The algorithm is completely analogous to Diffie-Hellman key exchange in that you efficiently raise a number to a power times and send the result over while keeping as private key.
The only difference is that a different group is used: instead of using the cyclic group, we use the elliptic curve group of an elliptic curve over a finite field.
Video 1.
Elliptic curves by Computerphile (2018)
Source. youtu.be/NF1pwjL9-DE?t=143 shows the continuous group well, but then fails to explain the discrete part.
Delft OpenCourseWare by Ciro Santilli 37 Updated 2025-07-16
They have a lot of stuff, well done.
CC BY-NC-SA by default unfortunately, but what can you do...
One of the most beautiful things is how they paywall even public domain works. E.g. here: www.nature.com/articles/119558a0 was published in 1927, and is therefore in the public domain as of 2023. But it is of course just paywalled as usual throughout 2023. There is zero incentive for them to open anything up.
Video 1.
What they don't tell you about academic publishing by Andy Stapleton (2021)
Source.
Video 2.
The publishing scandal happening right now by Andy Stapleton (2023)
. Source. TOOD get the name of the academic who quit.
Freedom of speech by Ciro Santilli 37 Updated 2025-07-16
Ciro has the radical opinion that absolute freedom of speech must be guaranteed by law for anyone to talk about absolutely anything, anonymously if they wish, with the exception only of copyright-related infringement.
And Ciro believes that there should be no age restriction of access to any information.
People should be only be punished for actions that they actually do in the real world. Not even purportedly planning those actions must be punished. Access and ability to publish information must be completely and totally free.
If you don't like someone, you should just block them, or start your own campaign to prepare a counter for whatever it is that they are want to do.
This freedom does not need to apply to citizens and organizations of other countries, only to citizens of the country in question, since foreign governments can create influence campaigns to affect the rights of your citizens. More info at: cirosantilli.com/china-dictatorship/mark-government-controlled-social-media
Limiting foreign influence therefore requires some kind of nationality check, which could harm anonymity. But Ciro believes that almost certainly such checks can be carried out in anonymous blockchain consensus based mechanisms. Governments would issues nationality tokens, and tokens are used for anonymous confirmations of rights in a way that only the token owner, not even the government, can determine who used the token. E.g. something a bit like what Monero does. Rights could be checked on a once per account basis, or yearly basis, so transaction costs should not be a big issue. Maybe expensive proof-of-work systems can be completely bypassed to the existence of this central token authority?
Some people believe that freedom of speech means "freedom of speech that I agree with". Those people should move to China or some other dictatorship.
As mentioned at the prize was claimed at 8d31992805518fd62daa3bdd2a5c4fd2cd3054c9b3dca1d78055e9528cff6adc (2017-02-23) which spends several inputs with the same unlock script that presents two different constantants that have the same SHA-1:
printf 255044462d312e330a25e2e3cfd30a0a0a312030206f626a0a3c3c2f57696474682032203020522f4865696768742033203020522f547970652034203020522f537562747970652035203020522f46696c7465722036203020522f436f6c6f7253706163652037203020522f4c656e6774682038203020522f42697473506572436f6d706f6e656e7420383e3e0a73747265616d0affd8fffe00245348412d3120697320646561642121212121852fec092339759c39b1a1c63c4c97e1fffe017f46dc93a6b67e013b029aaa1db2560b45ca67d688c7f84b8c4c791fe02b3df614f86db1690901c56b45c1530afedfb76038e972722fe7ad728f0e4904e046c230570fe9d41398abe12ef5bc942be33542a4802d98b5d70f2a332ec37fac3514e74ddc0f2cc1a874cd0c78305a21566461309789606bd0bf3f98cda8044629a1 | xxd -r -p | sha1sum
printf 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 | xxd -r -p | sha1sum
both giving
f92d74e3874587aaf443d1db961d4e26dde13e9c
It was claimed on the same day that Google disclosed the collision: security.googleblog.com/2017/02/announcing-first-sha1-collision.html
Both of these are PDF prefixes, so they start with the PDF file signature, but are not fully viewable PDFs on their own.
Protesters were posting large chunks of text multiple times into the blockchain as a way to protest against the controversial increase of block size.
tx 08893442680a20c4d0548dec2c8c421fa43336528b4e274dbf2652774f9c9f2d has the first copy of:
I like big blocks and I can not lie
which is the first line of a parody on:
I like big butts and I cannot lie
from the Baby Got Back hip-hop song.
tx 52159222289cd0a5afe0644150d0e23d5d272a57365627d5e869fdb458289858 has the first copy of:
Time to roll out bigger blocks
which is likely a copy of an email from the bitcoin development mailing list. This message is repeated dozens of times in other transactions.
Saint Seiya by Ciro Santilli 37 Updated 2025-07-16
This was THE craze thing in Brazil before Pokemon, it was shown from 1994 to 1997. In particular the collectible action figures! It was possibly more popular in Brazil than e.g. in the US: www.quora.com/Why-was-Saint-Seiya-so-popular-in-Brazil
The thing as quite violent, rated for 14-year olds, but no one gave a fuck, 7 yo Ciro was happily watching it. We protect children too much.
That series also had quite a religious feel to it (as obviously suggested by the series English name itself). It must also have been a great motivator to getting young kids into astronomy!
Ciro's favorite character was definitely Andromeda Shun. He was smart and thoughtful, and had the coolest most complex weapon: his chain whips. He's also a bit effeminate, with his pink clothing and a gentle way. Perhaps that is the reason for adult Ciro's mild fascination with the Andromeda Galaxy.
The English name is horrendous... the Portuguese/French name is so much better: Knights of the Zodiac! Saying this in English just reminded Ciro Santilli of the Zodiac Killer. But nevermind.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact