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Theoretical Computer Science

Chosen ciphertext attacks on lattice-based public key encryption and modern (non-quantum) cryptography in a quantum environment

Oleg Izmerly, Tal Mor

Published Sep 29, 2006• 9 citations
Publisher
DOI
10.1016/j.tcs.2006.07.060

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Threshold public key encryption is a cryptographic primitive where a secret key of an organization is distributed among special members called decryption servers (insiders) and a certain threshold number of insiders must cooperate to decrypt any ciphertext. Threshold public key encryption with an additional randomized algorithm Tsplit is called resplittable threshold public key encryption (RTPKE). Cryptographic primitive RTPKE was introduced by Hanaoka et al. [Generic construction of chosen ciphertext secure proxy re-encryption, in CT-RSA, San Francisco, CA, USA, LNCS, O. Dunkelman, ed., Springer-Verlag, Heidelberg, 2012, pp. 349–364] in a generic construction of chosen ciphertext attack secure proxy re-encryption scheme. In MIST 2013 conference Singh et al. [Lattice based efficient threshold public key encryption scheme, J. Wirel. Mob. Netw. Ubiquitous Comput. Dependable Appl. (JoWUA) 4(4) (2013), pp. 93–107] presented lattice-based RTPKE scheme based on Regev's LWE [On lattices, learning with errors, random linear codes, and cryptography, in STOC, Baltimore, MD, USA, H.N. Gabow and R. Fagin, eds., ACM, University of Wales, Cardiff, 2005, pp. 84–93] assumption. In this paper, we propose lattice-based RTPKE scheme in the identity-based setting.
Data is typically encrypted before transmission to a cloud server to safeguard user privacy. However, such encryption prevents the server from performing searches on the data, necessitating the introduction of novel cryptographic primitives, such as public key encryption with multi-ciphertext equality test (PKEMET). PKEMET allows the cloud server to execute a single equality test on multiple ciphertexts, determining if the underlying messages are identical disclosing any extra information. Ciphertext-policy attribute-based encryption (CP-ABE) facilitates secure and efficient data sharing in cloud computing environments by supporting fine-grained access control and flexible encryption. In this work, we integrate the concepts of PKEMET and CP-ABE, introducing a novel cryptographic primitive of CP-ABE with multi-ciphertext equality test (CP-ABEMET). We present the first quantum-resistant CP-ABEMET scheme based on the learning with errors (LWE) problem. This scheme enables the receiver to delegate the cloud server to perform a single equality test among multiple messages encrypted under distinct access policies. Importantly, during the multi-ciphertexts equality test, the server gains no knowledge of the encrypted messages. Furthermore, our proposed scheme not only achieves traditional indistinguishability against chosen plaintext attack (IND-CPA) and one-way against chosen plaintext attack (OW-CPA) security but is also proven to be number secure and resilient against collusion attacks. Finally, a comparative performance analysis between our CP-ABEMET and existing equality test schemes demonstrates that our approach is more practical, efficient, and secure.