Equivalent Key Recovery Attacks Against HMAC and NMAC with Whirlpool Reduced to 7 Rounds

A main contribution of this paper is an improved analysis against HMAC instantiating with reduced Whirlpool. It recovers equivalent keys, which are often denoted as Kin and Kout, of HMAC with 7-round Whirlpool, while the previous best attack can work only for 6 rounds. Our approach is applying the meet-in-the-middle (MITM) attack on AES to recover MAC keys of Whirlpool. Several techniques are proposed to bypass different attack scenarios between a block cipher and a MAC, e.g., the chosen plaintext model of the MITM attacks on AES cannot be used for HMAC-Whirlpool. Besides, a larger state size and different key schedule designs of Whirlpool leave us a lot of room to study. As a result, equivalent keys of HMAC with 7-round Whirlpool are recovered with a complexity of (Data,Time,Memory) = (2, 2, 2).