Fuzzy signatures differ from standard signature schemes in that they use noisy strings as keys, thereby eliminating the need for user-specific auxiliary data. With the advent of quantum computing, lattice-based digital signatures are considered potential candidates for resisting quantum attacks. In this work, we revisited the lattice-based fuzzy signature scheme proposed by Zhenget al. and demonstrated how the scheme can be implemented more efficiently and securely. In our new signature scheme, our contributions are as follows: The utilization of bimodal Gaussian sampling reduces the number of aborting terminations while simultaneously decreasing the signature size. By eliminating the T matrix from the verification equation, we improve verification efficiency. Additionally, in response to the linear sketch proposed by the authors, we provide a proof of the collision resistance of the mappingh, which further enhances the correctness of the scheme.
Fuzzy signatures differ from standard signature schemes in that they use noisy strings as keys, thereby eliminating the need for user-specific auxiliary data. With the advent of quantum computing, lattice-based digital signatures are considered potential candidates for resisting quantum attacks. In this work, we revisited the lattice-based fuzzy signature scheme proposed by Zhenget al. and demonstrated how the scheme can be implemented more efficiently and securely. In our new signature scheme, our contributions are as follows: The utilization of bimodal Gaussian sampling reduces the number of aborting terminations while simultaneously decreasing the signature size. By eliminating the T matrix from the verification equation, we improve verification efficiency. Additionally, in response to the linear sketch proposed by the authors, we provide a proof of the collision resistance of the mappingh, which further enhances the correctness of the scheme.
With the emergence of quantum computers, traditional digital signature schemes based on problems such as large integer solutions and discrete logarithms will no longer be secure, and it is urgent to find effective digital signature schemes that can resist quantum attacks. Lattice cryptography has the advantages of computational simplicity and high security. In this paper, we propose an identity-based digital signature scheme based on the rejection sampling algorithm. Unlike most schemes that use a common Gaussian distribution, this paper uses a bimodal Gaussian distribution, which improves efficiency. The identity-based signature scheme is more convenient for practical application than the traditional certificate-based signature scheme.
A myriad of conditional privacy-preserving signature (CPPS) schemes have emerged recently, aiming to secure communication data while preserving user privacy. However, many of these schemes, relying on classical mathematical problems and identity based cryptographic mechanism, suffer from key escrow vulnerabilities and are susceptible to quantum attacks. In this paper, we propose a lattice based conditional privacy-preserving certificateless signature scheme. By leveraging the ring small integer solution problem and the decisional compact knapsack problem, our scheme demonstrates robust resistance against quantum attacks with high asymptotic efficiency. We utilize certificateless signature to circumvent the key escrow issue inherent in identity based CPPS schemes. While ensuring conditional privacy preservation, we enhance the security and efficiency of the signature process through a rejection sampling algorithm based on the bimodal Gaussian distribution. Furthermore, our security analysis demonstrates resilience against type I and type II adversaries, meeting diverse security requirements such as traceability and unlinkability. Through a comparative analysis of communication traffic, we observe commendable efficiency in signature generation, making our scheme particularly suitable for wireless communication scenarios. Finally, we detail implementation strategies tailored for drone networks, enhancing the practicality and relevance of our contributions in wireless communication contexts.
With the advancement of quantum computing, the utilization of quantum algorithms such as Shor’s algorithm enables the efficient resolution of problems that are intractable in classical computing paradigms, posing a significant threat to traditional signature schemes. Lattice-based cryptography is considered one of the most promising post-quantum cryptographic algorithms due to its computational advantages and potential resistance to quantum attacks. Proxy signature is an authorization mechanism that allows the original signer to delegate the signing power to a proxy. The security of existing proxy signature schemes is mostly based on classical hard problems, which cannot guarantee security under quantum attacks. Therefore, this paper combines lattice-based cryptography with proxy signatures to propose a new lattice-based proxy signature scheme (NLBPS). NLBPS constructs signatures using lattice-based trapdoor sampling algorithms and preimage sampling algorithms. Comparative analysis shows that the proposed scheme has relatively smaller key and signature sizes compared to some existing lattice-based proxy signature schemes, and it also offers a certain improvement in computational efficiency.
