# Bitcoin’s signing algorithm: Elliptic Curves with Finite fields

Notes and analysis from Programming Bitcoin by Jimmy Song

This is post will cover the material in chapter 3. Also be sure to check out parts 1 and 2.

In the previous post we described the Elliptic curve group as a continuous curve over the real numbers. We defined a way to generate points from other points using a geometrical method we called “point addition”. There is still one more operation we will need for cryptographic purposes.

Scalar multiplication

This operation is defined using repeated point addition. Recall that adding distinct points requires finding a third collinear point whereas adding…

# Bitcoin’s signing algorithm: Intro to the Elliptic Curve Group

## Notes and analysis from Programming Bitcoin by Jimmy Song

This is post will cover the material in chapter 2.

In part one that we created a field, which I said was similar to a number system because it has two closed operations over its elements. This chapter is about a different kind of algebraic structure, called a group. Groups have only addition and subtraction, so no multiplication or division.

This post will introduce the elliptic curve group over the real numbers, E(ℝ). Technically the group works over any field. …

# Bitcoin’s signing algorithm: Intro to Finite Fields

## Notes and analysis from Programming Bitcoin by Jimmy Song

This is my first post in a continuing series for people interested in Bitcoin at a software-design level such as a software engineer, mathematician or network security professional. The post will cover the material in chapter 1.

As an aspiring contributor to the Bitcoin open source project I have read many books and articles previously, including the terrific Mastering Bitcoin by Andreas Antonopoulos. Despite this I still don’t know my way around the code base at all and the math behind the crypto is not at all clear to me. …

## Eric Price

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