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Theoretical Computer Science

A novel identity-based multi-signature scheme over NTRU lattices

Xinjian Chen, Qiong Huang, Hongbo Li, Zhijian Liao, Willy Susilo

Published Sep 5, 2022• 11 citations
Publisher
DOI
10.1016/j.tcs.2022.08.022

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Summary Proxy signature scheme is an important cryptographic primitive, for an entity can delegate his signing right to another entity. Although identity‐based proxy signature schemes based on conventional number‐theoretic problems have been proposed for a long time, the researchers have paid less attention to lattice‐based proxy signature schemes that can resist quantum attack. In this paper, we first propose an identity‐based proxy signature scheme over Number Theory Research Unit (NTRU)‐lattice. We proved that the proposed paradigm is secure under the hardness of the γ‐shortest vector problem on the NTRU lattice in random oracle model; furthermore, the comparison with some existing schemes shows our scheme is more efficient in terms of proxy signature secret key size, proxy signature size, and computation complexity. As the elemental problem of the proposed scheme is difficult even for quantum computation model, our scheme can work well in quantum age.

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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.

Security and Communication Networks•Nov 8, 2016•14 citations
Summary Proxy signature scheme is an important cryptographic primitive, for an entity can delegate his signing right to another entity. Although identity‐based proxy signature schemes based on conventional number‐theoretic problems have been proposed for a long time, the researchers have paid less attention to lattice‐based proxy signature schemes that can resist quantum attack. In this paper, we first propose an identity‐based proxy signature scheme over Number Theory Research Unit (NTRU)‐lattice. We proved that the proposed paradigm is secure under the hardness of the γ‐shortest vector problem on the NTRU lattice in random oracle model; furthermore, the comparison with some existing schemes shows our scheme is more efficient in terms of proxy signature secret key size, proxy signature size, and computation complexity. As the elemental problem of the proposed scheme is difficult even for quantum computation model, our scheme can work well in quantum age.
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.