Research On The Application Of Weighted SN P Systems With Rules On Synapses In Breaking RSA Encryption

RSA(Rivest-Shamir-Adleman)algorithm is the most representative public key encryption algorithm.How to break RSA encryption has always been a hotspot in research.Based on the difficulty of large integers factorization,it is very difficult to crack RSA encryption,so it is also a research difficulty.Factorizing large integers is the most commonly used way for researchers to break RSA encryption,but it is difficult to solve this problem by using general computational models.In this thesis,a biological computing model — Spiking Neural P(SN P)system is used to factorize large integers to study the way of breaking RSA encryption in theory for the first time.Firstly,the operational performance of an extended model of SN P systems — The Weighted Spiking Neural P Systems with Rules on Synapses(RWSN P)is analyzed in this thesis.The RWSN P systems that perform the addition and the multiplication are compared with the systems constructed by the basic SN P systems,reducing the number of neurons effectively.And the RWSN P systems are applied to solve the greatest common divisor based on modularization.The greatest common divisor is the basis of many complex applications,and applying the SN P systems to realize its solution process has not been studied by the predecessors.The above description shows that in addition to the distributed parallel architecture of the basic SN P system,this SN P system variant can also make the operation more flexible,simplify the system structure,and reduce the number of neurons.It can also be extended to other complex areas.So RWSN P systems have better operational performance.Based on these characteristics,the RWSN P systems are used as the computation model in this thesis.The implementation of general operations lays the foundation for the application of RWSN P systems to realize RSA encryption breaking.Secondly,in this thesis,a RWSN P system for the RSA encryption breaking is constructed based on the idea of factorizing large integers,and the implementation process of each sub-module in the system is analyzed in detail,which are input module,random number module,multiplication module,comparison module and output module.Since the number of neurons is massive,within the allowable range of computing power of the SN P systems,the parallel structure of the SN P systems is used in the system constructed above,and enough factorization modules are set to be worked in parallel,so that the probability of successful factorization is approached to 1.The factoring modules working in parallel are used to test each set of possible prime factors as much as possible to find out the prime factors that make the product of them equal to the given large integer.After the system output,the RSA encryption is broken successfully.Finally,through analysis and comparison,the RWSN P systems constructed in this thesis can theoretically break RSA encryption in a linear time,which is effective and efficient.