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Journal of Communications and Networks

Hierarchical identity-based broadcast encryption scheme from LWE

Chunli Yang, Shihui Zheng, Licheng Wang, Xiuhua Lu, Yixian Yang

Published Jun 1, 2014• 7 citations
Publisher

Abstract

A hierarchical identity-based broadcast encryption (H-IBBE) scheme is an identity-based broadcast encryption (IBBE) scheme in a hierarchical environment. In order to obtain secure H-IBBE schemes in the quantum era, we propose an H-IBBE scheme based on the learning with errors problem assumption. Our scheme achieves indistinguishability from random under adaptive chosen-plaintext and chosen-identity attacks in the random oracle model.

DOI
10.1109/jcn.2014.000045

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A hierarchical identity-based broadcast encryption (H-IBBE) scheme is an identity-based broadcast encryption (IBBE) scheme in a hierarchical environment. In order to obtain secure H-IBBE schemes in the quantum era, we propose an H-IBBE scheme based on the learning with errors problem assumption. Our scheme achieves indistinguishability from random under adaptive chosen-plaintext and chosen-identity attacks in the random oracle model.
Motivated by an identity-based broadcast encryption scheme from lattice(1) and a forward-secure identity-based encryption scheme(2), we propose a forward-secure identity-based broadcast encryption scheme from lattice by adding the forward-security mechanism on broadcast encryption scheme. Our scheme satisfies the security requirements of both the broadcast encrypt ion scheme and forward-security scheme, that is, it is forward-secure for the secret keys used previously, and we prove that it is semantic secure based on LWE (Learning With Error)assumption(3) in the random oracle model. In addition, our construction is believed to be secure against quantum computer.
In this paper, we propose a hierarchical identity-based encryption (HIBE) scheme in the random oracle (RO) model based on the learning with rounding (LWR) problem over small modulus qqq. Compared with the previous HIBE schemes based on the learning with errors (LWE) problem, the ciphertext expansion ratio of our scheme can be decreased to 1/2. Then, we utilize the HIBE scheme to construct a deterministic hierarchical identity-based encryption (D-HIBE) scheme based on the LWR problem over small modulus. Finally, with the technique of binary tree encryption (BTE) we can construct HIBE and D-HIBE schemes in the standard model based on the LWR problem over small modulus.
To design a post-quantum secure broadcast encryption scheme,by using the bonsai trees model,an identity-based broadcast encryption scheme over lattice is proposed.The proposed scheme can avoid the decryption failure problem in the existing scheme.The new scheme is provable securied against chosen-plaintext attack where the security is reduced to the hardness of learning with errors in the standard model.Moreover the proposed scheme supports the dynamic expansion of client and deals with the setting of stateless receivers.
Using a known lattice-based chosen plain-text secure encryption scheme and the Bonsai trees primitive, a identity-based encryption (IBE) scheme is proposed in this paper. A public matrices chosen rule that has been used in a known efficient lattice-based chosen ciphtertext secure encryption scheme is used in this paper to reduce the public key size and the message-to ciphtertext expanse factor. Under the hardness of the decision variant of the learning with errors (LWE) problem, we prove that the proposed IBE scheme is indistinguishable against the adaptive chosen identities and chosen-plaintext attack in the standard model. Since a new public key chosen rule is used in our design scheme, the public key size of the proposed scheme would be short. Moreover, the message-to-ciphtertext expanse factor of this scheme is also controlled efficiently which is nearly closed to that of Gentry's scheme. Due to the quantum intractability of the LWE problem on which the scheme is based, the proposed IBE scheme is secure even in quantum-era.
In this paper, a hierarchical identity-based broadcast encryption scheme is proposed based on the learning with errors problem, which is a classic hard problem on lattices. In the proposed scheme, each user's identity is associated with a lattice matrix, then the relationship between the lattice and its sub lattice could easily represent the hierarchical identity construction. Short basis of a lattice can function as a private key of a user, so based on the Sample Basis algorithm the private key of each level's user can be derived. The security proof of our proposed scheme is also given in this paper, which is IND-CCA2 secure against the attacks by outsider users and FS-CCA secure against the attacks by authorized receivers. In addition, compared with the broadcast encryption scheme based on the bilinear mapping, the scheme in this paper is more efficient in the encryption and decryption.
Identity-based encryption (IBE), and its hierarchical extension (HIBE), are interesting cryptographic primitives that aim at the implicit authentication on the users' public keys by using users' identities directly. During the past several decades, numerous elegant pairing-based (H)IBE schemes were proposed. However, most pairing-related security assumptions suffer from known quantum algorithmic attacks. Therefore, the construction of lattice-based (H)IBE became one of the hot directions in recent years. In the setting of most existing lattice-based (H)IBE schemes, each bit of a user's identity is always associated with a parameter matrix. This always leads to drastic but unfavorable increases in the sizes of the system public parameters. To overcome this issue, we propose a flexible trade-off mechanism between the size of the public parameters and the involved computational cost using the blocking technique. More specifically, we divide an identity into l' segments and associate each segment with a matrix, while increasing the lattice modulo slightly for maintaining the same security level. As a result, for the setting of 160-bit identities, we show that the size of the public parameters can be reduced by almost 89.7% (resp. 93.8%) while increasing the computational cost by merely 5.2% (resp. 12.25%) when l' is a set of 16 (resp. 8). Finally, our IBE scheme is extended to an HIBE scheme, and both of them are proved to achieve the indistinguishability of ciphertexts against adaptively chosen identity and chosen plaintext attack (IND-ID-CPA) in the standard model, assuming that the well-known ring learning with error (RLWE) problem over the involved ideal lattices is intractable, even in the post-quantum era.