Algebraic aspects of cryptography

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This text serves as a course resource on cryptography, focusing on algebraic methods and designed for graduate or advanced undergraduate students, as well as scientists from other fields. The initial three chapters provide a self-contained introduction to fundamental concepts and techniques, using an intuitive and informal approach. For instance, Chapter 2 discusses computational complexity with a focus on its relevance to cryptography, despite lacking formal rigor. Chapters 4-6 and the Appendix introduce material that has not been widely available in textbooks, featuring three innovative types of cryptography: "hidden monomial" systems, combinatorial-algebraic systems, and hyperelliptic systems, which are still in early development. The practical utility of these cryptosystems remains uncertain, but exploring new one-way constructions from various mathematical areas is essential in the evolving field of cryptography. The book encourages readers to engage in ongoing research. It is not intended as a comprehensive reference but as a selective textbook, complete with numerous exercises (answers provided) to support math or computer science courses and independent study programs.