Coding Theory, Cryptography, and Finite Fields: Technology and Applications

Coding Theory, Cryptography, and Finite Fields explores the theory and applications of finite fields, from basic concepts such as the modular arithmetic and polynomial interpolation to advanced topics such construction and counting of polynomials. This book: Addresses a wide range of topics within coding theory, cryptography, and finite fields, offering a holistic understanding of these interconnected fields. Discusses cutting-edge subjects such as quantum cryptography and multimedia security, making it relevant to current and future technological advancements. Explores polynomials over finite fields and their applications in coding theory and cryptography to enhance the reader's understanding of the mathematical foundations critical to these areas. Emphasizes real-world applications of theoretical concepts, particularly in error correction, data security, and encryption algorithms. Explains critical challenges in protecting multimedia data, offering cutting-edge techniques for securing images, videos, and audio files against unauthorized access and piracy. The text is primarily written for senior undergraduates, graduate students, and academic researchers in electrical engineering, electronics and communications engineering, computer science and engineering, and information technology.