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.
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.
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.
The transition to post-quantum cryptography (PQC) marks a pivotal shift in ensuring digital security, prompted by the potential of quantum computers to compromise classical systems such as Rivest-Shamir-Adlema and elliptic-curve cryptography. In response, NIST has standardized three foundational PQC algorithms: Module-lattice-based Key-encapsulation Mechanism for key establishment; Module-lattice-based Digital Signature, and Stateless Hash-based Digital Signature algorithms for digital signatures. Meanwhile, FALCON and Hamming Quasi-cyclic (HQC) schemes, both selected as finalists, are expected to join the standards soon. This paper presents a comprehensive survey of these NIST-selected PQC standards, with a dual focus on software implementations and hardware architecture designs. We analyze their mathematical frameworks, distinctive features, and optimization strategies related to performance, security, and resource efficiency. The software review examines algorithmic complexity, memory usage, and programming considerations, while the hardware review discusses FPGA and ASIC implementations, emphasizing modular arithmetic, polynomial operations, and resource efficiency challenges. A comparative analysis highlights the strengths and trade-offs of each algorithm, offering insights into their applicability across various platforms-from resource-constrained internet of things devices to high-performance computing environments. This study provides a foundational understanding of NIST’s selected PQC standards and their practical deployment in securing the post-quantum era.
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.
Post-quantum cryptography (PQC) has emerged as a critical research area for securing communications in the quantum era. Among the selected algorithms, lattice-based schemes have gained particular attention due to their strong security foundations and practical efficiency.This paper presents a comparative analysis of latticebased PQC algorithms from the U.S. National Institute of Standards and Technology (NIST) standardization process and the Korean PQC (KpqC) competition. The evaluation considers security levels, key and ciphertext/signature sizes, and implementation performance. The results highlight fundamental trade-offs between security, efficiency, compactness, and implementation complexity, providing insights into the strengths and limitations of current latticebased algorithms. These findings offer practical guidance for assessing their suitability for deployment in real-world post-quantum systems.
The quantum computing continues to advance, the security of conventional cryptographic systems faces significant risks, prompting rapid developments in post-quantum cryptography (PQC). This paper presents a series of targeted improvements to the Falcon digital signature scheme in post-quantum cryptography. The analysis of Falcon’s framework, several areas can be identified where optimizations could enhance performance. This lowers the computing overhead while maintaining the algorithm’s resilience to quantum attacks by using GPU offloading, parameter recalibration, and other optimization strategies. Experimental evaluation shows an approximate 11% reduction in execution time without compromising the security guaranteed by the original method. These enhancements make it more practical for resource-constrained environments.
Quantum computing challenges the mathematical problems anchoring the security of the classical public key algorithms. For quantum-resistant public key algorithms, the National Institute of Standards and Technology (NIST) has undergone a multi-year standardization process and selected the post-quantum cryptography (PQC) public key digital signatures of Dilithium, Falcon, and SPHINCS+. Finding common ground to compare these algorithms can be difficult because of their design differences, including the fundamental math problems (lattice-based vs. hash-based). We use a visualization model to show the key/signature size vs. security trade-offs for all PQC algorithms. Our performance analyses compare the algorithms’ computational loads in the execution time. Building on the individual algorithms’ analyses, we analyze the communication costs and implementation overheads when integrated with Public Key Infrastructure (PKI) and with Transport Layer Security (TLS) and Transmission Control Protocol (TCP)/Internet Protocol (IP). Our results show that the lattice-based algorithms of Dilithium and Falcon induce lower computational overheads than the hash-based algorithms of SPHINCS+. In addition, the lattice-based PQC can outperform the classical algorithm with comparable security strength; for example, Dilithium 2 and Falcon 512 outperform RSA 4096 in the TLS handshake time duration.