Cryptography

Cryptocurrency transactions can be tracked from point to point because all transaction data is public. The transaction data needs to be public to ensure the financial integrity of the system, which is non-negotiable. So, given that we cannot get rid of transparency, how do we achieve privacy? In Bitcoin, one way to achieve privacy is through Coinjoins. Many users come together, add their own coins as inputs to a specific large transaction, get equivalent coins as outputs on the other side of the same large transaction, and confirm this transaction on the blockchain. If enough users participate in such coinjoins frequently, every user gets a measure of privacy about where their coins came from, or where their coins went. The problem is – if these users don’t know each other, they need a central coordinator to build this large transaction. To make the central coordinator as trustless as possible, coinjoin protocols use blind signatures. ...

BIP-32 is a Bitcoin Improvement Proposal that allows Alice to start with a single private key, and generate a series of private and public keys from it, where the public keys can be generated independently from the private keys. This is not as easy as it sounds, because in most public key crypto-systems, you can generate a public key only if you have the private key in hand. BIP-32 uses a nifty little crypto-trick to generate public keys without having access to their corresponding private keys, and the trick is rather simple, once you know it. ...

If Zero Knowledge Proofs are the kind of magic seen in a full fledged opera theater, Homomorphisms in Cryptography are like intimate card tricks done in a 1-1 setting. Less grand, less machinery at work, but elegant and counter-intuitive all the same. You hear about homomorphism in encryption first. They also appear in commitment schemes – and given my interest in Bitcoin, homomorphic commitments more appropriate for this blog. But let’s see encryption first, as it’s a bit more accessible. ...

This article is ostensibly about why the challenge space in an interactive zero knowledge proof has to be large. Understanding this rather obscure theoretical aspect of zero knowledge proofs is quite rewarding intellectually. I promise. Let me start with a trivial question. How do you convince yourself that something happened before something else? Here’re some possible answers. You literally see Event-X happen. You wait for a bit. You then literally see Event-Y happen. You know that X happened before Y because you saw it yourself. You are convinced because you trust your memory of what you have seen. Sometimes, things are physically structured such that Y cannot happen before X. Let’s say I see you wearing socks and shoes, you could not have worn shoes before wearing socks. Someone you trust tells you that Event-X happened before Event-Y and you believe them. These are so intuitive that you don’t bother to reflect on this till someone specifically asks you this question. In fact, the 2nd example is used in many magic tricks – you expect a certain order because of obvious structure, but the magician circumvents that order to enthrall you with his magic. One such trick is where the magician pretends to cut an unpeeled banana with an imaginary knife, and then peels the banana to reveal a precise cut in the same location on the inner fruit. The magic works because it belies the natural order of events that you are used to. ...

What is power, really? Power comes about when someone has the ability to destroy someone else’s accumulated capital. What is capital, then? Capital Capital comes about as a result of raw materials, labour, and time. A healthy body, stored grains, a house to live in, a bank account with money earned through a job, or any sort of owned property – all of that is capital. Capital comes about as a combination of raw materials, labour, and time. Capital can either be consumed directly by its owner, or can be exchanged for other things like the labour of others. ...

“Zero Knowledge”, contrary to what it sounds like, is actually quite interesting and fun. It might even be a solution to our long standing problem of validating the world’s transactions without a trusted third party or government or central bank. If you Google for the terms Zero Knowledge and Blockchains, you will be flooded with whitepapers, articles, explainers, investment advice, and everything in between. What does Zero Knowledge (ZK) even mean? Let me start with a toy example, and then we can work our way up to world peace. ...