The book, “Elliptic Curves and Crypto Safety” offers a comprehensive mathematical  exploration of the mathematical foundations of blockchain technology and its connection to elliptic curves.
The book is organized into five chapters, each focusing on a specific topic. In Chapter 1 we introduce group theory. For various groups we investigate the properties, subgroups and classes.
Chapter 2 delves into modular arithmetic, covering number theory, modular arithmetic, rings, fields, polynomials, and concepts like Euler’s theorem. We also touch upon the Riemann zeta function and divisor sum.
In Chapter 3 we turn our attention to elliptic curves. We start by examining rational points on a circle and progress to exploring elliptic curves, their arithmetic, torsion, torsion lines, and rational points. We also delve into modular counting on elliptic curves.
Chapter 4 builds upon the previous chapter, focusing on modular elliptic curves. We explore modular counting on specific elliptic curves.
Finally, in Chapter 5, we dive into the world of cryptography. We consider fundamental concepts, discuss number bases, and explore Bitcoin ECDSA, hash functions, blockchain technology and mining.
“Elliptic Curves and Crypto Safety” serves as a comprehensive resource for those seeking a deeper understanding of the mathematical aspects behind blockchain technology.

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