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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Secure Hierarchical Identity-Based Identification without Random Oracles

Atsushi Fujioka, Taiichi Saito, Keita Xagawa

Published Jan 1, 2014• 0 citations
Publisher

Abstract

This paper proposes a generic construction of hierarchical identity-based identification (HIBI) protocols secure against impersonation under active and concurrent attacks in the standard model. The proposed construction converts a digital signature scheme existentially unforgeable against chosen message attacks, where the scheme has a protocol for showing possession of a signing key, not a signature. Our construction is based on the so-called certificate-based construction of hierarchical identity-based cryptosystems, and utilizes a variant of the well-known OR-proof technique to ensure the security against impersonation under active and concurrent attacks. We also present several concrete examples of our construction employing the Waters signature (EUROCRYPT 2005), and other signatures. As results, its concurrent security of each instantiation is proved under the computational Diffie-Hellman (CDH) assumption, the RSA assumption, or their variants in the standard model. Chin, Heng, and Goi proposed an HIBI protocol passively and concurrently secure under the CDH and one-more CDH assumption, respectively (FGIT-SecTech 2009). However, its security is proved in the random oracle model.

DOI
10.1587/transfun.e97.a.1307

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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Mar 23, 2022•1 citation
This paper proposes a generic construction of hierarchical identity-based identification (HIBI) protocols secure against impersonation under active and concurrent attacks in the standard model. The proposed construction converts a digital signature scheme existentially unforgeable against chosen message attacks, where the scheme has a protocol for showing possession of a signing key, not a signature. Our construction is based on the so-called certificate-based construction of hierarchical identity-based cryptosystems, and utilizes a variant of the well-known OR-proof technique to ensure the security against impersonation under active and concurrent attacks. We also present several concrete examples of our construction employing the Waters signature (EUROCRYPT 2005), and other signatures. As results, its concurrent security of each instantiation is proved under the computational Diffie-Hellman (CDH) assumption, the RSA assumption, or their variants in the standard model. Chin, Heng, and Goi proposed an HIBI protocol passively and concurrently secure under the CDH and one-more CDH assumption, respectively (FGIT-SecTech 2009). However, its security is proved in the random oracle model.
Abstract. We propose a variant of the “bonsai tree ” signature scheme, a lattice-based existentially unforgeable signature scheme in the standard model. Our construction offers the same efficiency as the “bonsai tree” scheme but supports the stronger notion of strong unforgeability. Strong unforgeability demands that the adversary is unable to produce a new message-signature pair (m, s), even if he or she is allowed to see a different signature s ′ for m. In particular, we provide the first treeless signature scheme that supports strong unforgeability for the post-quantum era in the standard model. Moreover, we show how to directly implement identity-based, and even hierarchical identity-based, signatures (IBS) in the same strong security model without random oracles. An additional advantage of this direct approach over the usual generic conversion of hierarchical identity-based encryption to IBS is that we can exploit the efficiency of ideal lattices without significantly harming security. We equip all constructions with strong security proofs based on mild worst-case assumptions on lattices and we also propose concrete security parameters.
Abstract We construct the first tightly secure hierarchical identity-based encryption (HIBE) scheme based on standard assumptions, which solves an open problem from Blazy, Kiltz, and Pan (CRYPTO 2014). At the core of our constructions is a novel randomization technique that enables us to randomize user secret keys for identities with flexible length. The security reductions of previous HIBEs lose at least a factor of Q, which is the number of user secret key queries. Different to that, the security loss of our schemes is only dependent on the security parameter. Our schemes are adaptively secure based on the Matrix Diffie-Hellman assumption, which is a generalization of standard Diffie-Hellman assumptions such as k-Linear. We have two tightly secure constructions, one with constant ciphertext size, and the other with tighter security at the cost of linear ciphertext size. Among other things, our schemes imply the first tightly secure identity-based signature scheme by a variant of the Naor transformation.
A two-party authenticated key exchange (AKE) protocol allows each of the two parties to share a common secret key over insecure channels, even in the presence of active adversaries who can actively control and modify the exchanged messages. To capture the malicious behaviors of the adversaries, there have been many efforts to define security models. Amongst them, the extended Canetti–Krawczyk (eCK) security model is considered one of the strongest security models and has been widely adopted. In this paper, we present a simple construction of a pairing-based eCK-secure AKE protocol in the standard model. Our protocol can be instantiated with a suitable signature scheme (i.e., an existentially unforgeable signature scheme against adaptive chosen message attacks). The underlying assumptions of our construction are the decisional bilinear Diffie–Hellman assumption and the existence of a pseudorandom function. Note that the previous eCK-secure protocol constructions either relied on random oracles for their security or used somewhat strong assumptions, such as the existence of strong-pseudorandom functions, target collision-resistant functions, etc., while our protocol construction uses fewer and more-standard assumptions in the standard model. Furthermore, preserving the same security argument, our protocol can be instantiated with any appropriate signature scheme that comes in the future with better efficiency.
In Asiacrypt 2003, Al-Riyami and Paterson proposed the notion of certificateless cryptography, a technique to remove key escrow from traditional identity-based cryptography as well as circumvent the certificate management problem of traditional public key cryptography.Subsequently much research has been done in the realm of certificateless encryption and signature schemes, but little to no work has been done for the identification primitive until 2013 when Chin et al. rigorously defined certificateless identification and proposed a concrete scheme.However Chin et al.'s scheme was proven in the random oracle model and Canetti et al. has shown that certain schemes provable secure in the random oracle model can be insecure when random oracles are replaced with actual hash functions.Therefore while having a proof in the random oracle model is better than having no proof at all, a scheme to be proven in the standard model would provide stronger security guarantees.In this paper, we propose the first certificateless identification scheme that is both efficient and show our proof of security in the standard model, that is without having to assume random oracles exist.
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.
Hierarchical ID-based authenticated key exchange (HID-AKE) is a cryptographic protocol to establish a common session key between parties with authentication based on their IDs with the hierarchical delegation of key generation functionality. All existing HID-AKE schemes are selective ID secure, and the only known standard model scheme relies on a non-standard assumption such as the q-type assumption. In this paper, we propose a generic construction of HID-AKE that is adaptive ID secure in the HID-eCK model (maximal-exposure-resilient security model) without random oracles. One of the concrete instantiations of our generic construction achieves the first adaptive ID secure HID-AKE scheme under the (standard) k-lin assumption in the standard model. Furthermore, it has the advantage that the computational complexity of pairing and exponentiation operations and the communication complexity do not depend on the depth of the hierarchy. Also, the other concrete instantiation achieves the first HID-AKE scheme based on lattices (i.e., post-quantum).