Practical Lattice-based Digital Signature Schemes (original) (raw)

Lattices in Quantum-ERA Cryptography

International Journal of Research Publication and Reviews, 2023

The use of Mathematic in cryptography can result a safe encryption scheme. Lattices have emerged as a powerful mathematical tool in the field of cryptography, offering a diverse set of applications ranging from encryption to secure multi-party computation. This research paper provides a comprehensive review of the role of lattices in cryptography, covering both theoretical foundations and practical implementations. The paper begins by introducing the basic concepts of lattices and their relevance in cryptographic protocols. Subsequently, it explores key cryptographic primitives based on lattice problems, such as lattice-based encryption schemes, digital signatures, and fully homomorphic encryption. The paper also proposes a new lattice based cryptographic scheme.

Practical Lattice-Based Cryptography: A Signature Scheme for Embedded Systems

Lecture Notes in Computer Science, 2012

Nearly all of the currently used and well-tested signature schemes (e.g. RSA or DSA) are based either on the factoring assumption or the presumed intractability of the discrete logarithm problem. Further algorithmic advances on these problems may lead to the unpleasant situation that a large number of schemes have to be replaced with alternatives. In this work we present such an alternative -a signature scheme whose security is derived from the hardness of lattice problems. It is based on recent theoretical advances in lattice-based cryptography and is highly optimized for practicability and use in embedded systems. The public and secret keys are roughly 12000 and 2000 bits long, while the signature size is approximately 9000 bits for a security level of around 100 bits. The implementation results on reconfigurable hardware (Spartan/Virtex 6) are very promising and show that the scheme is scalable, has low area consumption, and even outperforms some classical schemes.

Compact and provably secure lattice-based signatures in hardware

2017 IEEE International Symposium on Circuits and Systems (ISCAS)

Lattice-based cryptography is a quantum-safe alternative to existing classical asymmetric cryptography, such as RSA and ECC, which may be vulnerable to future attacks in the event of the creation of a viable quantum computer. The efficiency of lattice-based cryptography has improved over recent years, but there has been relatively little investigation into hardware designs of digital signature schemes. In this paper, the first hardware design of the provably secure Ring-LWE digital signature scheme, Ring-TESLA, is presented, targeting a Xilinx Spartan-6 FPGA. The results better compactness of all previous lattice-based digital signature schemes in hardware, and can achieve between 104-785 signatures and 102-776 verifications per second.

Efficient Certificate-Based Signature with Short Key and Signature Sizes from Lattices

Informatica

Certificate-based cryptography (CB-PKC) is an attractive public key setting, which reduces the complexity of public key infrastructure in traditional public key settings and resolves the key escrow problem in ID-based public key settings. In the past, a large number of certificate-based signature and encryption schemes were proposed. Nevertheless, the security assumptions of these schemes are mainly relied on the difficulties of the discrete logarithm and factorization problems. Unfortunately, both problems will be resolved when quantum computers come true in the future. Public key cryptography from lattices is one of the important candidates for post-quantum cryptography. However, there is little work on certificate-based cryptography from lattices. In the paper, we propose a new and efficient certificate-based signature (CBS) scheme from lattices. Under the short integer solution (SIS) assumption from lattices, the proposed CBS scheme is shown to be existential unforgeability agai...

Efficient lattice-based signature scheme

International Journal of Applied Cryptography, 2008

In Crypto 1997, Goldreich, Goldwasser and Halevi (GGH) proposed a lattice analogue of McEliece public key cryptosystem, in which security is related to the hardness of approximating the Closest Vector Problem in a lattice. Furthermore, they also described how to use the same principle of their encryption scheme to provide a signature scheme. Practically, this cryptosystem uses the Euclidean norm, l 2 -norm, which has been used in many algorithms based on lattice theory. Nonetheless, many drawbacks have been studied and these could lead to cryptanalysis of the scheme. In this article, we present a novel method of reducing a vector under the l -norm and propose a digital signature scheme based on it. Our scheme takes advantage of the l -norm to increase the resistance of the GGH scheme and to decrease the signature length. Furthermore, after some other improvements, we obtain a very efficient signature scheme, that trades the security level, speed and space.

