Hard and Easy Components of Collision Search in the Zémor-Tillich Hash Function: New Attacks and Reduced Variants with Equivalent Security

Abstract. The Zémor-Tillich hash function has remained unbroken since its introduction at CRYPTO’94. We present the first generic collision and preimage attacks against this function, in the sense that the attacks work for any parameters of the function. Their complexity is the cubic root of the birthday bound; for the parameters initially suggested by Tillich and Zémor they are very close to being practical. Our attacks exploit a separation of the collision problem into an easy and a hard component. We subsequently present two variants of the Zémor-Tillich hash function with essentially the same collision resistance but reduced outputs of 2n and n bits instead of the original 3n bits. Our second variant keeps only the hard component of the collision problem; for well-chosen parameters the best collision attack on it is the birthday attack.