Computes \( v \) for the public key:
Computes the fingerprint of the message and selects the ephemeral key:
Computes the signature for the message:
Enter the message (or integer) that Samantha wants to sign:
Press Enter to generate the parameters. Use the Left and Right arrow keys to navigate between steps.
A trusted third party publishes a prime number \( p \) and a generator \( g \) of the group \( \mathbb{Z}_{p}^{*} \).
Samantha chooses the secret key \( sk = s \) and computes \( v \). She then sends the public key \( pk = (p, g, v) \) to Victor.
Samantha computes the fingerprint \( \mathcal{H}(m) \) of the message \( m \) using a publicly known hash function \( \mathcal{H} \).
To compute the signature, which consists of the two values \( \sigma_{1} \) and \( \sigma_{2} \), she needs a random ephemeral key \( e \) that is unique for this signature, as well as its inverse \( e^{-1} \).
She randomly chooses a value \( 1 \leq e \leq p-1 \) until \( \gcd(e, p-1) = 1 \), and then computes the inverse \( e^{-1} \) using the extended Euclidean algorithm.
Samantha computes the signature of the fingerprint \( \mathcal{H}(m) \), which consists of the two values \( \sigma_{1} \) and \( \sigma_{2} \).
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 obtains the same fingerprint as Samantha.
Victor verifies the signature of the fingerprint \( \mathcal{H}(m) \).
If the two computed values are equal, the message was signed by Samantha and nobody has tampered with its content.
Receives the public key \( pk = (p, g, v) \).
Receives the signature \( (\sigma_{1}, \sigma_{2}) \) and the message \( m \).
Computes the fingerprint \( \mathcal{H}(m) \):
Verifies the signature of the fingerprint: