Multimixer-156: Universal Keyed Hashing Based on Integer Multiplication and Cyclic Shift

In this paper, we introduce Multimixer-156, a new keyed hash function based on 32-bit integer multiplication and cyclic shift operations. Presence of vector instructions for these operations on many CPUs make Multimixer-156 an efficient keyed hash function in software on many platforms. We claim Multimixer-156 is \(2^{-156}\) -universal and provide concrete arguments supporting our claim. This small universality is achieved at an expense of efficiency and we treat the interesting security/efficiency trade-off in the paper. We compare the efficiency of our implementation of Multimixer-156 with the NH hash function family and Multimixer-128, other keyed hash functions based on integer multiplication that are \(2^{-128}\) -universal and \(2^{-127}\) -universal respectively, and also with the two fastest NIST LWC candidates on ARMv7 architecture. While Multimixer-156 is slower than the keyed hash functions, it is significantly faster than the other candidates.