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International Journal of Computer Mathematics

Efficient chosen ciphertext secure key encapsulation mechanism in standard model over ideal lattices

Xiaopeng Yang, Wenping Ma, Chengli Zhang

Published Feb 6, 2016• 3 citations
Publisher

Abstract

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.

DOI
10.1080/00207160.2016.1149578

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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.
Key Encapsulation Mechanism (KEM) is a foundational cryptography primitive, which can provide secure symmetric cryptographic key material for transmission by using public key algorithms. Until now, many Chosen-Ciphertext (IND-CCA) secure KEM schemes are constructed from Chosen-Plaintext (IND-CPA) or One-Way (OW-CPA) secure PKE via the generic Fujisaki-Okamoto (FO) transformations (TCC 2017). However, the security relies on the Random Oracle Model (ROM). To the best of our knowledge, there are no IND-CCA secure KEM schemes based on Learning Parity with Noise (LPN) assumption that can against post quantum attacks in the standard model. In this work, we propose the first direct construction of LPN-based KEM, which is secure in the standard model. In particular, we use double-trapdoor technique to answer adversary’s decryption queries correctly and a Target Collision Resistant (TCR) hash function to check the validity of the ciphertext. The encapsulated key is determined by a special LPN problem (with no random oracle required). The scheme is IND-CCA secure against post-quantum attacks under the low-noise LPN assumptions by a series of games and the security reduction is tight. Compared with previous schemes on 128-bit security level, our CCA-secure scheme only holds 50.78MB public keys, 62.50MB secret keys and 4.54KB ciphertexts, which is more efficient than the schemes of Döttlinget al.(ASIACRYPT 2012), Kiltzet al.(PKC 2014) and Yuet al.(CRYPTO 2016) ((7.27GB, 7.24GB, 7.03KB), (80.89MB, 46.23MB, 6.80KB) and (70.95MB, 70.65MB, 86.50KB) respectively).
In this paper, we present a novel multi-receiver identity-based key encapsulation mechanism (mID-KEM) scheme which is provably secure against chosen ciphertext attacks in the standard model and has several advantages over previous constructions without random oracles, including short public parameters, short private keys, computational efficiency in decapsulation algorithm and tight security reduction. To our best knowledge, our construction is the first in the literature to achieve such a high security level (CCA-security in the full security model).
Abstract. We use hybrid encryption with Fuzzy Identity-Based Encryption (Fuzzy-IBE) schemes, and present the first and efficient fuzzy identity-based key encapsulation mechanism (Fuzzy-IB-KEM) schemes which are chosen-ciphertext secure (CCA) without random oracle in the selective-ID model. To achieve these goals, we consider Fuzzy-IBE schemes as consisting of separate key and data encapsulation mechanisms (KEM-DEM), and then give the definition of Fuzzy-IB-KEM. Our main idea is to enhance Sahai and Waters ' "large universe " construction, chosen-plaintext secure (CPA) Fuzzy-IBE, by adding some redundant information to the ciphertext to make it CCA-secure.
In this article, we propose a double-NTRU (D-NTRU)-based key encapsulation mechanism (KEM) for the key agreement requirement of the post-quantum world. The proposed KEM is obtained by combining one-way D-NTRU encryption and Dent's KEM design method. The main contribution of this article is to construct a D-NTRU-based KEM that provides indistinguishability under adaptive chosen-ciphertext attack (IND-CCA2) security. The IND-CCA2 analysis and primal/dual attack resistance of the proposed D-NTRU KEM are examined in detail. A comparison with similar protocols is provided regarding parameters, public/secret keys, and ciphertext sizes. The proposed scheme presents arithmetic simplicity and IND-CCA2 security that does not require any padding mechanism.
Signcryption is a basic cryptographic primitive that simultaneously captures the functions of encryption and signature. To realize comprehensive information security against quantum computing attacks, lattice-based signcryption schemes have been successively proposed. However, the performance of signcryption schemes should be improved in the lattice setting. An efficient lattice-based signcryption scheme in the standard model is proposed in this paper. Under the ring learning with errors (RLWE) assumption and the ideal short integer solution (ISIS) assumption, the proposed signcryption scheme achieves indistinguishability against adaptive chosen ciphertext attacks (IND-CCA2) and existential unforgeability under an adaptive chosen-message attack (EUF-ACMA). Our scheme not only reduces the communication and computational overhead but also realizes a new design that combines the partitioning technique with the idea of tag-based key encapsulation. The performance analysis results show that our scheme is more efficient than previous lattice-based signcryption schemes in the standard model.