  This paper introduces Generalized Quantum-assisted Digital Signature (GQaDS),
an improved version of a recently proposed scheme whose information theoretic
security is inherited by adopting QKD keys for digital signature purposes. Its
security against forging is computed considering a trial-and-error approach
taken by the malicious forger and GQaDS parameters are optimized via an
analytical approach balancing between forgery and repudiation probabilities.
The hash functions of the previous implementation are replaced with
Carter-Wegman Message Authentication Codes (MACs), strengthening the scheme
security and reducing the signature length. For particular scenarios where the
second verifier has a safe reputation, a simplified version of GQaDS, namely
deterministic GQaDS, can further reduce the required signature length, keeping
the desired security strength.
