This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It is also shown that there is a remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory.

这本书是关于数学和理论计算机科学三个不同领域之间的关系：组合群论、密码学和复杂性理论。本文探讨了组合群论中典型的非交换（无限）群在公钥密码中的应用。研究还表明，密码学对组合群论有着显著的反馈作用，因为密码学引起的一些问题对群论来说似乎是新的，它们在群论中开辟了许多有趣的研究途径。