Weisstannen-tal is a reasonably remote valley in Eastern Switzerland, but quite easy to access from the main A3- highway from Zürich to Chur. Not surprisingly, there is a bus-service from the Sargans station to get to the valley. The route I had planned was a “rundeweg”. I spend an unreasonable amount of time on SchweizMobil planning routes to hike. Weisstannen, being a stop on the Via Alpina official route – was bound to have some interesting routes starting from there. This is one such route that I made up ad-hoc, and suits my fitness level and fear of exposure (avoid blue-white trails). ...

I am fairly skeptical of AI-based chatbots. I have seen them hallucinate a non-existent paper once. I have been taken down useless rabbit holes. Or just to put it bluntly, they have never given me a “over-and-beyond-Google” moment. And then this happened. I was discussing the 8-queens problem with my sons (place 8 queens on a regular chess board so that no 2 queens attach each other) and I wanted to quickly generate a few solutions to show it to them. ...

I have found a new love: Abstract Strategy Games. I have spent an entire lifetime playing chess as a weak-ish amateur, reading books on its history, theory, openings, strategy, and having watched a gazillion hours of commentary online. Let me just say that chess has been a great friend over the years, in moments of solitude, in moments of kinship with family, and everything in between. It was obvious to me even as a kid, that chess was just one game in a family of such games – there was dots and boxes, tic-tac-toe, and other such “pen-and-paper” games. There was Chinese Checkers, Go, Othello, and other such games with boards and pieces. These games and others like them – abstract strategy games – share most of these traits. ...

Luna token’s hyperinflation was a thing to behold. On 05/May/2022, each Luna token was valued at ~$85 in markets where it was listed. On 11/May/2022, there were 377,000,000 Luna tokens in circulation. On 14/May/2022, there were 6,530,575,000,000 tokens in circulation. That’s a 1,700,000% inflation over a 72 hour period. How did that happen? Read Swan Bitcoin’s fascinating account of the episode, even drawing parallels with Soros’s attack on the Bank of England peg. ...

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. ...

No, this article is not about whether it’s Bitcoin’s moment to shine. It is a somewhat technical explainer on how Bitcoin implements time, or timestamps. First, we need to understand why Bitcoin needs a notion of time at all. If you don’t care for this, you can directly jump to the “How” section of the article below. The “Why” section of this article is somewhat opinionated. Why? Does money need timestamps? Bitcoin’s peers are a mixed bag when it comes to timestamping. ...

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. ...

Ken Thompson is a Turing Award winner and an all-around genius – gave a seminal talk during his 1984 Turing Award acceptance called “Reflections on Trusting Trust.” In this lecture, he shows how to sneak a Trojan horse into your application (in his case, the Unix operating system) while you compile the source code of the application using the C compiler. Say the C compiler has malicious code in it that patiently waits for pieces of code that look like Unix’s source code, and the moment it knows that it is compiling this particular source code, it adds the Trojan horse code into the final Unix compiled binary. This Unix binary now has a Trojan horse and is no longer secure. ...