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Security and Communication Networks

Efficient and strongly unforgeable identity‐based signature scheme from lattices in the standard model

Zhenhua Liu, Yupu Hu, Xiangsong Zhang, Fagen Li

Published Mar 7, 2012• 29 citations
Publisher

Abstract

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.

DOI
10.1002/sec.531

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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.
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 Signcryption as a cryptographic primitive can carry out signature and encryption simultaneously at a remarkably reduced cost. Identity‐based cryptography is more convenient than public key infrastructure‐based cryptography in certificate management. As a result, identity‐based signcryption has been studied extensively, and many efficient and provably secure constructions have been proposed. However, most of these schemes are based on intractability assumptions from number theory, and these assumptions have been threatened by the booming quantum computation. Therefore, a recent trend in cryptography is to construct cryptosystems that are based on lattice‐based intractability assumptions because of their plausible features of quantum attack resistance. In this paper, several identity‐based signcryption schemes from lattice hardness assumptions are proposed. In the standard model, these schemes are indistinguishable againstinneradaptively chosen ciphertext attacks (IND‐CCA2) and strongly unforgeable againstinnerchosen message attacks. In our construction, it does not matter whether the original encryption scheme used to construct signcryption is deterministic or probabilistic; the resulted signcryption schemes can reach IND‐CCA2 security. To achieve this, we carefully combine three techniques—the identity‐based encryption from lattice due to Agrawal–Boneh–Boyen (EUROCRYPT 2010), the framework of lattice‐based short signature due to Boyen (Public Key Cryptography 2010), and the Canetti–Halevi–Katz (abbr. CHK) technique, with necessary and tailored optimization—for transforming an (ℓ+ 1)‐level indistinguishable under chosen plaintext attack secure hierarchical identity‐based encryption (HIBE) into anℓlevel IND‐CCA2 secure HIBE scheme. In addition, our security proof also contains a more efficient simulation tool that might have separate interest in cryptographic applications. Copyright © 2015 John Wiley & Sons, Ltd.
Abstract Two ring signature schemes over number theory research unit (NTRU) lattices are presented. The first scheme constructed in the random oracle model is an extension of Ducas, Lyubashevsky, and Prest's identity‐based encryption scheme over NTRU lattices (in Asiacrypt 2014). Moreover, motivated by Boyen's lattice mixing and vanishing trapdoors (in PKC 2010), the second scheme in the standard model is achieved. Under the chosen‐message attack, our new constructions are proved strongly existentially unforgeable, and the security can be reduced to the hardness of NTRU lattices. Compared with the existing lattice‐based ring signatures, our schemes are more efficient and with shorter signature length. Copyright © 2016 John Wiley & Sons, Ltd.
Abstract In a strong designated verifier signature scheme, only the designated verifier can determine the identity of the signer; others cannot identify the signer or the verifier. To date, one strong designated verifier signature scheme from lattices has been proposed, only in the random oracle model. In this paper, we propose the first strong designated verifier signature scheme from lattices in the standard model. The proposed scheme satisfies the requirements of unforgeability, nontransferability, and privacy of the signer's identity. This scheme can be easily extended to an identity‐based strong designated verifier signature scheme and an (identity‐based) strong multi‐designated verifiers signature scheme. Copyright © 2017 John Wiley & Sons, Ltd.
Hierarchical identity-based signature (HIBS), which plays an important role in large communities, is a generaliza-tion of identity-based signature (IBS). In this paper, we present a new HIBS scheme from lattices without ran-dom oracles. The new scheme is proven to be strongly unforgeable against selective identity attacks under the standard hardness assumption of the short integer so-lution (SIS) problem. Furthermore, the secret key size and the signature length of our scheme are both invariant and much shorter than those of the previous lattice-based HIBS schemes. To the best of our knowledge, our con-struction is the first short lattice-based HIBS scheme in the standard model.
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.