Quantum Key Distribution (QKD) technology, based on principles of quantum mechanics, can generate unconditional security keys for communication parties. Information-theoretically secure (ITS) authentication, the compulsory procedure of QKD systems, avoids the man-in-the-middle attack during the security key generation. The construction of hash functions is the paramount concern within the ITS authentication. In this extended abstract, we proposed a novel Efficient NTT-based ε-Almost Strongly Universal Hash Function. The security of our NTT-based ε-ASU hash function meets ε ≤ L(n + 1)/2n − 2. With ultra-low computational amounts of construction and hashing procedures, our proposed NTT-based ε-ASU hash function is suitable for QKD systems.