Cryptanalysis of the Shpilrain-Ushakov Protocol in Thompson's Group

基于有限域上一元仿射映射的Cayley哈希函数的密码分析

Cryptanalysis of a Cayley Hash Function Based on Affine Maps in one Variable over a Finite Field

本文分析基于有限域上一元仿射映射的Cayley哈希函数，证明Ghaffari和Mostaghim方案不安全，通过构造碰撞揭示其漏洞。

Cryptanalysis of three matrix-based key establishment protocols

We cryptanalyse a matrix-based key transport protocol due to Baumslag, Camps, Fine, Rosenberger and Xu from 2006. We also cryptanalyse two recently proposed matrix-based key agreement protocols, due to Habeeb, Kahrobaei and Shpilrain, and due to Romanczuk and Ustimenko.

Length-based cryptanalysis: The case of Thompson's Group

The length-based approach is a heuristic for solving randomly generated equations in groups which possess a reasonably behaved length function. We describe several improvements of the previously suggested length-based algorithms, that make them applicable to Thompson's group with significant success rates. In particular, this shows that the Shpilrain-Ushakov public key cryptosystem based on Thompson's group is insecure, and suggests that no practical public key cryptosystem based on this group can be secure.

公钥密码学中的群的子集

Subsets of groups in public-key cryptography

本文提出在公钥密码学中使用代数子集替代子群，给出了Shpilrain和Ushakov两个协议的子集版本及示例，分析了其对长度和距离攻击的抵抗力，并引出了若干新的群论问题。

Polynomial-time solutions of computational problems in noncommutative-algebraic cryptography

We introduce the \emph{linear centralizer method}, and use it to devise a provable polynomial time solution of the Commutator Key Exchange Problem, the computational problem on which, in the passive adversary model, the security of the Anshel--Anshel--Goldfeld 1999 \emph{Commutator} key exchange protocol is based. We also apply this method to the computational problem underlying the \emph{Centralizer} key exchange protocol, introduced by Shpilrain and Ushakov in 2006. This is the first provable polynomial time cryptanalysis of the Commutator key exchange protocol, hitherto the most important k…