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Lecture notes in computer science

Towards Tightly Secure Lattice Short Signature and Id-Based Encryption

Xavier Boyen, Qinyi Li

Published Jan 1, 2016• 74 citations
Publisher
DOI
10.1007/978-3-662-53890-6_14

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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.

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In CRYPTO 2021, Han et al. proposed a PKI-based authenticated key exchange (AKE) scheme that satisfies tight security in the standard model by using KEM and digital signature with multi-user security as building blocks. On the other hand, no tightly secure ID-based AKE (ID-AKE) scheme is known. ID-AKE has the advantage that certificate management is unnecessary, and the authentication can be based on the party’s public ID, such as an e-mail address. In this paper, we propose the first tightly secure ID-AKE scheme in the standard model. First, we extend the security model of Han et al.’s PKI-based AKE to the security model for ID-AKE. Next, we introduce a generic construction with multi-user secure KEM and ID-based signature (IBS) as building blocks and prove the tight security in our security model. For instantiating the underlying IBS, we also revisit the security proof of the existing generic construction of tightly secure IBS proposed by Lee et al. We point out a problem in their proof and correct it by strengthening an assumption. As an instantiation of our scheme, a tightly secure ID-AKE scheme under the MDDH assumption can be realized in the standard model.
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.