Generic Related-Key Attacks for HMAC

In this article we describe new generic distinguishing and forgery attacks in the related-key scenario (using only a single relatedkey) for the HMAC construction. When HMAC uses a k-bit key, outputs an n-bit MAC, and is instantiated with an l-bit inner iterative hash function processing m-bit message blocks where m = k, our distinguishing-R attack requires about 2(n/2) queries which improves over the currently best known generic attack complexity 2(l/2) as soon as l > n. This means that contrary to the general belief, using wide-pipe hash functions as internal primitive will not increase the overall security of HMAC in the related-key model when the key size is equal to the message block size. We also present generic related-key distinguishing-H, internal state recovery and forgery attacks. Our method is new and elegant, and uses a simple cyclesize detection criterion. The issue in the HMAC construction (not present in the NMAC construction) comes from the non-independence of the two inner hash layers and we provide a simple patch in order to avoid this generic attack. Our work finally shows that the choice of the opad and ipad constants value in HMAC is important.