LEE- Bilgi Güvenliği Mühendisliği ve Kriptografi Lisansüstü Programı
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Konu "public key cryptosystems" ile LEE- Bilgi Güvenliği Mühendisliği ve Kriptografi Lisansüstü Programı'a göz atma
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ÖgeA new public key algorithm and complexity analysis(Graduate School, 2023-06-23) Çağlar, Selin ; Özdemir, Enver ; 707201029 ; Cybersecurity Engineering and CryptographyWith the development of technology, many processes have begun to digitize. As a result of this digitalization, digital communication has become inevitable in our lives. Digital communication is faster and easier to access than traditional communication methods. Especially with the Covid-19 pandemic, the contribution of digitalized processes to our daily life has been visibly felt. As a result of digitization, a lot of data belonging to different data classes has been transferred to the digital environment. The transfer of information to digital media has brought about a change in the methods of storing and using data. At this point, the importance of issues such as data privacy and security has increased and the concept of secure digital communication has come to the fore. Secure digital communication deals with the provision of cornerstones of security such as confidentiality, integrity, and authentication while transferring data over digital channels. Confidentiality is the process of preventing unauthorized parties from viewing sensitive data and ensuring that only those who have been given permission can do so. This can be achieved through data encryption, access controls, and secure channels. Integrity refers to the assurance that data remains unaltered and uncorrupted during transmission, storage, and processing, ensuring that the data can be trusted and relied upon. Techniques such as digital signatures and hash functions can be used to verify the integrity of data. Verifying a user's or a device's identity when they want to access data or services is referred to as authentication. This is typically achieved through the use of digital signatures, which are cryptographic techniques that provide a way to verify the authenticity of data by verifying the identity of the sender. Together, these three principles form the foundation of secure communication. When sharing data in a public environment, the data to be transferred must be protected. In other words, there is a need to ensure that the principle of confidentiality, which is the main starting point of this study, can be provided. Cryptography, which enables encryption structures, is used to ensure confidentiality. Symmetric key cryptography, which is more efficient in terms of key length and cryptographic operation and uses the same key in encryption and decryption processes, is widely used in encryption processes. In symmetric key cryptography, the party that encrypts and decrypts the data must use the same cryptographic key. Sharing of this cryptographic key must be done securely between the parties. Asymmetric key cryptography is used at the point of sharing the symmetric key, especially in processes that are established in a public environment and where there is no opportunity for the parties to directly share keys physically. Symmetric key cryptography is based on the use of a key pair consisting of a public and private key. A public key is a key that can be shared publicly with the parties used to send encrypted data. The private key, on the other hand, is the key used in decrypting the sent encrypted data, which the owner of the key pair must keep securely. Asymmetric key cryptography is used to provide confidentiality and authentication. The fact that it can also provide authentication is a factor that increases security in key exchange processes. After the parties verify each other cryptographically at the key exchange, asymmetric key cryptography provides an environment for sharing the symmetric key to be used to secure the communication. The RSA algorithm is one of the oldest and most widely used asymmetric key algorithms. The security of the algorithm is based on the difficulty of factoring integers. In the RSA algorithm, the public key modulus is equal to the product of two large prime numbers of the same size. Revealing these two prime numbers is enough to break the algorithm. At the same time, there is the possibility of returning the message without factoring from the encrypted data. This is called the RSA problem. Research studies have shown that there may be an easier way to return a message from encrypted data without factoring. If an effective method is developed for the RSA problem, the security of many RSA-based systems will be under threat. In this thesis, a new public key algorithm, which can be an alternative to the RSA algorithm, is proposed in the case of solving the RSA problem. This algorithm is based on the use of nodal curves and the group structure is different from the RSA algorithm. In the proposed algorithm, the discrete logarithm problem is thought to be harder, since the group structure in which the algorithm works is based on polynomial arithmetic and is also inspired by elliptic/hyperelliptic curves. At this point, it is assumed that the proposed new algorithm may be more durable to the problem in the RSA algorithm. At the same time, a new group operation algorithm, which is an addition algorithm, is presented by modification of the Mumford Representation and Cantor Algorithm in order to perform the group operation on the nodal curves. The performance comparison of the group operation presented on the nodal curves and the Cantor algorithm has been made. Compared to the Cantor algorithm, the presented new group operation was found to be more effective. In addition, the proposed algorithm has a probabilistic behavior. In other words, even if the data to be encrypted does not change, a structure is presented that can enable the encrypted data to be formed differently. The RSA algorithm has a deterministic behavior, additional padding is needed to produce different encrypted results from the same data. Since the proposed public key algorithm is based on polynomial arithmetic, there is no performance advantage compared to the RSA algorithm. We can state that there is a trade-off between security and performance. In order to show the practical applicability of the presented new solution, a performance comparison with the RSA algorithm has also been made. The performance problem is caused by the exponential increase in the secret key with the increase in the degree of the nodal curve used. In other words, it has been seen that the algorithm proposed in the decryption phase is slower than the RSA algorithm. However, since the decryption process in asymmetric key cryptography is generally not performed by individual users, it is thought that powerful servers will not be affected by this performance problem. During the tests, the SageMath library and the Python programming language were used.