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Symmetry

Lattice-Based Revocable Certificateless Signature

Ying-Hao Hung, Yuh‐Min Tseng, Sen‐Shan Huang

Published Oct 20, 2017• 15 citations
Publisher

Abstract

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.

DOI
10.3390/sym9100242

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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.
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 against adaptive chosen message attacks. Performance comparisons are made to demonstrate that the proposed CBS scheme from lattices is better than the previous lattice-based CBS scheme in terms of private key size and signature size.
In the past, many ID-based signature (IBS) schemes based on the integer factorization or discrete logarithm problems were proposed. With the progress on the development of quantum technology, IBS schemes mentioned above would become vulnerable. Recently, several IBS schemes over lattices were proposed to be secure against attacks in the quantum era. As conventional public-key settings, ID-based public-key settings have to offer a revocation mechanism to revoke misbehaving or malicious users. However, in the past, little work focuses on the revocation problem in the IBS schemes over lattices. In this article, we propose a new revocable IBS (RIBS) scheme with short size over lattices. Based on the short integer solution (SIS) assumption, we prove that the proposed RIBS scheme provides existential unforgeability against adaptive chosen-message attacks. As compared to the existing IBS schemes over lattices, our RIBS scheme has better performance in terms of signature size, signing key size, and the revocation mechanism with public channels.
The certificateless cryptography solves the certificate management and key escrow problems in the Internet of Things. However, these schemes are no longer safe in the quantum environment. Lattice cryptography has become the main method to solve quantum security. At present, only a few lattice-based certificateless signature schemes have been proposed and the use of the trapdoor function limits the efficiency of the lattice cryptography, and the security of these schemes can only reach existential unforgeability. We construct a lattice-based certificateless signature scheme based on Lyubashevsky's signature scheme. The security of our scheme can reach strong unforgeability and the computational efficiency of our scheme is lower than the previous schemes.
The security of traditional identity-based signatures wholly depends on the security of secret keys.Exposure of secret keys requires reissuing all previously assigned signatures.Based on this,to revoke private key leaks or malicious users in the signature scheme,an adaptive secure revocable identity-based signature over lattices is proposed,which provides an efficient revocation mechanism to revoke misbehaving or compromised users from the systems.The scheme is proved to be strongly Unforgeable against adaptive Chosen-message Attacks(sUFCMA)under Small Integer Solution(SIS)assumption.Security analysis results show that the proposed scheme not only can meet the security of revocable identity-based signature,but also can resist the quantum attack.
Threshold signature has been widely used in electronic wills, electronic elections, cloud computing, secure multi-party computation and other fields. Until now, certificateless threshold signature schemes are all based on traditional mathematic theory, so they cannot resist quantum computing attacks. In view of this, we combine the advantages of lattice-based cryptosystem and certificateless cryptosystem to construct a certificateless threshold signature from lattice (LCLTS) that is efficient and resistant to quantum algorithm attacks. LCLTS has the threshold characteristics and can resist the quantum computing attacks, and the analysis shows that it is unforgeable against the adaptive Chosen-Message Attacks (UF-CMA) with the difficulty of Inhomogeneous Small Integer Solution (ISIS) problem. In addition, LCLTS solves the problems of the certificate management through key escrow.
Certificateless signcryption can simultaneously provide certificateless signature and encryption. In recent years, many certificateless signcryption schemes have been proposed. However, these schemes are based on traditional mathematical theory and not have the ability of resisting the quantum computing attacks. Up to now, lattice-based certificateless signature or encryption schemes have been proposed; however, these schemes only have one function and cannot fulfill two functions of certificateless signature and encryption at the same time. In consideration of this reason, in this article, a certificateless signcryption scheme from lattice (L-CLSS) is constructed. L-CLSS has three advantages. First, in the random oracle model, it is provably indistinguishable against adaptive ciphertext-chosen attacks under the intractability of the learning with errors (LWE) problem and unforgeable against adaptive message-chosen attacks under the hardness of small integer solution (SIS) problem. Second, comparison with the cryptographic algorithms under the difficulty of large integer decomposition, L-CLSS can resist the quantum computing attacks. Third, L-CLSS has higher computation efficiency and a lower communication cost than the existing schemes.