A Miniature CCA2 Public key Encryption scheme based on non-Abelian factorization problems in Lie Groups

TL;DR

This paper introduces a new public key encryption scheme based on non-Abelian factorization problems in Lie groups, leveraging exponential mapping and intractable assumptions, and proves its IND-CCA2 security.

Contribution

It presents a novel cryptosystem based on Lie group theory and non-Abelian factorization problems, with formal security proof in the random oracle model.

Findings

Proposes a secure encryption scheme based on Lie groups.

Establishes new intractable assumptions related to exponential mapping.

Proves IND-CCA2 security in the random oracle model.

Abstract

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.