Falcon is an efficient and secure postquantum signature scheme for services based on quantum computing. It employs the hash-and-sign approach in conjunction with the Gentry, Peikert, and Vaikuntanathan (GPV) framework on Number Theory Research Unit (NTRU) lattices. This study evaluated the operation procedure and the capacity to run the Falcon scheme using a key length of 1024 bits on different hardware and software platforms, such as personal computers and Raspberry Pi 4 and Windows, Ubuntu, and Android operating systems. The following results were obtained: file sizes ranged from 30 to 5449268 KB, digital signature times ranged from 50 to 19500ms, and signature verification times ranged from 14 to 19000ms. The results show that the Falcon post-quantum signature scheme works stably and ensures execution speed on different platforms, similar to current digital signature schemes.
Falcon is an efficient and secure postquantum signature scheme for services based on quantum computing. It employs the hash-and-sign approach in conjunction with the Gentry, Peikert, and Vaikuntanathan (GPV) framework on Number Theory Research Unit (NTRU) lattices. This study evaluated the operation procedure and the capacity to run the Falcon scheme using a key length of 1024 bits on different hardware and software platforms, such as personal computers and Raspberry Pi 4 and Windows, Ubuntu, and Android operating systems. The following results were obtained: file sizes ranged from 30 to 5449268 KB, digital signature times ranged from 50 to 19500ms, and signature verification times ranged from 14 to 19000ms. The results show that the Falcon post-quantum signature scheme works stably and ensures execution speed on different platforms, similar to current digital signature schemes.
This paper presents a comparative analysis of two lattice-based post-quantum digital signature schemes: FALCON and SOLMAE. FALCON which was finallty selected by NIST for PQC standardization, represents an efficient realization of the GPV framework over NTRU lattices. SOLMAE, inspired by FALCON, Mitaka, and Antrag, aims to improve implementation simplicity and performance while preserving strong security guarantees. Adopting a pedagogical approach, we provide algorithmic insights into both schemes and conduct practical evaluations using their Python implementations, focusing on key generation, signing, and verification procedures. Performance comparisons at two NIST security levels (512 and 1024 bits) highlight SOLMAE’s potential advantages in simplicity and execution time, suggesting its suitability for deployment in resource-constrained environments.
Conventional public-key cryptographic systems are increasingly threatened by advances in quantum computing, accelerating the need for robust post-quantum cryptographic solutions. Among these, Falcon, a compact lattice-based digital signature scheme, has emerged as a leading candidate in the NIST post-quantum standardization process due to its efficiency and theoretical security grounded in hard lattice problems. This work introduces Falcon-M, a modified version of the Falcon algorithm that significantly reduces implementation complexity. It does so by replacing Falcon’s intricate trapdoor-based key-generation mechanism with a simplified approach that utilizes randomized polynomial Gaussian sampling and fast Fourier transform (FFT) operations. Falcon-M incorporates SHA-512 hashing and discrete Gaussian sampling to preserve cryptographic soundness and statistical randomness while maintaining the core structure of Falcon’s signing and verification processes. We formally specify the Falcon-M algorithm, provide an updated pseudocode, and offer a comparative analysis with the original Falcon in terms of algorithmic complexity, security assumptions, and implementation overhead. Additionally, we present formal lemmas and theorems to ensure correctness and define theoretical bounds on forgery resistance. Although Falcon-M does not rely on a formal cryptographic trapdoor, we demonstrate that it achieves strong practical security based on assumptions related to the Short Integer Solution (SIS) problem. Falcon-M is thus well-suited for lightweight post-quantum applications, particularly in resource-constrained environments, such as embedded systems and Internet-of-Things (IoT) platforms.
This article provides an expanded computational evaluation of three standardized lattice-based post-quantum signature schemes—ML-DSA-44, ML-DSA-65 and Falcon-512—using reference implementations from the Open Quantum Safe (liboqs) project. Unlike prior benchmarking efforts that rely on optimized implementations or hardware-specific tuning, this work focuses on reproducible baseline performance on a conventional CPU platform. We measure key generation, signing and verification times across 5,000 iterations and analyze the effect of message length on signing cost. Results confirm that ML-DSA variants achieve significantly faster signing and key generation, whereas Falcon-512 produces substantially smaller keys and signatures. The study further highlights the computational dominance of lattice operations over hashing, explaining the weak dependence of signing cost on message size. These findings aim to support system architects evaluating the practical feasibility of standardized post-quantum signature algorithms.
