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29th January 2023 > > Cryptography part 1.

tl;dr

Some concepts of cryptography part 1.


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BTC spent two months in a very tight trading range anchored with a 16-handle until the breakout earlier this month. Now a week into low volatility with a much healthier 23-handle, my optimism for an ever-improving macro environment - economically and politically - in 2023 has yet to be tested.


Curious Cryptos’ Commentary — Let’s talk cryptography part 1!

Starting with a disclaimer, the last time I studied maths was just before the summer of 1985. I am a touch rusty on some of the concepts and terminology, but I do hope those of you who are more knowledgeable forgive my indiscretions. My objective in this series of articles is simply to give some conceptual flavour to cryptography as I understand it. I doubt that what I say is entirely intellectually rigorous.


SHA-256 is an algorithm that uses 2^256 possibilities for creating a private key.


Allegedly, you could express this number as this:


115 quattuorvigintillion 792 trevigintillion 89 duovigintillion 237 unvigintillion 316 vigintillion 195 novemdecillion 423 octodecillion 570 septendecillion 985 sexdecillion 8 quindecillion 687 quattuordecillion 907 tredecillion 853 duodecillion 269 undecillion 984 decillion 665 nonillion 640 octillion 564 septillion 39 sextillion 457 quintillion 584 quadrillion 7 trillion 913 billion 129 million 639 thousand 936.


Which I think we can all agree is an uncommon phrase in general parlance.


Does it help to describe it as 1.1 with 77 zeros after it? That is, 1.1 x 10^77?


Probably not.


So, a comparison or two is in order.


The number of grains of sand on the Earth is estimated – and undoubtedly with a reasonable margin of error – at 7.5 x 10^18, which is such a tiny, small, insignificant number relative to our private key algorithm.


The upper boundary of stars in the “observable” universe - a concept which still blows my mind (*) – is estimated at 1 x 10^24 which might not seem on the face of it to be that much smaller than our algo but trust me, it is.


In fact, the number of possible private keys used for the current encryption for BTC, and other cryptos, lies at the lower bound for the estimate of the number of atoms in the Universe.


That is such an unfeasibly large number that it is simply impossible that two private keys are ever created to be the same.


This by the way is the reason why quantum computing does not threaten cryptos.


If the technology to stabilise quantum computers at the level of being able to create all possible private keys, or even a significant subset, within a reasonable timespan (let’s say our lifetimes) ever came to pass, then AI as the dominant force is already in existence, and our communal fate would no longer rest upon the success or otherwise of the crypto revolution.


But odd things do happen in cryptos.


A research paper explored the possibilities of recreating private keys.


A tall task one would think, given the plethora of private key possibilities.


In a moment of madness, or perhaps genius, they used this private key:


0x0000000000000000000000000000000000000000000000000000000000000001

to generate this public key:


0x7e5f4552091a69125d5dfcb7b8c2659029395bdf.


What is quite extraordinary is that if you put this public key into etherscan ( https://etherscan.io/address/0x7e5f4552091a69125d5dfcb7b8c2659029395bdf) there are – at the time of writing – 3,097 transactions dating from 3 days ago all the way back to more than 6 years ago.


Immediately any ETH is transferred into this wallet, it is moved on again.


Transfers have come in from many unidentified wallets but also Coinbase, OKX, Kraken, and KuCoin, all of which are centralised cryptocurrency exchanges.


Strange happenings. Strange times.


(*) The observable universe is estimated at 46 billion light years across even though the Big Bang happened less than 14 billion years ago. This phenomenon relies upon an appreciation that the Big Bang happened at all points of the Universe simultaneously whilst also being a singularity, but I am not sure that helps.


Much, or indeed probably most, of the Universe is beyond our ken as it lies too far away for light to ever reach us - Hubble expansion prevents that from happening. Yes, objects can move away from us faster than the speed of light, or indeed multiples of it, another concept which if contemplated for too long can also cause your head to hurt.


Fortunately for us, the expansion effect seems only to impact bodies whose size is equal or greater to that of galaxies. One might cuss at the mess caused by dropping a glass on the floor, but we do have a lot to thank gravity for.

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