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Cryptography

Efficient CCA2-Secure IBKEM from Lattices in the Standard Model

Ngoc Ai Van Nguyen, Dung Hoang Duong, Minh Thuy Truc Pham, Willy Susilo

Published Dec 10, 2025• 1 citation
Publisher

Abstract

At SCN’2020, Boyen-Izabach`ene-Li proposed a simple and efficient CCA2-secure lattice KEM in standard model that does not rely on any generic constructions. However, the security proof does have some gap and hence is not complete. In addition, it is not possible to directly obtain an identity-based KEM (IBKEM) from their construction. In this paper, we revisit the construction of that CCA2-secure KEM and modify it to obtain an efficient CCA2-secure KEM with a complete security proof. This also enables us to construct a simple and efficient CCA2-secure IBKEM from lattices in the standard model.

DOI
10.3390/cryptography9040079

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At present, most of the identity based encryption (IBE) schemes from the lattice originate from the results of Gentry et.al., and regard each identity as a bit string with equal length and then map a matrix to every bit of identity string. Consequently, they are considerably less efficient. In our paper, we construct an IBE which is efficient from standard learning with errors problem and handles identities as a chunk for performance. In the standard model, our paper gives a proof which our IBE is IND-sID-CCA secure. Mean-while, we also show which our IBE construction is also IND-ID-CCA secure via the technique i.e., imposing additional restrictions on the identities, presented by Boyen and Boneh.
Key encapsulation mechanism (KEM) is an important key distribution mechanism that not only allows both sender and receiver to safely share a random session key, but also can be mainly applied to construct a hybrid public key encryption scheme. In this paper, we give an positive answer to the question of if it is possible to build an efficient KEM over lattices. More precisely, we design an efficient KEM scheme in standard model based on ideal lattices. We prove that the proposed scheme captures indistinguishability against active chosen ciphertext attacks (IND-CCA) under the ring learning with errors problem, or more formally, IND-CCA security. Compared with the current CCA secure KEM schemes based on lattices in the standard model, our scheme has shorter public key, secret key and encapsulation ciphertext. In addition, our KEM scheme realizes IND-CCA security in the standard model.
Recent developments have been made in the construction of cryptosystems with security based on the hardness of the lattice isomorphism problem (LIP). Due to lattice conjectures, one may expect in the future that breaking such schemes is computationally harder than most current lattice-based cryptosystems. To the best of our knowledge, there have not been any attempts to concretely instantiate a key encapsulation mechanism (KEM) based on LIP. In this work, we propose the first instance of such a KEM, following the framework of Ducas and van Woerden (EUROCRYPT 2022), using simple lattices. We present a randomness extractor derived from a hash function based on the short integer solution problem; define a concrete set of parameters for instantiating the scheme; provide a rigorous security estimation of an attacker trying to decode an encapsulated key through reductions to hard lattice problems; and use well-known methods to convert the IND-CPA secure KEM into an IND-CCA2 secure KEM, comparing the latter with other modern lattice-based KEMs. The resulting security is estimated under the assumption that an adversary cannot efficiently solve related instances of LIP, which is a consequence of the lack of cryptanalysis towards identifying isomorphism between lattices.