Some NTRU-like cryptosystems and their comparisons

This thesis consists of five chapters. The first chapter presents introductory information concerning the mathematically hard problems underlying public-key cryptosystems and the current status of existing cryptographic systems in the face of quantum computing. The second chapter provides references to the existing literature on the NTRU cryptosystem—which holds a prominent place in quantum cryptography—as well as to several NTRU-like cryptosystems that have been developed subsequently. In the third chapter, some fundamental notions related to polynomial rings, lattice theory, and the mathematically hard problems within this theory—such as the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP), which underpin the security of NTRU and related cryptosystems—are explained. In the fourth chapter, the processes of key generation, encryption, and decryption in the NTRU cryptosystem are demonstrated by encrypting and decrypting a concrete message using a key generated through appropriate parameter selection based on theoretical foundations. Additionally, several NTRU-like cryptosystems such as MaTRU, CTRU, DTRU, ETRU and QTRU are examined in detail. The fifth chapter offers a comparative discussion evaluating the security and efficiency of the NTRU cryptosystem against quantum attacks, in comparison with other NTRU-like cryptosystems addressed in the study.