Tightly Secure Inner-Product Functional Encryption Revisited: Compact, Lattice-Based, and More

Currently, the only tightly secure inner-product functional encryption (IPFE) schemes in the multi-user and multi-challenge setting are the IPFE scheme due to Tomida (Asiacrypt 2019) and its derivatives. However, these tightly secure schemes have large ciphertext expansion and are all based on the matrix decisional Diffie-Hellman (DDH) assumption.

To improve the efficiency of tightly secure IPFE and enrich the diversity of its underlying assumptions, we construct a set of tightly secure IPFE schemes, with very compact ciphertexts and efficient algorithms, from the matrix DDH, the decisional composite residuosity (DCR), and the learning-with-errors (LWE) assumptions, respectively. In particular,

-- our DDH-based scheme has about 5× 100× shorter public/secret keys, 2× 2.9× shorter ciphertexts and about 5× 100× faster algorithms than all existing tightly secure IPFE schemes, at the price of 3 7 bits of decreased security level, resolving an open problem raised by Tomida (Asiacrypt 2019);

-- our DCR-based scheme constitutes the first tightly secure IPFE scheme from the DCR assumption;

-- our LWE-based scheme is the first almost tightly secure IPFE scheme from lattices, hence achieving post-quantum security.

We obtain our schemes by proposing a generic and flexible construction of IPFE with a core technical tool called two-leveled inner-product hash proof system (TL-IP-HPS). Specifically, our IPFE construction is in a compact design, and to achieve tight security, we propose an economic proof strategy to reuse the spaces in such compact IPFE. Interestingly, our new proof strategy also applies to the loosely secure IPFE schemes proposed by Agrawal, Libert and Stehlé (Crypto 2016), and yields a tighter bound on their security loss.