Length-Based Attacks for Certain Group Based Encryption Rewriting Systems
James Hughes, Allen Tannenbaum
Abstract
In this note, we describe a probabilistic attack on public key cryptosystems based on the word/conjugacy problems for finitely presented groups of the type proposed recently by Anshel, Anshel and Goldfeld. In such a scheme, one makes use of the property that in the given group the word problem has a polynomial time solution, while the conjugacy problem has no known polynomial solution. An example is the braid group from topology in which the word problem is solvable in polynomial time while the only known solutions to the conjugacy problem are exponential. The attack in this paper is based on having a canonical representative of each string relative to which a length function may be computed. Hence the term length attack. Such canonical representatives are known to exist for the braid group.
Create a lesson
Related papers
Bilateral Protection for Private LoRA Inference with Intel TDX
Xiaodong Li, Mingyuan Ma, Dongbo Yan
Can Benign Skills Induce Misaligned Behavior in LLM Agents?
Xuanye Zhang, Yongsen Zheng, Kaiyu Zhou et al.
The Native Menace: Host-to-Browser Cross-Boundary Attacks via Native Messaging
Jyotirmay Chauhan, Rownak Islam, Jason Polakis
When Debate Amplifies Risk: Social-Bias Vulnerabilities in Multi-Agent Safety Deliberation
Qinghua Mao, Xi Lin, Yuxin Qi et al.
VerfGraph: Efficient Zero-Knowledge Verifiable Graph Query Evaluation System
Tianyi Ma, Yuncong Zhang, Yuanzhuo Yu et al.
ScrambleMark: Zero-Query Watermark-Agnostic Black-Box Evasion of Modern Speech Watermarking
Binhao Ma, Weikang Ding, Hanqing Guo et al.