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Math

A collection of 5 issues

Climbing the tower: field extensions

Introduction Finite fields are a central piece in every cryptography and zk-SNARKs. The most common finite fields appearing in practice are the fields with prime order $\mathbb F_p$. There are multiple ways of defining them. A usual one is seeing $\mathbb F_p$ as the set $$ \{0, 1, \cdots,

Weird ways to multiply really fast with Karatsuba, Toom–Cook and Fourier

Introduction The applicability and performance of algorithms depend on how fast certain routine computations can be done. For example, in elliptic curve cryptography, one needs to calculate the public key as $k\times g=g+g+g+....+g$, where $k$ is a very large integer (typically a number with a

Math Survival Kit for Developers

Introduction When working with cryptographic applications you need to understand some of the underlying math (at least, if you want to do things properly). For example, the RSA cryptographic system (which was one of the earliest methods and most widely adopted, until it lost ground to better methods, such as

What every developer needs to know about elliptic curves

Elliptic curves (EC) have become one of the most useful tools for modern cryptography. They were proposed in the 1980s and became widespread used after 2004. Its main advantage is that it offers smaller key sizes to attain the same level of security of other methods, resulting in smaller storage

A brief introduction to the beauty of Information Theory

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