On the Security of NMAC and Its Variants

We first propose a general equivalent key recovery attack to a H-MAC variant NMAC1, which is also provable secure, by applying a generalized birthday attack. Our result shows that NMAC1, even instantiated with a secure Merkle-Damg̊ard hash function, is not secure. We further show that this equivalent key recovery attack to NMAC1 is also applicable to NMAC for recovering the equivalent inner key of NMAC, in a related key setting. We propose and analyze a series of NMAC variants with different secret approaches and key distributions, we find that a variant NMAC-E, with secret envelop approach, can withstand most of the known attacks in this paper. However, all variants including NMAC itself, are vulnerable to on-line birthday attack for verifiable forgery. Hence, the underlying cryptographic hash functions, based on Merkle-Damg̊ard construction, should be re-evaluated seriously.