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International Conference on Intelligent Networking and Collaborative Systems (INCoS)

Post-quantum Strongly Unforgeable Identity-Based Signature Scheme from Lattices without Random Oracles

Zhenhua Liu, Xiangsong Zhang, Tsuyoshi Takagi

Published Sep 1, 2013• 1 citation
Publisher

Abstract

Inspired by Agrawal, Boneh and Boyen's identity-based encryption scheme, we proposed a post-quantum identity-based signature scheme from lattices. In this construction, two distinct trapdoors are used to find short bases. One trapdoor enables the real implementation to generate short bases for all lattices. The other trapdoor enables the simulator to generate short bases for all lattices. Moreover, the generating short bases are used to sample short vectors as signatures. Based on the hardness of the small integer solution (SIS) problem, the proposed scheme is proven to be strongly unforgeable against adaptive chosen-identity and adaptive chosen-message attacks without using random oracles. Compared with the existing strongly unforgeable identity-based signature schemes, our scheme has the advantages of full security and resistance to quantum computing attacks.

DOI
10.1109/incos.2013.107

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Inspired by Agrawal, Boneh and Boyen's identity-based encryption scheme, we proposed a post-quantum identity-based signature scheme from lattices. In this construction, two distinct trapdoors are used to find short bases. One trapdoor enables the real implementation to generate short bases for all lattices. The other trapdoor enables the simulator to generate short bases for all lattices. Moreover, the generating short bases are used to sample short vectors as signatures. Based on the hardness of the small integer solution (SIS) problem, the proposed scheme is proven to be strongly unforgeable against adaptive chosen-identity and adaptive chosen-message attacks without using random oracles. Compared with the existing strongly unforgeable identity-based signature schemes, our scheme has the advantages of full security and resistance to quantum computing attacks.
ABSTRACT An identity‐based signature scheme from lattices is constructed. The scheme is obtained from a modification of Agrawal, Boneh, and Boyen's lattice identity‐based encryption scheme. In this construction, we use two distinct trapdoors for finding short bases. One trapdoor enables the real implementation to generate short bases for all lattices. The other trapdoor enables the simulator to generate short bases for all lattices. Furthermore, the generating short bases are used to sample short vectors as signatures. Our scheme is computationally efficient. The scheme's strong unforgeability is proven in the standard model and rests on the hardness of the small integer solution problem. Finally, we extend the basic construction to obtain a hierarchical identity‐based signature scheme. Copyright © 2012 John Wiley & Sons, Ltd.
With the rapid development of electronic information technology, digital signature has become an indispensable part of our lives. Traditional public key certificate cryptosystems cannot overcome the limitations of certificate management. Identity-based cryptosystems can avoid the certificate management issues. The development of quantum computers has brought serious challenges to traditional cryptography. Post-quantum cryptography research is imperative. At present, almost all post-quantum identity-based signature (IBS) schemes are constructed using Gaussian sampling or trapdoor technologies. However, these two technologies have a great impact on computational efficiency. To overcome this problem, we construct an IBS scheme on lattices by employing Lyubashevsky’s signature scheme. Based on the shortest vector problem on lattices, our scheme does not use Gaussian sampling or trapdoor technologies. In the random oracle model, it is proved that our scheme is strongly unforgeable against adaptive chosen messages and identity attacks. The security level of our scheme is strongly unforgeable, which is a higher level than the existential unforgeability of other schemes. Compared with other efficient schemes, our scheme has advantages in computation complexity and security.
Lattice-based hierarchical identity-based signature (HIBS) schemes are receiving significant attention due to provable security reductions and potential security for quantum computers. However, most of the existing HIBS schemes based on lattices are less efficient for practical applications. To make lattice-based HIBS schemes become more practical, this paper presents an efficient HIBS scheme from lattices. Both the secret key size and the signature length of our proposal are much shorter than those of other lattice-based HIBS proposals. Our scheme is proven to be strongly unforgeable against adaptive identity attacks in the random oracle model. The security of the construction relies on the standard short integer solution (SIS) assumption.
On the basis of the signatures scheme without trapdoors from lattice, which was proposed by Vadim Lyubashevsky in 2012, we present a new ring signature scheme from lattice. The proposed ring signature scheme is an extension of the signatures scheme without trapdoors. We prove that our scheme is strongly unforgeable against adaptive chosen message in the random oracle model, and prove that the security of our scheme can be reduced to the hardness of the small integer solution (SIS) problem by rejection samplings. Compared with the existing lattice-based ring signature schemes, our new scheme is more efficient and with shorter signature length.
On the basis of the signatures scheme without trapdoors from lattice, which was proposed by Vadim Lyubashevsky in 2012, we present a new ring signature scheme from lattice. The proposed ring signature scheme is an extension of the signatures scheme without trapdoors. We prove that our scheme is strongly unforgeable against adaptive chosen message in the random oracle model, and prove that the security of our scheme can be reduced to the hardness of the small integer solution (SIS) problem by rejection samplings. Compared with the existing lattice-based ring signature schemes, our new scheme is more efficient and with shorter signature length.
Blind signature allows a user to get a signature of a signer on an arbitrary message, and the verifier can convince that the signature is indeed signed by the signer without leaking any information about the message. This property is necessary when the user’s privacy needs protection, such as a bank bill, a trade secret, etc. As an alternative of public key infrastructure, the identity-based system can simplify the key management procedures in certificate-based public key systems. Inspired by the requirement of identity-based blind signature in the post quantum world, we research on identity-based blind signature based on hard lattice problems under the random Oracle model. We propose a construction built upon the blind signature by Rückert, and it is proved to be one-more unforgeable against selective identity and chosen message attacks (sID-CMA) and unconditionally blind. The proposed scheme has 2 moves, and its security can be reduced to the small integer solution (SIS) problem.