| Summary: | As special types of factorization of finite groups, logarithmic signatures and covers have been used as the main components of cryptographic keys for secret key cryptosystems such as PGM and public key cryptosystems like MST<sub>1</sub>, MST<sub>2</sub>, MST<sub>3</sub> and eMST<sub>3</sub>. In particular, as a natural analogue of integer factorization problem (IFP), group factorization problem (GFP) and its hardness assumption over certain factorization basis, referred as logarithmic signature, play a core role in the security arguments for the family of MST cryptosystems. Security is not the unique goal of designing a cryptosystem. Instead, efficiency is also a major issue. In this paper, we design a new secure encryption scheme based on group factorization problem (GFP). Furthermore, we present the security analysis and demonstrate the performance of our scheme. Comparing with eMST<sub>3</sub>, our scheme is simplified with more efficiency.
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