

Special Issue Editors

Dr. Xianhui Lu

E-Mail Website
Guest Editor
Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China
Interests: post-quantum cryptography; fully homomorphic encryption; physical layer cryptography
Prof. Dr. Jianfeng Wang

E-Mail Website
Guest Editor
School of Cyber Engineering, Xidian University, Xi'an 710126, China
Interests: applied cryptography; privacy-enhanced technique; cloud data security

Special Issue Information

Dear Colleagues,

Quantum computation is currently one the most biggest threat to cryptography. Theoretically, the security of modern cryptography is built on computational complexity theory, while quantum computation has changed the edge and structure of the computational complexity map and thus brings a transformative threat to the cryptography field. To prepare for the threat of quantum computing, many countries and international standard organizations have initiated the standardization and migration of post-quantum cryptography. To promote the development of post-quantum cryptography, we are organizing this Special Issue. Topics of interest include, but not limited to, the foundational theory of quantum secure cryptography; design and analysis of post-quantum cryptography schemes; implementation of post-quantum cryptography  based on CPU, FPGA, GPU, ASIC, ARM, and RISC-V; security proof in the quantum random oracle model; design and analysis of quantum circuit for cryptography; migration of secure protocols; and applications of post-quantum cryptography in financial systems, mobile communication, power systems, intelligent transportation systems, and blockchain.

Dr. Xianhui Lu
Prof. Dr. Jianfeng Wang
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Cryptography is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • post-quantum cryptography
  • privacy
  • authentication
  • access control
  • intrusion detection
  • cloud system
  • blockchain
  • machine learning
  • deep learning

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

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23 pages, 1341 KB  
Article
DPS: A Post-Quantum Proxy Signature Scheme from Dilithium for IoT Applications
by Yuteng Wang, Ruoyu Ding, Tianrun Yu, Zhen Han, Jian Weng and Jiasi Weng
Cryptography 2026, 10(3), 33; https://doi.org/10.3390/cryptography10030033 - 15 May 2026
Viewed by 370
Abstract
Proxy signatures enable the secure delegation of signing authority, which is particularly useful in resource-constrained Internet of Things (IoT) environments. However, most existing schemes rely on classical hardness assumptions and therefore cannot resist quantum attacks. To address the challenge, we propose a post-quantum [...] Read more.
Proxy signatures enable the secure delegation of signing authority, which is particularly useful in resource-constrained Internet of Things (IoT) environments. However, most existing schemes rely on classical hardness assumptions and therefore cannot resist quantum attacks. To address the challenge, we propose a post-quantum proxy signature scheme based on Dilithium for IoT scenarios. We first propose an asynchronous remote key generation (ARKG) scheme based on CRYSTALS-Kyber, enabling the delegator and proxy signer to generate proxy keys of Dilithium without real-time interaction. We further integrate ARKG with the Dilithium signature scheme to construct a proxy signature scheme called DPS while ensuring the unlinkability of proxy signatures. Additionally, our proposed DPS achieves post-quantum security and provides unforgeability, distinguishability, verifiability, and undeniability with formal proofs. Experimental performance evaluation shows that our scheme yields significant efficiency gains over existing quantum-safe proxy signature solutions, with 10× speedup for both the delegation and proxy signing phases, as well as a 2.4× improvement in the verification phase. Full article
(This article belongs to the Special Issue Advances in Post-Quantum Cryptography)
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68 pages, 5976 KB  
Article
A Hybrid Module-LWE and Hash-Based Framework for Memory-Efficient Post-Quantum Key Encapsulation
by Elmin Marevac, Esad Kadušić, Nataša Živić, Sanela Nesimović and Christoph Ruland
Cryptography 2026, 10(3), 30; https://doi.org/10.3390/cryptography10030030 - 3 May 2026
Viewed by 483
Abstract
Deploying post-quantum cryptography on highly constrained devices remains challenging due to the large key sizes and substantial storage and memory-traffic demands of leading lattice-based schemes. Although constructions such as Kyber, Dilithium, and NTRU offer strong resistance against quantum adversaries, their multi-kilobyte public keys [...] Read more.
Deploying post-quantum cryptography on highly constrained devices remains challenging due to the large key sizes and substantial storage and memory-traffic demands of leading lattice-based schemes. Although constructions such as Kyber, Dilithium, and NTRU offer strong resistance against quantum adversaries, their multi-kilobyte public keys and intensive memory access patterns limit practical adoption in microcontrollers, smart cards, and low-power edge environments. This work proposes a hybrid key-encapsulation mechanism that integrates a compact, seed-generated Module-LWE structure with a quantum-secure hash-based authentication layer. The design employs a small public seed to instantiate lattice matrices on demand via a lightweight pseudorandom generator and incorporates a Merkle-tree commitment to represent compressed auxiliary error information. Additional design considerations—including sparsity-aware secret keys, SIMD-friendly polynomial operations, and cache-efficient decryption paths—are intended to reduce runtime memory usage and computational overhead. The security of the proposed construction is analysed under both Module-LWE and hash-based one-way assumptions, with further consideration of constant-time execution and cache-line alignment to mitigate side-channel risks. This hybrid approach outlines a design pathway toward post-quantum key-encapsulation mechanisms suitable for deployment on memory-limited and energy-constrained platforms. Full article
(This article belongs to the Special Issue Advances in Post-Quantum Cryptography)
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Review

