We define new families of Tillich-Z\'emor hash functions, using higher dimensional special linear groups over finite fields as platforms. The Cayley graphs of these groups combine fast mixing properties and high girth, which together give rise to good preimage and collision resistance of the corresponding hash functions. We justify the claim that the resulting hash functions are post-quantum secure.

翻译：我们定义了Tillich- ⁇'emor 散列函数的新组, 使用高维特殊线性组作为平台, 这些组群的凯利图形结合了快速混合特性和高亮度, 共同导致相应的散列函数具有良好的预感和碰撞阻力。 我们有理由认为, 由此产生的散列函数在数量后是安全的。