This paper presents Dilithium, a lattice-based signature scheme that is part of the CRYSTALS (Cryptographic Suite for Algebraic Lattices) package that will be submitted to the NIST call for postquantum standards.The scheme is designed to be simple to securely implement against side-channel attacks and to have comparable efficiency to the currently best lattice-based signature schemes.Our implementation results show that Dilithium is competitive with lattice schemes of the same security level and outperforms digital signature schemes based on other post-quantum assumptions.
This paper presents Dilithium, a lattice-based signature scheme that is part of the CRYSTALS (Cryptographic Suite for Algebraic Lattices) package that will be submitted to the NIST call for postquantum standards.The scheme is designed to be simple to securely implement against side-channel attacks and to have comparable efficiency to the currently best lattice-based signature schemes.Our implementation results show that Dilithium is competitive with lattice schemes of the same security level and outperforms digital signature schemes based on other post-quantum assumptions.
We propose a new lattice-based digital signature scheme MLWRSign by modifying Dilithium, which is one of the second-round candidates of NIST's call for post-quantum cryptographic standards. To the best of our knowledge, our scheme MLWRSign is the first signature scheme whose security is based on the (module) learning with rounding (LWR) problem. Due to the simplicity of the LWR, the secret key size is reduced by approximately 30% in our scheme compared to Dilithium, while achieving the same level of security. Moreover, we implemented MLWRSign and observed that the running time of our scheme is comparable to that of Dilithium.
As the advent of quantum computing threatens traditional cryptographic protocols, hybrid classical-quantum secure communication infrastructures have emerged as a critical frontier in cybersecurity. This paper explores the integration of post-quantum cryptographic algorithms—specifically CRYSTALS-Kyber for key encapsulation and CRYSTALS-Dilithium for digital signatures—into hybrid communication architectures designed to resist quantum-level attacks. Leveraging lattice-based cryptographic primitives, both algorithms have been selected for standardization by NIST due to their robust security and performance characteristics. This study evaluates their implementation in real-world communication stacks, assesses latency and throughput under hybrid channel configurations, and proposes a layered security architecture combining classical and quantum-resilient mechanisms. Furthermore, it examines key management, digital trust, and infrastructure scalability in a post-quantum context. Simulation results and hardware-based validations are used to determine practical deployment feasibility in critical sectors such as finance, defense, and healthcare. The findings offer a comprehensive framework for securing data in transitional computing eras, ensuring forward secrecy, and maintaining operational integrity against future adversarial quantum threats.
The National Institute of Standards and Technology is in the process of selecting post-quantum public-key cryptography (PQC) algorithms through a public competition-like process. Dilithium, a lattice-based signature scheme, is a PQC candidate submitted to the NIST. It offers a fairly good performance with relatively straightforward implementation. In this study, we considered a secure two-party Dilithium signing protocol. We described how to build a distributed key generation and distributed signing protocol for Dilithium. Our protocol achieves a coordinated two-party Dilithium signature generation using Brakersiki/Fan-Vercauteren homomorphic encryption scheme. Our protocol is proven secure against active adversaries corrupting one of the players. Compared with other protocols, our protocol has advantage in resisting quantum computing attacks.
This paper proposes a novel lattice-based aggregate signature (LAS) scheme that bring post-quantum security to the Bitcoin system without sacrificing its transaction efficiency. Bitcoin currently employs Elliptic Curve Digital Signature Algorithm (ECDSA), which is insecure against the emerging quantum technology, so post-quantum signature schemes like the proposed LAS will become necessary in the near future. However, most of the post-quantum signatures schemes have large signature sizes which decrease Bitcoin’s efficiency while our proposed scheme does not have this negative side effect. Our LAS scheme is based on CRYSTALS-Dilithium and a zero-knowledge Scalable Transparent Arguments of Knowledge (STARK) protocol. CRYSTALS-Dilithium is the most prominent algorithm chosen by the National Institute of Standards and Technology (NIST), yet it still has an adverse limitation: it would cause Bitcoin’s transaction efficiency to fall by 17 times due to its relatively large signature size. On the other hand, the proposed LAS scheme takes full advantage of signature aggregation using the STARK protocol and Dilithium’s easy and fast implementation, thus generating signatures with post-quantum security and small signature sizes which are critical to transaction efficiency. Our proofs convey the correctness, compactness, and post-quantum security of our construction in the quantum random oracle model, and our implementation conveyed that the proposed scheme would only decrease Bitcoin’s transaction efficiency by 3 times, a significant improvement from using Dilithium and other lattice-based aggregate signature schemes. Our proposed scheme has many advantages over the existing schemes and may become very valuable to Bitcoin.
With the advancement in quantum computing technology, the number theory-based hard problems underlying traditional searchable encryption algorithms are now vulnerable to efficient quantum attacks. To address this challenge, this paper proposes Dilithium-PAEKS (Dilithium-Public Authenticated Encryption with Keyword Search), a searchable encryption scheme based on the post-quantum cryptographic algorithm CRYSTALS-Dilithium. By transforming the verification relationship of digital signatures into a matching relationship between trapdoors and ciphertexts, the scheme not only meets the functional requirements of searchable encryption but also demonstrates quantum resistance. The implementation enhances algorithm efficiency through keyword-based signatures and dynamic matching testing mechanisms. The security of the scheme is defined by the MLWE and MSIS hard problems, with proofs of keyword ciphertext indistinguishability and trapdoor indistinguishability under the random oracle model. Additionally, the scheme provides strong resistance against both outside and insider keyword guessing attacks through sender–receiver binding mechanisms and trapdoor indistinguishability properties. Experimental results show that, compared to the post-quantum schemes CP-Absel and LB-FSSE, the proposed scheme demonstrates superior overall computational efficiency while maintaining stronger quantum resistance than the traditional scheme SM9-PAEKS.
Due to the scalability of the stateless and compact JSON Web Tokens (JWT), they are increasingly used in securing modern applications to support single-sign-on context and establish trust in microservices or connected-devices architectures. However, currently JWT relies on traditional encryption algorithms that are based on integer factorization or discrete logarithm problems; this exposes JWT signatures to vulnerability when quantum computers become available. Recently, NIST has announced new standards which are quantum safe. In this paper, we investigate the usage of two quantum-resistant algorithms, which are NIST candidates of round 2 standardization process in 2019, to create and verify JWT signatures. Namely, we consider lattice-based schemes (DILITHIUM and qTESLA) and compare their performance against RSA for digital signature for different security levels defined by NIST. The results show that lattice-based digital signature schemes have better performance than RSA in terms of request per seconds and average response time. DILITHIUM has demonstrated the best performance while also having smaller performance loss when scaling the security level.