A New Secure Encryption Scheme Based on Group Factorization Problem

Abstract

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$PGM$ </tex-math></inline-formula> and public key cryptosystems like <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$MST_{1}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$MST_{2}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$MST_{3}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$eMST_{3}$ </tex-math></inline-formula> . 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$MST$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$eMST_{3}$ </tex-math></inline-formula> , our scheme is simplified with more efficiency.