Research On One Way Shell-Core Functions Based On Knapsack Problem

In the upcoming quantum era,due to the ultra-fast parallel computing and simulation capabilities of quantum computers,most of the public-key cryptography currently used are increasingly threatened by quantum computers,once the quantum computer is developed,these cryptosystems will be cracked quickly.On May 3,2017,the birth of China's photon quantum computer,pioneered by Professor Pan Jianwei at the University of Science and Technology of China,marks the China officially entered the ranks of quantum computer development.Therefore,it is imperative to develop a cryptosystem that can resist quantum computing.As far as we know,quantum computers are not very good at computing NPC problems,for this reason,constructing the cryptography based on NPC problems becomes the mainstream of quantum cryptography.However,knapsack problem is a typical NPC problem.Considering all the knapsack cryptosystems,we find that their common features are all based on the trapdoor one-way function,but due to the contradiction between unidirectional and trapdoor,the public-key cryptography based on the trapdoor one-way function has hidden security risks.The paper introduces the concept of “One Way Shell-Core Functions(OWSCFs)”,that is to use “One Shell and One Core” to disguise.The OWSCFs effectively solves the problem of boundary leakage in the trapdoor one-way function and enhances the security of the trapdoor,so the security of the public-key cryptography based on the OWSCFs is more higher.But at present,the researches on the OWSCFs are all biased towards hardware implementation,in order to explore the realization of the pure mathematics and make the public-key cryptography resist the quantum attack,the paper constructs the OWSCFs based on knapsack problem.This paper will focus on constructing OWSCFs based on knapsack problem,by using the idea of OWSCFs to realize asymmetric key exchange,a new method of constructing public-key cryptography is proposed,which is the public-key cryptography based on OWSCFs.In view of the difficulty of knapsack problem,designing and implementing OWSCFs and corresponding asymmetric key exchange,thus,a new knapsack cryptosystem can be obtained.The main job of this article as well as research results are as follows:1.According to the related literature,this paper explains the development of cryptography and the research progress of the knapsack cryptosystem at home and abroad,at the same time,the definition,theorem and security of knapsack cryptosystem are analyzed and proved.2.This paper analyzes a number of schemes of realizing key exchange by OWSCFs and gives the best key exchange scheme,that is KEP-SC.KEP-SC is the form of two shell functions,one of them can be shelling,the other can not be shelling.It can agree on the session key and effectively hide the boundary of the function so that the attacker will not be able to attack it.3.This paper constructs OWSCFs based on knapsack problem and gives the specific implementation of KEP-SC.Then,on account of the defects of the scheme,it proposes an optimized and improved key exchange scheme.4.On the basis of the KEP-SC scheme,this paper draws into “Half-Trapped One Way Functions” and changes the selection of shell function in the original scheme to form a new key exchange scheme,that is Half-KEP_SC.In view of “Half-Super Incrementing Knapsack Vector”,the paper constructs “Half-Trapped One Way Shell-Core Functions(Half-OWSCFs)” and gives the concrete implementation of Half-KEP_SC.