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Lecture notes in computer science

Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes

Jan-Pieter D’Anvers, Qian Guo, Thomas Johansson, Alexander Nilsson, Fréderik Vercauteren, Ingrid M.R. Verbauwhede

Published Jan 1, 2019• 63 citations
Publisher
DOI
10.1007/978-3-030-17259-6_19

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In 2013, Boneh and Zhandry introduced the notion of indistinguishability (IND) in chosen plaintext (CPA) and chosen ciphertext (CCA) attacks by a quantum adversary which is given superposition access to an oracle for encryption and decryption queries but is restricted to classical queries in the challenge phase. In this paper we define IND-CPA and IND-CCA notions for symmetric encryption schemes where the adversary has full quantum superposition access to the oracle, and give constructions that achieve these security notions. Our results are formulated in the concrete security framework.
Recently Liang et al. propose an interesting privacy-preserving ciphertext multi-sharing control for big data storage mechanism, which is based on the cryptographic primitive of anonymous multi-hop identity based conditional proxy re-encryption scheme AMH-IBCPRE. They propose a concrete AMH-IBCPRE scheme and conclude their scheme can achieve IND-sCon-sID-CCA secure (indistinguishable secure under selectively conditional selectively identity chosen ciphertext attack). However, our research show their scheme can not be IND-sConsID- CCA secure for single-hop and multi-hop data sharing. Also in 2014, Liang et al. propose an interesting deterministic finite automata-based functional proxy reencryption scheme DFA-based FPRE for secure public cloud data sharing, they also conclude their scheme can achieve IND-CCA secure (indistinguishable secure under chosen ciphertext attack), we also show their scheme can not be IND-CCA secure either. For these two proposals, the main reason of insecurity is that part of the re-encryption key has the same structure as the valid ciphertext, thus the adversary can query on the decryption oracle with this part of the re-encryption key to get secret keys, which will break the CCA-security of their scheme.We give an improved AMH-IBCPRE scheme and an improved DFA-based FPRE scheme for cloud data sharing and show the new schemes can resist our attack and be CCA-secure.We also demonstrate our improved AMH-IBCPRE scheme?s efficiency compared with other related identity based proxy re-encryption schemes, the results show our scheme is almost the most efficient one.
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.