Digital signatures and key exchange protocols are the two most important public key cryptographic primitives used in the electronic transmission of data. The goal of key exchange is to preserve the secrecy of the communication, while the goal of digital signatures is to guarantee the authenticity of the exchanged messages. Constructions of digital signature schemes based on classical mathematical assumptions appeared shortly following the invention of public key cryptography in the late 1970s. And just like with key exchange, the most efficient variants are based on number-theoretic problems that are believed to be (sub)-exponentially hard for classical machines, but are solved in polynomial time by Shor’s algorithm on a powerful-enough quantum computer. Also, like for key exchange, the most efficient constructions that we believe to be quantum safe are based on the presumed hardness of lattice problems over polynomial rings. One interesting difference between key exchange and digital signatures is that key exchange appears to inherently require that some mathematical problem be computationally hard. Digital signatures, on the other hand, can be generically constructed from any one-way function [1,2]. So even though they certainly fall into the category of public key primitives based on their usage, their existence requires much weaker assumptions. Additionally, the transformation from a one-way function to a digital signature is not too inefficient. For example, the total parameter size (public key + signature) of the SPHINCS+ scheme [3] is around 40 kB. While these sizes are larger, and signing times considerably longer, than those of signatures based on factoring or discrete log, it is still a usable scheme for many applications. And being only based on symmetric assumptions (e.g. one wayness and collision resistance of cryptographic hash functions), its security is very attractive. In order to be considered an interesting alternative to the above-mentioned signature, a scheme based on a mathematical assumption would need to have significant performance advantages. Schemes based on factoring and the discrete logarithm problem were significantly shorter and faster, and so the generic approach lay dormant for over four decades. The new quantum-safe schemes will need to have similar performance advantages if they are to be used in lieu of this safe approach. Below, we describe two techniques for constructing lattice-based digital signatures with output sizes being just a few kilobytes. On a very high level, lattice-based signature constructions follow the two known approaches for constructing classical signatures. In the first approach, the signer outputs a function f and an image y = f(x) as his public key and keeps x as his secret key. To sign a message μ, he gives a non-interactive zero-knowledge proof that he knows an x satisfying y = f(x), using the message μ to create the ‘challenge’ H(μ) for the proof (where H is a public function that maps μ to something ‘random looking’). If the function f is one way then the verifier should be convinced that the proof could have only been created by the entity who knows x. A classic example of this type of scheme is the Schnorr signature scheme [4] based on the hardness of the discrete logarithm problem. The second approach is to create a function f together with a trapdoor f−1, output f as the public key and keep f−1 as the secret key. A message μ is signed by using the secret trapdoor to create a pre-image x such that f(x) = H(μ). Again, if the function f is one way then only someone in possession of a trapdoor should be able to invert it. An example of such a construction based on a ‘factoring-like’ assumption is the RSA signature scheme [5]. The high-level ideas for lattice-based signatures follow the above blueprints, but the technical details are significantly more involved. The main reason for the complications is the different algebraic structure of the hard one-way function underlying lattice cryptography. While the domain of the function in discrete log and RSA-based one-way functions are groups, the domains in lattice-based signatures are sets that are not closed under any operation—in particular, they are elements in a group that have small norms. This crucial small norm requirement precludes us from using uniformly random masking as in Schnorr signatures or having a trapdoor for a bijective one-way function as in RSA signatures. These barriers have, nevertheless, been overcome and the resulting digital signatures are quite practical. In 2017, the US National Institute of Standards and Technology (NIST) began a ‘competition’ for a quantum-safe key exchange and digital signatures standard. At the time of this writing, this process is in the third round and there are two lattice-based signatures remaining—each following one of the above high-level designs. The CRYSTALS-Dilithium [6] scheme follows the Schnorr framework, but adds a crucial rejection-sampling step to keep the size of the coefficients small. The FALCON scheme [7] utilizes a randomized trapdoor sampling technique that uses a secret trapdoor for f−1 to produce random pre-images from a particular distribution. Because there is no longer a bijection, it is crucial to also have the property that the distribution of the outputted pre-images does not leak information about the trapdoor. Both schemes are relatively fast and their parameters (public key + signature size) are the shortest of all quantum-safe signature schemes. While both schemes are based on lattices, they have rather different characteristics. FALCON has very short parameters (see Table 1), but entails a rather complicated procedure for signature generation. In particular, it uses (an optimized version of) the GPV sampler [8], which requires floating-point arithmetic with approximately 64 bits of precision. Requiring such high precision means that subtle implementation errors may not get detected even with rigorous testing. Dilithium, on the other hand, has larger parameters but a very simple implementation where all the sampling in the signing is done in a power-of-2 range; it is thus much less prone to implementation errors. It is quite possible that in the future both schemes will be used for different applications. Approximate parameter sizes (in bytes) for the CRYSTALS-Dilithium and FALCON digital signature schemes at approximately 128-bit security levels. Approximate parameter sizes (in bytes) for the CRYSTALS-Dilithium and FALCON digital signature schemes at approximately 128-bit security levels. Conflict of interest statement. None declared.
A proxy signature scheme permits an entity to delegate its signing rights to another. Proxy signature scheme has been widely used in numerous applications. This paper proposed a proxy signature scheme based on lattice cryptography which is different from traditional proxy signature schemes. This scheme combines the idea of the traditional proxy signature and the lattice-based signature together. The security of the proposed scheme is based on the Short Integer Solution (SIS) problem, the proposed proxy signature scheme has smaller key size and lower computation cost. We use the Bimodal Gaussian Distribution, Reject Sampling, Hash matrix and other technologies to extend the original digital signature scheme to the proxy signature scheme. In this paper we will give the security proof of the proxy signature scheme. Moreover, since the key construction of the scheme is based on the operation of the ring, so the public and private key size can be greatly shrunk.
In response to the issues of low security and computational efficiency in current lattice-based proxy blind signature systems, a novel identity-based proxy blind signature scheme utilizing lattices is proposed. This scheme integrates the user's identity information through matrix accumulation operations to serve as the verification public key, simplifying the identity validation process and strengthening both security and privacy measures. The user's private key as well as the proxy signing key are produced through the extended algorithm of the left sampling algorithm, while the rejection sampling algorithm is employed to produce the proxy blind signature. These enhance the space utilisation of keys and signatures. Moreover, the scheme's security is reducible to solving the small integer solution problem, thereby attaining resilience against one-more unforgeability under the adaptive chosen-message attacks within the random oracle model. Compared to other schemes, our scheme features smaller key and signature sizes, resulting in greater efficiency.