Abstract In the rapidly evolving field of quantum computing technology, postquantum cryptography (PQC) plays a pivotal role in developing secure cryptographic systems that are resistant to both quantum and classical computers. This paper focuses on the integration and implementation of PQC algorithms such as Falcon and Dilithium for digital signatures, as well as Crystal-Kyber for key encapsulation mechanisms. Through a server–client model, the study has deployed a postquantum secure communication service achieving encryption times of less than 2 ms, signing performance up to 50 ms for small files and 11 073 ms for large files, and key exchange times as low as 16 ms. These metrics provide deep insights into the resilience and security of the proposed cryptographic solutions in real-world environments.
Public key cryptography plays a pivotal role in maintaining digital security and privacy, with its foundations built on the hardness of certain mathematical problems. However, the emergence of quantum computing threatens the security of current cryptographic systems, making the adoption of post-quantum cryptography (PQC) an urgent necessity. Digital signature schemes are essential components in secure communications, providing authentication, non-repudiation, and data integrity. This paper examines the state of post-quantum digital signature schemes across various cryptographic approaches, including lattice-based, code-based, multivariate polynomial-based, hash-based, symmetric-key-based, and isogeny-based systems, alongside advancements in Multi-Party Computation in the Head (MPC-in-the-head) schemes. The paper then explores application-specific signatures such as blind, undeniable, threshold, chameleon, aggregate, and ring signatures, explaining their main use cases and the existing post-quantum cryptographic classifications that support these constructions individually. Software implementations of selected prominent PQC digital signature schemes were carried out, and their performance was systematically analysed using metrics such as bandwidth consumption, latency, and computational efficiency. These results provide key observations regarding the suitability of different schemes for both resource-constrained and high-performance environments. Subsequently, a detailed literature review of implementations on embedded and hardware platforms is presented, focusing on ARM-based devices and FPGA accelerators to evaluate deployment feasibility beyond general-purpose processors. Based on the software and implementation-level findings, a comparative analysis across software, embedded, and hardware platforms is conducted to highlight architectural influences on performance, scalability, and practicality. Furthermore the cryptanalytic attacks on post-quantum digital signature schemes across various PQC classifications are examined in this paper, taking into account both classical and quantum adversarial models. To evaluate realistic security constraints, implementation-oriented vulnerabilities such as side-channel and fault-based attacks are also examined. In addition, the applicability of post-quantum digital signature schemes within TLS, IoT, and related practical deployment scenarios is analysed. The study also discusses possible directions for further investigation, focusing on the requirement for effective and expandable PQC systems that can satisfy changing cybersecurity requirements. In order to protect sensitive data in the digital era, this study emphasizes the need for implementing quantum-secure systems by fusing theoretical understandings with real-world applications.
Background: The rapid advancement of quantum computing threatens the cryptographic foundations of e-Government infrastructure, particularly classical public-key algorithms susceptible to Shor's algorithm. Post-Quantum Cryptography (PQC) offers a viable pathway for securing digital signature systems against emerging quantum adversaries. Objective: This study conducts a system-level comparative evaluation of three NIST-standardized PQC digital signature schemes CRYSTALS-Dilithium2, Falcon-512, and SPHINCS+-128s to assess their suitability for secure e-Government document signing workflows. Methods: A simulation-based system-level evaluation is employed, wherein timing values are estimated from official NIST PQC parameter specifications and open-source benchmarks (PQClean, OQS), rather than measured from native cryptographic library executions. Experiments were conducted over 100 iterations, reporting mean ± standard deviation for key generation, signing, and verification times, alongside signature sizes and a RESTful API prototype demonstration. Results: Falcon-512 demonstrates the lowest estimated signing latency approximately five to six times faster than Dilithium2 and over fifty times faster than SPHINCS+-128s with the smallest signature size (666 bytes versus 2,420 and 7,856 bytes respectively). Dilithium2 provides a balanced trade-off between computational efficiency and signature robustness, while SPHINCS+-128s, despite its computational overhead, offers the strongest long-term security guarantees through its stateless hash-based construction. The RESTful API prototype confirms successful multi-scheme integration feasibility. Conclusion: This study recommends Falcon-512 for real-time mobile services, Dilithium2 for centralized server-side authentication, and SPHINCS+-128s for long-term archival security, providing evidence-based guidance for PQC adoption in national e-Government systems aligned with SPBE frameworks and NIST standards.