Timed Commitments and Timed Encryption: Generic Constructions and Instantiations from Isogenies

Introduced by Boneh and Naor (CRYPTO 2000), timed commitments are a versatile primitive that found numerous applications in e-voting, contract signing and auctions. In TCC 2020, Katz, Loss and Xu showed that non-interactive timed commitments (NITC) can be generically built from timed public key encryption (TPKE). Unfortunately, almost all constructions for either primitive rely on classical, i.e. non post-quantum, assumptions or require inefficient building blocks like indistinguishable obfuscation or fully homomorphic encryption.

In this work, we propose generic constructions for non-interactive timed commitments and timed encryption, assuming only efficient building blocks like verifiable random functions, trapdoor delay functions and NIZK proof systems. Both our NITC (called LEIBNITC) and our TPKE (called NYTPKE) can be instantiated from isogenies, making them post-quantum secure. The instantiation of LEIBNITC with isogenies is very efficient and yields commitments of size 2328 bits, representing one of the most efficient timed commitments in the literature.