Lattice-Based Revocable Certificateless Signature

Symmetry

Certificateless signatures (CLS) are noticeable because they may resolve the key escrow problem in ID-based signatures and break away the management problem regarding certificate in conventional signatures. However, the security of the mostly previous CLS schemes relies on the difficulty of solving discrete logarithm or large integer factorization problems. These two problems would be solved by quantum computers in the future so that the signature schemes based on them will also become insecure. For post-quantum cryptography, lattice-based cryptography is significant due to its efficiency and security. However, no study on addressing the revocation problem in the existing lattice-based CLS schemes is presented. In this paper, we focus on the revocation issue and present the first revocable CLS (RCLS) scheme over lattices. Based on the short integer solution (SIS) assumption over lattices, the proposed lattice-based RCLS scheme is shown to be existential unforgeability against adaptive chosen message attacks. By performance analysis and comparisons, the proposed lattice-based RCLS scheme is better than the previously proposed lattice-based CLS scheme, in terms of private key size, signature length and the revocation mechanism.

A Lightweight Post-Quantum Lattice-Based RSA for Secure Communications

IEEE Access

Conventional RSA algorithm, being a basis for several proposed cryptosystems, has remarkable security laps with respect to confidentiality and integrity over the internet which can be compromised by state-of-the-art attacks, especially, for different types of data generation, transmission, and analysis by IoT applications. This security threat hindrance is considered to be a hard problem to solve on classical computers. However, bringing quantum mechanics into account, the concept no longer holds true. So, this calls out for the modification of the conventional pre-quantum RSA algorithm into a secure post-quantum cryptographic-based RSA technique. In this research, we propose a post-quantum lattice-based RSA (LB-RSA) for IoT-based cloud applications to secure the shared data and information. The proposed work is validated by implementing it in 60-dimensions. The key size is about 1.152 × 10 5 -bits and generation time is 0.8 hours. Furthermore, it has been tested with AVISPA, which confirms security in the presence of an intruder. Moreover, the proposed LB-RSA technique is compared with the existing state-of-the-art techniques. The empirical results advocate that the proposed lattice-based variant is not only safe but beats counterparts in terms of secured data sharing.

Exploiting Determinism in Lattice-based Signatures

Proceedings of the 2019 ACM Asia Conference on Computer and Communications Security

In this paper, we analyze the implementation level fault vulnerabilities of deterministic lattice-based signature schemes. In particular, we extend the practicality of skip-addition fault attacks through exploitation of determinism in certain variants of Dilithium (Deterministic variant) and qTESLA signature scheme (originally submitted deterministic version), which are two leading candidates for the NIST standardization of post-quantum cryptography. We show that single targeted faults injected in the signing procedure allow to recover an important portion of the secret key. Though faults injected in the signing procedure do not recover all the secret key elements, we propose a novel forgery algorithm that allows the attacker to sign any given message with only the extracted portion of the secret key. We perform experimental validation of our attack using Electromagnetic fault injection on reference implementations taken from the pqm4 library, a benchmarking and testing framework for post quantum cryptographic implementations for the ARM Cortex-M4 microcontroller. We also show that our attacks break two well known countermeasures known to protect against skip-addition fault attacks. We further propose an efficient mitigation strategy against our attack that exponentially increases the attacker's complexity at almost zero increase in computational complexity. CCS CONCEPTS • Security and privacy → Digital signatures; Hardware attacks and countermeasures; Side-channel analysis and countermeasures; Embedded systems security.

High-Speed Signatures from Standard Lattices

Lecture Notes in Computer Science, 2015

At CT-RSA 2014 Bai and Galbraith proposed a lattice-based signature scheme optimized for short signatures and with a security reduction to hard standard lattice problems. In this work we first refine the security analysis of the original work and propose a new 128-bit secure parameter set chosen for software efficiency. Moreover, we increase the acceptance probability of the signing algorithm through an improved rejection condition on the secret keys. Our software implementation targeting Intel CPUs with AVX/AVX2 and ARM CPUs with NEON vector instructions shows that even though we do not rely on ideal lattices, we are able to achieve high performance. For this we optimize the matrixvector operations and several other aspects of the scheme and finally compare our work with the state of the art.

Post-Quantum Lattice-Based Cryptography Implementations

ACM Computing Surveys, 2019

The advent of quantum computing threatens to break many classical cryptographic schemes, leading to innovations in public key cryptography that focus on post-quantum cryptography primitives and protocols resistant to quantum computing threats. Lattice-based cryptography is a promising post-quantum cryptography family, both in terms of foundational properties as well as in its application to both traditional and emerging security problems such as encryption, digital signature, key exchange, and homomorphic encryption. While such techniques provide guarantees, in theory, their realization on contemporary computing platforms requires careful design choices and tradeoffs to manage both the diversity of computing platforms (e.g., high-performance to resource constrained), as well as the agility for deployment in the face of emerging and changing standards. In this work, we survey trends in lattice-based cryptographic schemes, some recent fundamental proposals for the use of lattices in c...