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Lecture notes in computer science

On Black-Box Reductions between Predicate Encryption Schemes

Vipul Goyal, Virendra Kumar, Satya Lokam, Mohammad Mahmoody

Published Jan 1, 2012• 13 citations
Publisher
DOI
10.1007/978-3-642-28914-9_25

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Matchmaking encryption constructed in the identity-based encryption setting, named identity-based matchmaking encryption (IB-ME), requires both sender and receiver to specify target identity simultaneously for each other for message decryption. The IB-ME schemes can not only ensure the privacy of the sender and the message but also provide authentication for the data source. In order to resist quantum-attacks, we put forward a post-quantum secure IB-ME scheme. Compared with Ateniese et al.'s scheme and Francati et al.'s scheme, our approach eliminates the use of functional encryption, predicate encryption and signature scheme, and only uses a more simple preimage sampling function and an IBE scheme in the way of non-black-box. Compared with post-quantum secure IB-MEs proposed currently, our scheme is the first non-black-box construction based on standard lattice assumptions such as LWE and ISIS.
Proving whether it is possible to build IND-CCA public-key encryption (PKE) from IND-CPA PKE in a black-box manner is a major open problem in theoretical cryptography. In a significant breakthrough, Gertner, Malkin and Myers showed in 2007 that shielding black-box reductions from IND-CCA to IND-CPA do not exist in the standard model. Shielding means that the decryption algorithm of the IND-CCA scheme does not call the encryption algorithm of the underlying IND-CPA scheme. In other words, it implies that every tentative construction of IND-CCA from IND-CPA must have a re-encryption step when decrypting. This result was only proven with respect to classical algorithms. In this work we show that it stands in a post-quantum setting. That is, we prove that there is no post-quantum shielding black-box construction of IND-CCA PKE from IND-CPA PKE. In the type of reductions we consider, i.e. post-quantum ones, the constructions are still classical in the sense that the schemes must be computable on classical computers, but the adversaries and the reduction algorithm can be quantum. This suggests that considering quantum notions, which are stronger than their classical counterparts, and allowing for quantum reductions does not make building IND-CCA public-key encryption easier.