Lattice-based Cryptosystems Security And Functionality Enhancement

Cryptosystems can be used for many applications which are necessary in our digital world.This includes executing secure encryption and following to that decryption;Issuance and authentication of message signatures.Hash functions,symmetric or private key usages like stream ciphers and block ciphers are still widely used as a quick way for message encryption alongside more modern proposed asymmetric crypto like RSA(Rivest–Shamir–Adleman),DLP(Discrete Logarithm Problem)and ECC(Elliptic-Curve Cryptography)which are crucial for utilization in their own rights.In recent years some other terminologies like block-chain for usage in crypto-currencies,MPC(Multi-party computation),etc.have been innovated top fulfill the future demands of our society.Due to instantiation of quantum algorithms suggested prior to emerge of quantum computers in the coming years the aforementioned classic symmetric and asymmetric cryptosystems will lose their security against powerful quantum computation.New structures suggested by scientist like hashbased,code based and lattice based systems are designed to remain secure in PQC(Post Quantum Computing)era.In this study we first analyze both of first and second generations of Lattice based Cryptography.We point out how the classic sampling method which has been used conventionally suffers from active attack threats.Our comprehensive analysis shows that first generation systems lack enough security measures which put them dangerously under LLL(Lenstra–Lenstra–Lovász)dimension reduction attack.They also turn weak against new active attacks.On the other hand although second generation constructions provide better efficiency and security against active attacks,they still lack considerable security limitations caused by ineffective and simple method of sampling.Subsequently we managed to propose two new sampling algorithms named by APDF(Appointment of Probability Distribution Functions)and CPDF(Combination of Probability Distribution Functions)which can improve second generation systems dramatically compared to previous method.The core idea of Algorithm APDF is to fetch samples from arbitrary resources with aid of True Random Number Generator(TRNG)and Pseudo Random Number Generator(PRNG).Algorithm CPDF suggests the novel idea of combining numerous PDFs which has been exploited by the previous Algorithm APDF to increase the confusion against adversary and therefore make the system even more secure.We conducted simulations and mathematical analysis based on initial conjectures.The results demonstrate that Algorithms APDF and CPDF respectively improve efficiency and security in due course.Eventually we demonstrate that Algorithms APDF and CPDF can be easily applied for any proposed second generation Lattice based structure.