This post explores the group structure in the Tate pairing. I explain the terms embedding degree, torsion groups, twists and multiplicative group in the context of the Reduced Tate Pairing for BN Elliptic Curves.
Extension Fields Some time ago, I started a series on the algebraic structure behind ZK-Snarks. My focus was to explain why the group elements in the pairing libraries are represented the way they are. In the previous posts, I introduced groups, fields, elliptic curves and the general structure of pairings. In this post, I expand …
ZK Snarks and Their Algebraic Structure – Part 4 Read More »
ZK-Snarks would not be possible without the use of bilinear pairings. In my series about their algebraic structure for beginners, I cover pairings in this post, after groups, fields and elliptic curves.
I give an explanation of what they are and how to operate with them, along with a simple example very famous in cryptography.
Elliptic Curves Previously I started peeling away at the different components that make a cryptographic pairing. I talked about the general structure, and then gave a basic introduction to groups and fields. Today I pick up at that point and take you to the next step: elliptic curves. So let’s up the game a bit. …
ZK Snarks and Their Algebraic Structure – Part 2 Read More »
ZK-SNARKs are complex and hard to understand. For the most part, one can use them without knowing the mathematical details underlying them. Unless, that is, if you are developing your own ZK-SNARK solution.
This is the first in a series of posts about the internals of ZK-SNARKs and elliptic curves. Stay tuned for more.
Ethereum Digital Signatures Digital Signatures Details of ECDSA Signatures ECRecover and Signature Verification in Ethereum ECDSA Malleability As seen in the previous post of this series, a signature scheme usually has a verification algorithm that computes directly over the public key and the signature to check if the latter is valid. Ethereum is different, and …
ECRecover and Signature Verification in Ethereum Read More »
Ethereum Digital Signatures Digital Signatures Details of ECDSA Signatures ECRecover and Signature Verification in Ethereum ECDSA Malleability In the previous post in this series, I introduced the concept of Digital Signatures. In this article, I give an outline of ECDSA, the signature algorithm that is used to secure the Bitcoin and Ethereum blockchains. This is …
Ethereum Digital Signatures Digital Signatures Details of ECDSA Signatures ECRecover and Signature Verification in Ethereum ECDSA Malleability If you are a cryptographer, the concept of Digital Signature will be as familiar to you as wooden blocks are to a toddler. If you are a developer, and you’ve done any work requiring some sort of authentication, …
In this post, I start a new series about zk-SNARKs, and explore where they might not be the best choice for your use case. Despite their popularity, they’re not a one-size-fits-all solution, and developers should be aware of where they could be advantageously replaced by other technologies.
My interest in ZK Snarks began at work, when I took the task to investigate this technology and implement a prototype that could later evolve into a product.
This post is the first of a series chronicling our progress in that exploration, and the difficulties we found.
