Quantum digital signatures with smaller public keys

Abstract

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 \cite{GC2001}, 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. Asymptotically the expenditure becomes as low as one qubit 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.