A trusted third party chooses two prime numbers \( q \) and \( p \) and a generator \( g_{1} \) of the group \( \mathbb{Z}_{p} \).

The generator \( g_{1} \) is used to compute another generator \( g \) of order \( q \) from the group \( \mathbb{Z}_{p}^{*} \).

Samantha and Victor receives the two prime numbers \( p \) and \( q \) and the generator \( g \).

Samantha computes the fingerprint \( \mathcal{H}(m) \) of the message \( m \) by using a public known hash function \( \mathcal{H} \).

Samantha chooses a secret signing exponent \( s \) and computes the public verification exponent \( v \), which she sends to Victor.

In the signature Samantha needs an ephemeral key \( e \) that is unique for this signature.

Samantha computes the signature of the fingerprint \( \mathcal{H}(m) \) which consists of two parts \( \sigma_{1} \) and \( \sigma_{2} \). In the computation she uses the concatenation operation \( \| \).

She then sends the message \( m \) and the signature \( (\sigma_{1}, \sigma_{2}) \) to Victor.

Victor uses the same hash function \( \mathcal{H} \) as Samantha to compute the fingerprint \( \mathcal{H}(m) \) of the message \( m \).

If nobody has tampered with the content of the message Victor gets the same fingerprint as Samantha.

Victor verifies the signature of the fingerprint \( \mathcal{H}(m) \) where he uses the concatenation operation \( \| \).

If the two computed values are equals, the message was signed by Samantha and nobody has tampered with the content of the message.