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24 pages, 455 KB  
Review
Post-Quantum Cryptography in Networking Protocols: Challenges, Solutions, and Future Directions
by Sang-Yoon Chang and Qaiser Khan
Cryptography 2026, 10(1), 12; https://doi.org/10.3390/cryptography10010012 - 12 Feb 2026
Cited by 4 | Viewed by 4389
Abstract
Post-quantum cryptography (PQC) provides the essential cryptographic algorithms needed to secure digital networking systems against future adversaries equipped with quantum computing. This paper reviews the PQC research landscape and identifies open challenges and future directions for the critical transition to PQC in digital [...] Read more.
Post-quantum cryptography (PQC) provides the essential cryptographic algorithms needed to secure digital networking systems against future adversaries equipped with quantum computing. This paper reviews the PQC research landscape and identifies open challenges and future directions for the critical transition to PQC in digital networking systems. Building on the NIST standardization process which has hardened the PQC cipher algorithm security, this paper analyzes and describes the recent research on PQC implementations and integrations into scalable and standardized networking systems (Internet, web and cellular networks). We review research on the security, side-channel threats, performances, overheads, and compatibility of PQC ciphers. We also study the research incorporating PQC into the standardized web and cellular networking protocols, ranging from testing the PQC feasibility to proposing protocol solutions and mechanisms to enable PQC. Our study highlights the PQC challenge of large parameter sizes, common across the PQC cipher algorithms, and the research proposing protocol- and system-level mechanisms to address them. Informed by the survey, this paper identifies and highlights the research gaps and future directions to facilitate further research and development for PQC and to secure next-generation digital networking systems. Full article
(This article belongs to the Special Issue Advances in Post-Quantum Cryptography)
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25 pages, 1156 KB  
Review
Post-Quantum PKI: A Survey of Applications and Benchmarking Practices
by Maya Thabet, Antonia Tsili, Konstantinos Krilakis and Dimitris Syvridis
Cryptography 2026, 10(1), 11; https://doi.org/10.3390/cryptography10010011 - 12 Feb 2026
Cited by 1 | Viewed by 1603
Abstract
Post-quantum cryptography (PQC) is, and should be, currently dominating the field of cybersecurity, with many works designing and evaluating the transition of communications security to quantum-safe solutions. As the security level and implementations of post-quantum algorithms become more mature, the research on their [...] Read more.
Post-quantum cryptography (PQC) is, and should be, currently dominating the field of cybersecurity, with many works designing and evaluating the transition of communications security to quantum-safe solutions. As the security level and implementations of post-quantum algorithms become more mature, the research on their application to realistic conditions changes accordingly, especially their application to widely adopted network architectures and corresponding protocols such as the Public Key Infrastructure (PKI). In this survey, we identified articles presenting ways of integrating PQC algorithms to PKI and classified related work according to the employed methods and benchmarking choices. The main results from many evaluations converge to similar conclusions on the performance of the most popular PC digital signature algorithms; however, modeling choices concerning architecture variants, hardware and measurement metrics vary. The diversity of the results and experimental setups makes comparison difficult and arrival at an objective conclusion regarding PKI requirements almost impossible. Ultimately, this review reveals a fragmented landscape of benchmarking practices for post-quantum PKI systems. The absence of standardized evaluation frameworks and common test environments limits the comparability and reproducibility of the findings. We aim to provide reference implementations, which are essential to guide the transition of PKI infrastructures toward robust, scalable, and quantum-resistant deployments. Full article
(This article belongs to the Special Issue Advances in Post-Quantum Cryptography)
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