Victor receives the two prime numbers \( p \) and \( q \) and the generator \( g_{1} \) of the group \( \mathbb{Z}_{p} \) which is used to compute another generator \( g \) of order \( q \) from the group \( \mathbb{Z}_{p}^{*} \).

He sends the prime number \( p \) and the generator \( g \) to Peggy.

Victor chooses the secret key \( a \) and computes the public key \( h \) which he sends to Peggy.

Victor generates the keys because the commitment scheme is unconditional hiding and computational binding.

Peggy makes a commitment to the value \( x \) by first choosing a random integer \( r \) and then computing the commitment \( c \), which she sends to Victor.

Peggy reveals the two values \( x \) and \( r \) to Victor, i.e. she opens the commitment.

Victor then verifies the commitment \( c \) by checking that the two values are equals. Only if this is the case is the received value \( x \) the same value that Peggy made a commitment to.