Key-agreement based on automaton groups

We suggest several automaton groups as key-agreement platforms for Anshl-Anshel-Goldfeld metascheme, they include Grigorchuk and universal Grigorchuk groups, Hanoi 3-Towers group, Basilica group and a subgroup of the affine group with the unsolvable conjugacy proble

Cryptography with right-angled Artin groups

In this paper we propose right-angled Artin groups as a platform for secret sharingschemes based on the efficiency (linear time) of the word problem. Inspired by previous work of Grigoriev-Shpilrain in the context of graphs, we de ne two new problems: SubgroupIsomorphism Problem and Group Homomorphism Problem. Based on them, we also proposetwo new authentication schemes. For right-angled Artin groups, the Group Homomorphismand Graph Homomorphism problems are equivalent, and the later is known to be NP-complete.In the case of the Subgroup Isomorphism problem, we bring some results due to Bridson whoshows there are right-angled Artin groups in which this problem is unsolvable.Professional Staff Congress-City University of New YorkCity Tech FoundationOffice of Naval ResearchEuropean Research CouncilNational Science FoundationMinisterio de Ciencia e Innovació

Cryptography with right-angled Artin groups

In this paper we propose right-angled Artin groups as a platform for secret sharingschemes based on the efficiency (linear time) of the word problem. Inspired by previous work of Grigoriev-Shpilrain in the context of graphs, we de ne two new problems: SubgroupIsomorphism Problem and Group Homomorphism Problem. Based on them, we also proposetwo new authentication schemes. For right-angled Artin groups, the Group Homomorphismand Graph Homomorphism problems are equivalent, and the later is known to be NP-complete.In the case of the Subgroup Isomorphism problem, we bring some results due to Bridson whoshows there are right-angled Artin groups in which this problem is unsolvable.Professional Staff Congress-City University of New YorkCity Tech FoundationOffice of Naval ResearchEuropean Research CouncilNational Science FoundationMinisterio de Ciencia e Innovació

Attacking a public key cryptosystem based on tree replacement

We point out several security flaws in the cryptosystem based on tree replacement systems proposed by Samuel, Thomas, Abisha and Subramanian at INDOCRYPT 2002. Due to the success of (among others) very simple ciphertext-only attacks, we evidence that this system does not, in its present form, offer acceptable security guarantees for cryptographic applications.Work partially supported by projects BFM2001-3239-C03-01 and BFM2001-1284