Analog Bitcoin Mining with Pen, Paper and Math

bitcoins

Der Krypto-Algorithmus SHA-256 zur Berechnung der benötigten Hash-Werte ist anscheinend simpel genug, um den mit Bleistift auf Papier auszurechnen. Analog schafft man einen kompletten Hash in grob 17 Minuten, das sind rund 0,67 Hashes pro Tag. Aber: Nur einer von 100 Trillionen Hashes mined einen Bitcoin.

[Bitcoin-Mining] consists of repeatedly performing a cryptographic operation called hashing until an extremely rare hash value is found - one that begins with around 17 zeros. Only one out of 1.4x1020 hashes will be successful. […] One round of the algorithm takes 16 minutes, 45 seconds which works out to a hash rate of 0.67 hashes per day.

Man braucht also rund 200 Trillionen Tage, um einen Bitcoin analog zu errechnen, das sind rund 547 Billiarden Jahre. Zu diesem Zeitpunkt ist das Universum schon lange in seiner Degenerativen Phase angekommen und auf der Timeline of the very far Future passiert grade das hier:

Over time, objects in a galaxy exchange kinetic energy in a process called dynamical relaxation, making their velocity distribution approach the Maxwell–Boltzmann distribution. Dynamical relaxation can proceed either by close encounters of two stars or by less violent but more frequent distant encounters. In the case of a close encounter, two brown dwarfs or stellar remnants will pass close to each other. When this happens, the trajectories of the objects involved in the close encounter change slightly. After a large number of encounters, lighter objects tend to gain kinetic energy while the heavier objects lose it.

Because of dynamical relaxation, some objects will gain enough energy to reach galactic escape velocity and depart the galaxy, leaving behind a smaller, denser galaxy. Since encounters are more frequent in the denser galaxy, the process then accelerates. The end result is that most objects (90% to 99%) are ejected from the galaxy, leaving a small fraction (maybe 1% to 10%) which fall into the central supermassive black hole.

Derzeit hat 1 Bitcoin einen Wert von rund 300 Euro. Wenn also Herr Math-Nerd Ken Shirriff aus dem Video oben aus seinen ersten Bitcoin zusammen hat, kann er uns davon eine dicke Runde ausgeben, während wir alle zusammen den Zusammensturz der Welt im Restaurant am Ende des Universums betrachten und für eine anständtige Anschaffung auf Analog-Bitcoin-Basis braucht man wahrscheinlich drölfhundert Parallelwelten. I love this.

The SHA-256 algorithm is surprisingly simple, easy enough to do by hand. (The elliptic curve algorithm for signing Bitcoin transactions would be very painful to do by hand since it has lots of multiplication of 32-byte integers.) Doing one round of SHA-256 by hand took me 16 minutes, 45 seconds. At this rate, hashing a full Bitcoin block (128 rounds) would take 1.49 days, for a hash rate of 0.67 hashes per day (although I would probably get faster with practice). In comparison, current Bitcoin mining hardware does several terahashes per second, about a quintillion times faster than my manual hashing. Needless to say, manual Bitcoin mining is not at all practical.

A Reddit reader asked about my energy consumption. There's not much physical exertion, so assuming a resting metabolic rate of 1500kcal/day, manual hashing works out to almost 10 megajoules/hash. A typical energy consumption for mining hardware is 1000 megahashes/joule. So I'm less energy efficient by a factor of 10^16, or 10 quadrillion. The next question is the energy cost. A cheap source of food energy is donuts at $0.23 for 200 kcalories. Electricity here is $0.15/kilowatt-hour, which is cheaper by a factor of 6.7 - closer than I expected. Thus my energy cost per hash is about 67 quadrillion times that of mining hardware. It's clear I'm not going to make my fortune off manual mining, and I haven't even included the cost of all the paper and pencils I'll need.

Mining Bitcoin with pencil and paper: 0.67 hashes per day (via Algopop)