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International Conference on Computational Intelligence and Security (CIS)

Hierarchical Identity-based Broadcast Encryption Scheme on Lattices

Zhang Jinman, Chen Qin

Published Dec 1, 2011• 5 citations
Publisher

Abstract

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.

DOI
10.1109/cis.2011.212

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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.
This paper proposes a broadcast encryption scheme over lattice which is dynamical and anonymous simultaneously. The dynamic property means that the authorized user is not fixed in proposed scheme, and the broadcaster can send the message to any receiver without any added operation. The anonymous property means that the identity of an authorized receiver is protected efficiently, any outsider attacker would not find the chosen receiver's identity. The semantic security of the proposed scheme is proven in the standard model under the hardness of the learning with errors problem (LWE).
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.
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.
Nowadays, emerging technologies such as smart terminals, cloud computing, and the Internet of Things are developing rapidly. The "One-to-one" encrypted transmission method is difficult to meet the communication needs in complex network environments due to high computational costs. Broadcast encryption technology can provide data encryption protection during information sharing among multiple users. However, most of the existing schemes are based on bilinear groups, which cannot resist quantum computing attacks. And these schemes also suffer from the key escrow problem. For this reason, a novel distributed broadcast encryption scheme is proposed based on the Learning with Errors (LWE) difficulty assumption on the lattice. The scheme avoids key interaction negotiation among users by introducing a public key bulletin board. Meanwhile, the scheme solves the security problem caused by the authoritative user's complete mastery of the user's private key.
Using lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption (HIBE) scheme in the standard model whose public key size is only ( dm 2 + mn ) log q bits and whose message-ciphertext expansion factor is only log q , where d is the maximum hierarchical depth and ( n , m , q ) are public parameters. In our construction, a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits, which implies that d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2 d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2 dm 2 + mn + m ) log q . To reduce the message-ciphertext expansion factor of the proposed scheme to log q , the encryption algorithm of this scheme is built based on Gentry’s encryption scheme, by which m 2 bits of plaintext are encrypted into m 2 log q bits of ciphertext by a one time encryption operation. Hence, the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem, we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks.
An efficient identity-based encryption (IBE) scheme over lattice is proposed in this paper. Under the hardness of the learning with errors (LWE) problem, the proposed scheme is semantic secure against adaptive chosen identity and chosen plaintext attack in the standard model. To improve the efficiency of the lattice-based IBE scheme, unlike the identity string is encoded into a matrix by a group of public matrices in several known constructions, the identity string of l bits is encoded into a vector with the help of l+1 vectors in this paper. With the help of this idea, we achieve the private key extraction of IBE scheme at the same lattice. Then, the public key of the proposed scheme only consists of one n×m matrix and l+1 vectors, compared with that the public keys of the known lattice-based IBE schemes all consist as a group of n×m matrices. Hence, the public key size of this scheme is shorter than that of the known constructions.