3C- A Provably Secure Pseudorandom Function and Message Authentication Code.A New mode of operation for Cryptographic Hash Function

We propose a new cryptographic construction called 3C, which works as a pseudorandom function (PRF), message authentication code (MAC) and cryptographic hash function. The 3Cconstruction is obtained by modifying the Merkle-Damg̊ard iterated construction used to construct iterated hash functions. We assume that the compression functions of Merkle-Damg̊ard iterated construction realize a family of fixed-length-input pseudorandom functions (FI-PRFs). A concrete security analysis for the family of 3Cvariable-length-input pseudorandom functions (VI-PRFs) is provided in a precise and quantitative manner. The 3CVI-PRF is then used to realize the 3CMAC construction called one-key NMAC (O-NMAC). O-NMAC is a more efficient variant of NMAC and HMAC in the applications where key changes frequently and the key cannot be cached. The 3C-construction works as a new mode of hash function operation for the hash functions based on Merkle-Damg̊ard construction such as MD5 and SHA-1. The generic 3Chash function is more resistant against the recent differential multi-block collision attacks than the Merkle-Damg̊ard hash functions and the extension attacks do not work on the 3Chash function. The 3C-X hash function is the simplest and efficient variant of the generic 3C hash function and it is the simplest modification to the Merkle-Damg̊ard hash function that one can achieve. We provide the security analysis for the functions 3C and 3C-X against multi-block collision attacks and generic attacks on hash functions. We combine the wide-pipe hash function with the 3C hash function for even better security against some generic attacks and differential attacks. The 3C-construction has all these features at the expense of one extra iteration of the compression function over the Merkle-Damg̊ard construction.