Public Key Encryption in Non-Abelian Groups
This work addresses cryptographic security in non-abelian groups, which is a domain-specific advancement for cryptography, but it appears incremental as it builds on existing techniques like FO.
The authors tackled the problem of constructing a public key encryption scheme in non-abelian Lie groups by introducing new intractability assumptions and using the FO technique, resulting in a CCA-secure scheme with a security proof based on the non-abelian inserting assumption.
In this paper, we propose a brand new public key encryption scheme in the Lie group that is a non-abelian group. In particular, we firstly investigate the intractability assumptions in the Lie group, including the non-abelian factoring assumption and non-abelian inserting assumption. After that, by using the FO technique, a CCA secure public key encryption scheme in the Lie group is proposed. At last, we present the security proof in the random oracle based on the non-abelian inserting assumption.