HighwayHash is a new pseudo-random function based on AVX2 multiply and permute instructions for thorough and fast hashing. It is 5.2 times as fast as SipHash for 1 KiB inputs. An open-source implementation is available under a permissive license. We discuss design choices and provide statistical analysis, speed measurements and preliminary cryptanalysis. Assuming it withstands further analysis, strengthened variants may also substantially accelerate file checksums and stream ciphers.