Commitment scheme

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A commitment scheme is a cryptographic primitive that allows one to commit to a chosen value (or chosen statement) while keeping it hidden to others, with the ability to reveal the committed value later. Commitment schemes are designed so that a party cannot change the value or statement after they have committed to it: that is, commitment schemes are binding. Commitment schemes have important applications in a number of cryptographic protocols including secure coin flipping, zero-knowledge proofs, and secure computation. A way to visualize a commitment scheme is to think of a sender as putting a message in a locked box, and giving the box to a receiver. The message in the box is hidden from the receiver, who cannot open the lock themselves. Since the receiver has the box, the message inside cannot be changed—merely revealed if the sender chooses to give them the key at some later time. Interactions in a commitment scheme take place in two phases: the commit phase during which a value is chosen and committed to the reveal phase during which the value is revealed by the sender, then the receiver verifies its authenticity In the above metaphor, the commit phase is the sender putting the message in the box, and locking it. The reveal phase is the sender giving the key to the receiver, who uses it to open the box and verify its contents. The locked box is the commitment, and the key is the proof. In simple protocols, the commit phase consists of a single message from the sender to the receiver. This message is called the commitment. It is essential that the specific value chosen cannot be extracted from the message by the receiver at that time (this is called the hiding property). A simple reveal phase would consist of...