Please note: This is a companion version & not the original book. Book Preview:

#1 Finite Fields are a bit more difficult to understand than Trigonomotry, but they are not that difficult to learn. They are essential for understanding elliptic curve cryptography, which is essential for how signing and verification work in Bitcoin.

#2 A Finite Field is defined as a set of numbers and two operations + and ⋅ that satisfy the following: if a and b are in the set, a+b and a⋅b is in the set.

#3 A finite field is a set of numbers that behave like a traditional field, but have some differences in how we add, subtract, multiply, and divide. The field is defined by what’s in the set.

#4 The class FieldElement represents an element in a field Fprime. It is initialized with the value of the num property, and the prime property is initialized with the value of the prime property. The __eq__ method checks if two objects of class FieldElement are equal or not.

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Rafbók: 4 juni 2022