Commitment

A commitment scheme is a two-phase cryptographic protocol between two parties, a sender and a receiver, satisfying the following constraints. At the end of the Commit phase the sender is committed to a specific value (often a single bit) that he cannot change later on (Commitments are binding) and the receiver should have no information about the committed value, other than what he already knew before the protocol (Commitments are concealing). In the Unveil phase, the sender sends extra information to the receiver that allows him to determine the value that was concealed by the commitment. Bit commitments are important components of zero-knowledge protocols [GMW91, BCC88], and other more general twoparty cryptographic protocols [Kil88]. A natural intuitive implementation of a commitment is performed using an envelope (see Figure 1). Some information written on a piece of paper may be committed to by sealing it inside an envelope. The value inside the sealed envelope cannot be guessed (envelopes are concealing) without modifying the envelope (opening it) nor the content may be modified (envelopes are binding).