Quantum digital signatures with smaller public keys

We introduce a variant of quantum signatures in which nonbinary symbols are signed instead of bits. The public keys are fingerprinting states, just as in the scheme of Gottesman and Chuang, but we allow for multiple ways to reveal the private key partially. The effect of this modification is a reduction of the number of qubits expended per message bit. We give a security proof and we present numerical results that show how the improvement in public key size depends on the message length.