A Miniature CCA2 Public key Encryption scheme based on non-Abelian factorization problems in Lie Groups
This addresses the need for new cryptographic schemes with potential applications in secure communications, though it appears to be an incremental adaptation of existing methods to a new mathematical framework.
The authors tackled the problem of designing secure public key encryption by proposing a novel cryptosystem based on non-Abelian factorization problems in Lie groups, which was proven to be IND-CCA2 secure in the random oracle model.
Since 1870s, scientists have been taking deep insight into Lie groups and Lie algebras. With the development of Lie theory, Lie groups have got profound significance in many branches of mathematics and physics. In Lie theory, exponential mapping between Lie groups and Lie algebras plays a crucial role. Exponential mapping is the mechanism for passing information from Lie algebras to Lie groups. Since many computations are performed much more easily by employing Lie algebras, exponential mapping is indispensable while studying Lie groups. In this paper, we first put forward a novel idea of designing cryptosystem based on Lie groups and Lie algebras. Besides, combing with discrete logarithm problem(DLP) and factorization problem(FP), we propose some new intractable assumptions based on exponential mapping. Moreover, in analog with Boyen's sceme(AsiaCrypt 2007), we disign a public key encryption scheme based on non-Abelian factorization problems in Lie Groups. Finally, our proposal is proved to be IND-CCA2 secure in the random oracle model.