杂凑函数在数字签名、消息认证、完整性校验和数字财产保护等信息安全领域应用广泛。Keccak杂凑函数是SHA-3竞赛的获胜算法，并于2015年正式成为美国国家标准技术研究所（NIST）第三代安全杂凑函数标准SHA-3。本项目以SHA-3及相关方案为目标，从密钥恢复攻击(带密钥模式下)、原像攻击、差分攻击和碰撞攻击的角度开展安全性分析。具体地，1）发展Keccak基于立方攻击的密钥恢复技术，研究Keccak团队提出的FSKD公开问题——如何利用全状态自由度提升立方攻击；2）研究基于低次非线性方程系统的原像攻击；3）开发Keccak置换差分路径并行搜索工具并改进碰撞攻击。通过本项目的研究，我们旨在进一步推进SHA-3及相关方案的安全性分析，提出若干有影响力的分析结果，并根据我们的研究深入认识基于大置换的类SHA-3设计。

Hash functions are widely used in digital signatures, message authentications, integrity verifications, digital asset protection and other fields of information security. The Keccak hash function is the winner of the SHA-3 competition and became the Secure Hash Algorithm standard SHA-3 of the National Institute of Standards and Technology of the U.S. (NIST) in 2015. This project studies SHA-3 and its relatives and carries out cryptanalysis on them with key recovery attacks (under keyed modes), preimage attacks, differential attacks and collision attacks. Specifically, we are to 1) develop techniques for cube attacks to recover the key of Keccak under keyed modes, work on the FSKD open problem---how to extend cube attacks by exploiting full-state degree of freedom; 2) study preimage attacks by solving systems of low degree non-linear equations; 3) build a new tool for searching differential paths of Keccak using parallel programming and improve collision attacks. Through this project, we aim to push the cryptanalysis of SHA-3 and its relatives one step further by providing some influential results, and learn in deep the SHA-3-like designs based on large permutations.