Articles

Sigma dance: commit, challenge, respond

Learn the fundamentals of Σ-protocols through the classic Schnorr protocol, exploring the three-step dance of commit, challenge, and respond. This post walks through knowledge soundness and witness extraction, then shows how to compose Sigma proofs with AND/OR logic and Pedersen commitments. See working SageMath implementations, discover how Fiat-Shamir transforms interactive proofs into non-interactive signatures, and understand the deeper mathematical structure as proofs of knowledge of homomorphism pre-images.

Stay in Range: Deeper Into Bulletproofs

This article breaks down how Bulletproofs enable range proofs: proofs that a hidden value lies within a range without revealing it. Starting from bit decomposition, it shows how to express and combine constraints into a single inner product, then make the proof zero-knowledge with blinding polynomials and commitments. By the end, you’ll understand how systems like Monero’s confidential transactions prove valid amounts while keeping values private.

Unfolding the Bulletproofs Magic

A SageMath Deep Dive

In this post, we dive deep into the Inner Product Argument (IPA), the mathematical core of Bulletproofs. Starting from simple vector folding, we build up to a full zero-knowledge proof with Pedersen commitments, explore how the mysterious `L` and `R` terms appear, and finish with smart verifier optimizations. All illustrated with clear, runnable SageMath code.

QuickSilver: Zero-Knowledge via VOLE and boolean circuits

How to build fast ZK proofs from MPC-friendly VOLE

VOLE: The engine behind modern MPC and ZK

From Oblivious Transfer to arithmetic correlations for secure computation

Oblivious Transfer: The cornerstone of MPC

From basics to extension

GKR: Sumcheck's best friend

Verifying Computations Layer by Layer

Sum-Check: The Backbone of ZK Proofs

Compressing Computation One Bit at a Time

FRI: Folding Polynomials and Catching Cheaters

Folding and Merkle trees, understand the magic behind STARKs

Reed-Solomon Codes: The Math Behind Error Correction and Zero-Knowledge Proofs

From QR codes to ZK, discover how Reed-Solomon codes correct errors and secure digital communication

Easy Sagemath setup

Using Sagemath's docker image

From 0 to Bi(ge)nius: field extensions

𝔽₂ and Beyond: A Gentle Guide to Field Extensions

Tornado Cash with Halo2

From theory to practice: implementing privacy

Open Source: adding a cheatcode to Foundry

Contributing to Ethereum's development toolkit

Solving the Ethernaut with Yul

Solve CTFs with low-level code

Open Source: Contributing to Foundry

How I contributed to Ethereum's development toolkit

Playing with Yul (Assembly)

Mastering low-level EVM programming