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Developments in ABE using Pairings

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What are the recent developments in Attribute-Based Encryption (ABE) using Pairings assumptions?

Is pairings the most viable assumption while designing ABE. What other assumptions are used for ABE schemes and are there any advantages it gives over pairings assumption?

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There was a great deal of interest in pairing-based ABE about ten years ago (see for example this paper from MicroSoft). However, all pairing-based cryptography is still using Diffie-Hellman like constructions at its heart and so will not be quantum safe. Trying to introduce new cryptographic libraries at a time when the cryptographic community is aiming to migrate to quantum-safe alternatives made life tricky for pairing-based cryptography. Homomorphic encryption enables a very wide range of functionality, including (when instantiated using learning-with-errors primitives) a presumed resistance to Shor's algorithm. A more likely approach is therefore given in a paper by Boneh, Gentry et al. I don't know if these ideas have been picked up by anybody in industry.

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