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The quantum key distribution (QKD) technology is achieving a growing interest in both the scientific and industrial communities. Based on principles of quantum mechanics, it can provide unconditional security in key exchanges over end-to-end communication channels. Information-theoretically secure (ITS) authentication, the compulsory procedure of QKD systems, avoids the man-in-the-middle attack during the security key generation. In this paper, we propose a novel family of almost strongly universal (ASU) hash functions based on number-theoretic transforms (N-ASU), and prove that N-ASU hash functions can meet the high security requirement of an ITS authentication procedure. With such N-ASU hash functions, we propose a novel efficient NTT-based authentication algorithm (N-Auth) for QKD systems. Such a solution offers nearly the same security guarantees provided by the available authentication algorithms built upon ASU hash functions, but is characterized by a much lower computational complexity. The experimental results show that the N-Auth algorithm can fully meet the real-time and high-performance demands of modern 10-GHz QKD systems, making it a viable solution for the implementation of industrial-strength unconditionally secure broadband communication solutions. [ABSTRACT FROM PUBLISHER]