Multi-Input Attribute Based Encryption and Predicate Encryption.

Motivated by several new and natural applications, we initiate the study of multi-input predicate encryption (miPE) and further develop multi-input attribute based encryption (miABE). Our contributions are: 1. Formalizing Security: We provide definitions for miABE and miPE in the symmetric key setting and formalize security in the standard indistinguishability (IND) paradigm, against unbounded collusions. 2. Two-input ABE for NC1 from LWE and Pairings: We provide the first constructions for two-input key-policy ABE for NC(1 )from LWE and pairings. Our construction leverages a surprising connection between techniques recently developed by Agrawal and Yamada (Eurocrypt, 2020) in the context of succinct single-input ciphertext-policy ABE, to the seemingly unrelated problem of two-input key-policy ABE. Similarly to Agrawal-Yamada, our construction is proven secure in the bilinear generic group model. By leveraging inner product functional encryption and using (a variant of) the KOALA knowledge assumption, we obtain a construction in the standard model analogously to Agrawal, Wichs and Yamada (TCC, 2020). 3. Heuristic two-input ABE for P from Lattices: We show that techniques developed for succinct single-input ciphertext-policy ABE by Brakerski and Vaikuntanathan (ITCS 2022) can also be seen from the lens of miABE and obtain the first two-input key-policy ABE from lattices for P. 4. Heuristic three-input ABE and PE for NC1 from Pairings and Lattices: We obtain the first three-input ABE for NC1 by harnessing the powers of both the Agrawal-Yamada and the Brakerski-Vaikuntanathan constructions. 5. Multi-input ABE to multi-input PE via Lockable Obfuscation: We provide a generic compiler that lifts multi-input ABE to multi-input PE by relying on the hiding properties of Lockable Obfuscation (LO) by Wichs-Zirdelis and Goyal-Koppula-Waters (FOGS 2018), which can be based on LWE. Our compiler generalises such a compiler for single-input setting to the much more challenging setting of multiple inputs. By instantiating our compiler with our new two and three-input ABE schemes, we obtain the first constructions of two and three-input PE schemes. Our constructions of multi-input ABE provide the first improvement to the compression factor of non-trivially exponentially efficient Witness Encryption defined by Brakerski et al. (SCN 2018) without relying on compact functional encryption or indistinguishability obfuscation. We believe that the unexpected connection between succinct single-input ciphertext-policy ABE and multi-input key-policy ABE may lead to a new pathway for witness encryption. We remark that our constructions provide the first candidates for a nontrivial class of miFE without needing LPN or low depth PRG.