Actually, the NIST post-quantum cryptosystem standardization competition reached its third round with seven finalist candidates. And NIST invites the cryptographic community to analyzing the selected candidates. In this context, we contribute by creating a new blind digital signature protocol over our release of NTRU post-quantum cryptosystem. Our protocol can be a variant of FALCON digital signature scheme, which is among of those finalist candidates. Because of our NTRU release is additively homomorphic, we successfully blind and unblind the digital signature by adding a random message. We obtained good results; the speed performance of our protocol outperforms FALCON by a factor up to 27, with a stronger security level, and perfect correctness.
Actually, the NIST post-quantum cryptosystem standardization competition reached its third round with seven finalist candidates. And NIST invites the cryptographic community to analyzing the selected candidates. In this context, we contribute by creating a new blind digital signature protocol over our release of NTRU post-quantum cryptosystem. Our protocol can be a variant of FALCON digital signature scheme, which is among of those finalist candidates. Because of our NTRU release is additively homomorphic, we successfully blind and unblind the digital signature by adding a random message. We obtained good results; the speed performance of our protocol outperforms FALCON by a factor up to 27, with a stronger security level, and perfect correctness.
Lattices lead to promising practical post-quantum digital signatures, combining asymptotic efficiency with strong theoretical security guarantees. However, tuning their parameters into practical instantiations is a delicate task. On the one hand, NIST round~2 candidates based on Lyubashevsky's design (such as dilithium and qtesla) allow several tradeoffs between security and efficiency, but at the expense of a large bandwidth consumption. On the other hand, the hash-and-sign falcon signature is much more compact and is still very efficient, but it allows only two security levels, with large compactness and security gaps between them. We introduce a new family of signature schemes based on the falcon design, which relies on module lattices. Our concrete instantiation enjoys the compactness and efficiency of falcon, and allows an intermediate security level. It leads to the most compact lattice-based signature achieving a quantum security above 128 bits.
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.
In recent years, there has been steady progress in the creation of quantum computers. If large-scale quantum computers are implemented, they will threaten the security of many widely used public-key cryptosystems. Key-establishment schemes and digital signatures based on factorization, discrete logarithms, and elliptic curve cryptography will be most affected. Symmetric cryptographic primitives such as block ciphers and hash functions will be broken only slightly. As a result, there has been an intensification of research on finding public-key cryptosystems that would be secure against cryptanalysts with both quantum and classical computers. This area is often called post-quantum cryptography (PQC), or sometimes quantum-resistant cryptography. The goal is to design schemes that can be deployed in existing communication networks and protocols without significant changes. The National Institute of Standards and Technology is in the process of selecting one or more public-key cryptographic algorithms through an open competition. New public-key cryptography standards will define one or more additional digital signatures, public-key encryption, and key-establishment algorithms. It is assumed that these algorithms will be able to protect confidential information well in the near future, including after the advent of quantum computers. After three rounds of evaluation and analysis, NIST has selected the first algorithms that will be standardized as a result of the PQC standardization process. The purpose of this article is to review and analyze the state of NIST's post-quantum cryptography standardization evaluation and selection process. The article summarizes each of the 15 candidate algorithms from the third round and identifies the algorithms selected for standardization, as well as those that will continue to be evaluated in the fourth round of analysis. Although the third round is coming to an end and NIST will begin developing the first PQC standards, standardization efforts in this area will continue for some time. This should not be interpreted as meaning that users should wait to adopt post-quantum algorithms. NIST looks forward to the rapid implementation of these first standardized algorithms and will issue future guidance on the transition. The transition will undoubtedly have many complexities, and there will be challenges for some use cases such as IoT devices or certificate transparency.
In order to meet the challenges brought by quantum computing, research on post-quantum cryptography has been carried out comprehensively. Among them, the most influential one is the post-quantum cryptography algorithm standardization project initiated by NIST. In July 2022, NIST announced that the Dilithium, Falcon, and SPHINCS+ algorithms were selected as candidate schemes for the standardization of post-quantum cryptographic digital signatures. The OQS project team is committed to promoting the transition of existing security protocols to standardized post-quantum algorithms and is currently the mainstream open-source post-quantum project. This paper improves the post-quantum hybrid digital signature scheme used by the OQS project team. Firstly, the hybrid digital signature scheme used in this project is studied, and it is found that there are security risks. Subsequently, an enhanced scheme is constructed and implemented using the hybrid algorithm combiner proposed by Nina Bindel et al., solving the security issues. The unforgeability and 2 -non-separability of the enhanced scheme are verified through formal analysis, and forward compatibility is achieved. The enhanced scheme shows obvious advantages in key generation efficiency and signature verification efficiency. Under some algorithms, the speed of signature verification of the improved scheme is 60 % of the original scheme. Meanwhile, the enhanced scheme also demonstrates stability in terms of time and storage overhead. Finally, the TLS1.3 protocol PSK mechanism is implemented using the enhanced scheme. This is the first implementation of post-quantum algorithm security protection in the PSK mechanism of the TLS protocol. This scheme can resist man-in-the-middle attacks while meeting the requirements of forward compatibility.
Public Key Infrastructure (PKI) generates and distributes digital certificates to provide the root of trust for securing digital networking systems. To continue securing digital networking in the quantum era, PKI should transition to use quantum-resistant cryptographic algorithms. The cryptography community is developing quantum-resistant primitives/algorithms, studying, and analyzing them for cryptanalysis and improvements. National Institute of Standards and Technology (NIST) selected finalist algorithms for the post-quantum digital signature cipher standardization, which are Dilithium, Falcon, and Rainbow. We study and analyze the feasibility and the processing performance of these algorithms in memory/size and time/speed when used for PKI, including the key generation from the PKI end entities (e.g., a HTTPS/TLS server), the signing, and the certificate generation by the certificate authority within the PKI. The transition to post-quantum from the classical ciphers incur changes in the parameters in the PKI, for example, Rainbow I significantly increases the certificate size by 163 times when compared with RSA 3072. Nevertheless, we learn that the current X.509 supports the NIST post-quantum digital signature ciphers and that the ciphers can be modularly adapted for PKI. According to our empirical implementations-based study, the post-quantum ciphers can increase the certificate verification time cost compared to the current classical cipher and therefore the verification overheads require careful considerations when using the post-quantum-cipher-based certificates.