The book, “Bitcoin, Blockchain, and Elliptic Curvesâ€ť offers a comprehensive mathematical exploration of the mathematical foundations of Bitcoin, blockchain technology, and their 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, mining, and even delve into Bitcoin rates.

“Bitcoin, Blockchain, and Elliptic Curves” serves as a comprehensive resource for those seeking a deeper understanding of the mathematical aspects behind Bitcoin and blockchain technology.

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