Lower Bounds

We prove a lower bound on the size of commitments and openings of algebraic vector commitment schemes with transparent public parameters in Maurer’s Generic Group Model with pairings, and give a pairing-based scheme that beats the lower bound for schemes without pairings.

Digital signature schemes based on one-way or hash functions that can sign a predetermined number of messages: a lower bound on signature size in terms of that number, and the benefits of letting signatures depend on previously signed messages.