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The Weierstrass normal form of elliptic curves (in fields with characteristic != 2 and != 3) $y^2 = x^3 + ax + b$ over the $Z_p$ field has found many applications in cryptography. But this curve form also has two types: non-singular (which can be used in crypto) and singular (which can’t). Let’s take a look at why singular curves cause problems ...

Recently, my team has been working mainly on launching the Linea L2 stack. It has been a long journey, starting with investigating the prover code with the aim of improving its performance and ending with launching the whole system. Here is a docker-compose example that can help any team launch their own L2. It also contains a brief overview of...

Definition 1 The set of all lines in three-dimensional space that pass through the origin is called the projective plane. Any line that passes through the origin and does not lie in the $XOY$ plane (i.e., $z \neq 0$) can be associated with a point $(x, y, 1)$. For a vector $l$ with coordinates $(X, Y, Z)$ where $Z \neq 0$, the corresponding poi...

A block cipher is an algorithm that performs encryption and decryption of plaintext in blocks (for example, 128-bit blocks). It’s obvious that to encode plaintext with a length different from the block size, we need a separate high-level module that will perform split and append operations on the plaintext, coupled with some other transformation...