Zot-Binary: A New Number System And Its Application On Number Theory Based Public-Key Cryptography

• Main Author: Jahani, Shahram
• Format: Thesis
• Language: English
• Published: 2016
• Subjects: QA75.5-76.95 Electronic computers. Computer science
• Online Access: http://eprints.usm.my/31685/1/SHAHRAM_JAHANI_24.pdf; http://eprints.usm.my/31685/

Kriptosistem Kunci Awam telah digunakan secara meluas dalam protokol seperti pengurusan kekunci, pengesahan, penyulitan kekunci, dan lain-lain. Teori Nombor yang berasaskan Kriptosistem Kunci Awam adalah salah satu cabang utama dalam sistem Kriptografi Kunci Awam. Dua operasi utama dalam Teori Nombor berasaskan Kriptografi Kunci Awam adalah pendaraban dan nombor besar. Antara contoh kriptosistem yang terkenal yang mendapat manfaat daripada operasi ini ialah enkripsi dan dekripsi RSA, tandatangan digital EIGamal, dan pertukaran kunci Diffie-Hellman. Prestasi kriptografi primitif ini sangat bergantung pada kecekapan kedua-dua operasi tersebut. Adalah menjadi sesuatu kebiasaan untuk melakukan penambahbaikan terhadap kecekapan pendaraban dan pengeksponen melalui penggunaan kaedah pengekodan semula atau penggunaan sistem nombor bagi mengurangkan ukuran berat Hamming. ZOT adalah kaedah pengekodan semula yang terkini bagi mengurangkan ukuran berat Hamming. Tetapi, oleh kerana ZOT bukan berasaskan sistem kedudukan nombor, maka kos perlaksanaannya adalah tinggi. Public-key cryptosystems are widely used in protocols such as key agreement, authentication, encryption; etc. Number theory based Public-key cryptosystems are one of the main branches in public-key cryptosystems. The two main operations in number theory based public-key cryptography are large number multiplication and exponentiation. For RSA encryption and decryption, ElGamal digital signature and Diffie-Hellman key exchange are some of the well-known example of these cryptosystems which benefit from these operations. The performance of these cryptographic primitives is highly dependent on the efficiency of these operations. Improving the efficiency of multiplication and exponentiation through the use of a recoding method or utilizing a number system which can decrease the Hamming weight of numbers is very common. ZOT recoding method is one of the latest recoding methods used to decrease the Hamming weight of numbers. However, since it is not positional number systems its cost is high.