Summary: A deterministic function with its time complexity being \(O(\log^3 q)\) is constructed for the first time from a finite field \(F_q\) to Huff curves. Based on this function, a hash function from plaintext into Huff curves is constructed. The hash function lays the foundation for identity-based protocols on elliptic curves and its experimental time cost on the elliptic curve of the Chinese elliptic curve standard SM2 is \(557.8\mu \text{s}\).