Quantum Key Distribution (QKD) protocols require Information-Theoretically Secure (ITS) authentication of the classical channel to preserve the unconditional security of the distilled key. Standard ITS schemes are based on one-time keys: once a key is used to authenticate a message, it must be discarded. Since QKD requires mutual authentication, two independent one-time keys are typically consumed per round, imposing a non-trivial overhead on the net secure key rate. In this work, we present the authentication-with-response scheme, a novel ITS authentication scheme based on $\varepsilon$-Almost Strongly Universal$_2$ ($\varepsilon$-ASU$_2$) functions, whose IT security can be established in the Universal Composability (UC) framework. The scheme achieves mutual authentication consuming a single one-time key per QKD round, halving key consumption compared to the state-of-the-art.