【摘要】 POSEIDON族杂凑函数定义在一个较大的有限素域上,包含POSEIDON和其优化版本POSEIDON2两类算法.算法均采用Sponge结构进行实例化,并基于HADES设计策略,安全界和迭代轮数由相关参数以及攻击的时间复杂度确定.本文首先发现设计者在使用Gr?bner基攻击POSEIDON和POSEIDON2的部分实例过程中,确定时间复杂度的安全界时建模方式存在问题,进而修订了安全界,并指出部分实例的安全冗余不够.其次,本文跳过SPN技术推广至Sponge结构,只引用1个变量,对两类算法构造了全轮的单变量多项式并以较小的时间复杂度对其求解,同时构造了次数为α的多变量多项式系统,进一步降低了Gr?bner基攻击的时间复杂度,可为POSEIDON族杂凑函数的参数选取提供理论指导.更多还原

【Abstract】 The POSEIDON family of hash functions includes POSEIDON and its optimized version POSEIDON2. Both algorithms are defined over a large prime finite field and are instantiated using the Sponge construction, based on the HADES design strategy, and their security bounds and round numbers are determined by related parameters as well as the time complexity of attacks. This study identifies issues in the polynomial modeling method utilized by designers to ascertain the time complexity of Gr?bner basis attacks for specific instances of POSEIDON and POSEIDON2. Subsequently,the security boundaries are re-evaluated, revealing that the security redundancy of certain instances is found to be inadequate. In addition, full rounds univariate polynomials are constructed for the two primitives to lower time complexity and the bypass SPN approach is applied to the Sponge structure,referencing only one variable. Additionally, a multivariate polynomials system is modelled with degreeα, which the time complexity of Gr?bner basis attacks is further decreased. As a consequence, the contributions provide theoretical guidance for parameter selection in the POSEIDON family of hash functions.更多还原