INTT Algorithm by Hand As seen in the previous article, the Inverse Number Theoretic Transform (INTT) is performed using a Vandermonde matrix, just like the NTT. This shows that both evaluation via...

Proof that the Inverse of a Vandermonde Matrix Is Another Vandermonde Matrix In the previous chapter on the Inverse Number Theoretic Transform, we claimed that the inverse of the Vandermonde matrix...

The Inverse Number Theoretic Transform In the previous chapters, we studied the Number Theoretic Transform (NTT), which evaluates a polynomial at its $k$-th roots of unity. It can be understood as...

Orthogonality of Roots of Unity The sum of powers of the $k$-th roots of unity generated by a primitive $k$-th root of unity is either zero or $k$. We call this property the orthogonality of roots of...

Solana Syscalls: Logging in sBPF Assembly In the previous tutorial, we learned how a program reads from memory into the sBPF VM registers. Now, we’ll build on that model by showing how programs...

Reading Solana Instruction inputs using sBPF assembly In the previous tutorial, we introduced the sBPF memory layout and explained the purpose of each register during program execution. In this...

sBPF Memory Layout and Register Conventions This tutorial introduces the Solana BPF (sBPF) memory layout and the roles of its virtual machine registers. We'll demonstrate the conventions for how...

Instruction Processor and Runtime Setup In part one, we covered the Solana program input serialization format and how program inputs are laid out in memory. In this part, we'll cover how programs...

Solana Program Execution and Input Serialization This article explains how the BPF loader serializes program instruction inputs, how the entrypoint receives them, and how programs deserialize that...

Rust program to SBF compilation Understanding how Rust compiles to SBF (Solana Bytecode Format) and how validators execute it is crucial for building complex Solana programs. This article explains...

Tracing SBF Instruction Execution and Compute Costs In the previous article, we covered the sBPF VM architecture, register conventions, and the instruction set. Now we'll analyze actual bytecode...

Organizing a Solana Program Solana programs don’t enforce a particular codebase structure, so code organization often depends on the developer’s preference and program complexity. In fact, a Solana...