Bilinear Pairings in Python, Solidity, and the EVM Sometimes also called bilinear mappings, bilinear pairings allow us to take three numbers, $a$, $b$, and $c$, where $ab = c$, encrypt them to become...

Groth16 Explained The Groth16 algorithm enables a quadratic arithmetic program to be computed by a prover over elliptic curve points derived in a trusted setup, and quickly checked by a verifier. It...

Solidity Mutation Testing Mutation testing is a method to check the quality of the test suite by intentionally introducing bugs into the code and ensuring the tests catch the bug. The kind of bugs...

Ethereum precompiled contracts Ethereum precompiles behave like smart contracts built into the Ethereum protocol. The nine precompiles live in addresses 0x01 to 0x09. The utility of precompiles falls...

The second preimage attack for Merkle Trees in Solidity The _second preimage attack_ in Merkle trees can happen when an intermediate node in a Merkle tree is presented as a leaf. The name of this...

ERC20 Snapshot ERC20 Snapshot solves the problem of double voting. If votes are weighed by the number of tokens someone holds, then a malicious actor can use their tokens to vote, then transfer the...

Solidity Gasleft Introduction The purpose of this article is to describe the behavior of the Solidity function and its uses. It is a built-in function that is used to check the remaining gas during a...

What makes blockchain immutable? Note: This article is intended to be understandable by non-technical readers, to gain a very technical understanding, refer to our blockchain bootcamp after reading...

EIP-150 and the 63/64 Rule for Gas Introduction EIP-150, or Ethereum Improvement Proposal 150, is a protocol upgrade for the Ethereum blockchain. It was proposed on March 18, 2016, and implemented on...

Solidity Events Solidity events are the closest thing to a or statement in Ethereum. We will explain how they work, best practices for events, and go into a lot of technical details often omitted in...