Timed commitments [Boneh and Naor, CRYPTO 2000] are the timed analogue of standard commitments, where the commitment can be non-interactively opened after a pre-specified amount of time passes. Timed commitments have a large spectrum of applications, such as sealed bid auctions, fair contract signing, fair multi-party computation, and cryptocurrency payments. Unfortunately, all practical constructions rely on a (private-coin) trusted setup and do not scale well with the number of participants. These are two severe limiting factors that have hindered the widespread adoption of this primitive.

In this paper we introduce a new probabilistic lattice-based bounded homomorphic encryption scheme. For this scheme the sum of two encrypted messages is the encryption of the sum of two messages and the scheme is able to preserve a vector spave structure of the message. The size of the public key is rather large ap 3 Mb but the encryption and the decryption operations are very fast (of the same speed order than NTRU). The homomorphic operation, i.e. the addition of ciphertexts is dramatically fast compared to homomorphic schemes based on group theory like Paillier or El Gamal.