  Digital signatures are widely used for providing security of communications.
At the same time, the security of currently deployed digital signature
protocols is based on unproven computational assumptions. An efficient way to
ensure an unconditional (information-theoretic) security of communication is to
use quantum key distribution (QKD), whose security is based on laws of quantum
mechanics. In this work, we develop an unconditionally secure signature scheme
that guarantees authenticity and transferability of arbitrary length messages
in a QKD network. In the proposed setup, the QKD network consists of two
subnetworks: (i) an internal network that includes the signer and with
limitation on the number of malicious nodes and (ii) an external network that
has no assumptions on the number of malicious nodes. A consequence of the
absence of the trust assumption in the external subnetwork is the necessity of
assistance from internal subnetwork recipients for the verification of
message-signature pairs by external subnetwork recipients. We provide a
comprehensive security analysis of the developed scheme, perform an
optimization of the scheme parameters with respect to the secret key
consumption, and demonstrate that the developed scheme is compatible with the
capabilities of currently available QKD devices.
