Random subgroups and analysis of the length-based and quotient attacks
| dc.creator | Myasnikov, Alexei G. | |
| dc.creator | Ushakov, Alexander | |
| dc.date | 2007-07-10 | |
| dc.date.accessioned | 2026-07-07T08:15:01Z | |
| dc.date.available | 2026-07-07T08:15:01Z | |
| dc.description | In this paper we discuss generic properties of "random subgroups" of a given group G. It turns out that in many groups G (even in most exotic of them) the random subgroups have a simple algebraic structure and they "sit" inside G in a very particular way. This gives a strong mathematical foundation for cryptanalysis of several group-based cryptosystems and indicates on how to chose "strong keys". To illustrate our technique we analyze the Anshel-Anshel-Goldfeld (AAG) cryptosystem and give a mathematical explanation of recent success of some heuristic length-based attacks on it. Furthermore, we design and analyze a new type of attacks, which we term the quotient attacks. Mathematical methods we develop here also indicate how one can try to choose "parameters" in AAG to foil the attacks. | |
| dc.identifier | https://arxiv.org/abs/0707.1501 | |
| dc.identifier | http://arxiv.org/abs/0707.1501 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133335 | |
| dc.subject | Group Theory | |
| dc.subject | Cryptography and Security | |
| dc.title | Random subgroups and analysis of the length-based and quotient attacks | |
| dc.type | text |