### Peggy

##### Parameters known by Peggy:

Receives the public key $h$

Computes the commitment $c$:

Opens the commitment

### Step y/x

Before Victor can start the Pedersen commitment scheme he needs two prime numbers $p$ and $q$:

• $p$
• $q$

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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.

### Victor

##### Parameters known by Victor:

Computes the generator $g$:

Computes the public key $h$:

Receives the commitment $c$

Verifies Peggy's commitment to the value $x$: