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The day has come.
Enter a thread on isogenies, random walks and automorphism groups.
🧵👇
(0/n)
I will explain some of the background we used to write these papers with Ben Smith, so I encourage you to go read them. There are some results at the end of the thread
The main objects in isogeny-based cryptography are elliptic curves and isogenies, usually defined over finite fields. And, of course, isogeny graphs.
(2/n)
You might want to read about elliptic curves
First of all, an isogeny is a nonconstant morphism of elliptic curves fixing the point at infinity.
So it is a group morphism, a morphism of algebraic curves, it is surjective, and it has finite kernel.
Enter a thread on isogenies, random walks and automorphism groups.
🧵👇
(0/n)
I will explain some of the background we used to write these papers with Ben Smith, so I encourage you to go read them. There are some results at the end of the thread
My first two papers are out in the arXiv! I'm very thrilled about them \U0001f604 pic.twitter.com/Az9gODokH9
— Enric Florit (@enricflorit) January 5, 2021
The main objects in isogeny-based cryptography are elliptic curves and isogenies, usually defined over finite fields. And, of course, isogeny graphs.
(2/n)
You might want to read about elliptic curves
\U0001f369 elliptic curves thread \U0001f369
— \u2133 \u2606\xb0\u30df (@computer_dream) December 31, 2020
Disclaimer: this thread is not meant to be technical but rather a bunch of facts I find beautiful about elliptic curves. I hope you can find them beautiful as well.
If you want to learn more about this, read Silverman's Arithmetic of Elliptic Curves!
First of all, an isogeny is a nonconstant morphism of elliptic curves fixing the point at infinity.
So it is a group morphism, a morphism of algebraic curves, it is surjective, and it has finite kernel.
To those saying that those who have got their public health advice wrong earlier in the pandemic should put up their hands and apologise... a little cautionary lesson from another sector
A short 🧵
1/
Public health is not my thing
But Brexit is
And throughout 2019 and 2020 I have been trying to make predictions as to what will happen in that story. Lives do not depend on this, only my professional reputation (marginally) does
2/12
The three series of #BrexitDiagram I made in 2019 were extraordinarily accurate
Series 1/2
https://t.co/wOSzIXxJ2M
Series 3
https://t.co/E4fKeGoa5n
Series 4
https://t.co/yRsQ8mLGj1
Each series got that stage of Brexit right
3/12
The 2020 series was nowhere near as good - at one stage I had No Deal Brexit at 78% chance in early December - and that was not what
I own this error - I was wrong
I know *why* I was wrong - I thought the European Parliament would fight more on Provisional Application, and I thought agreeing everything in a week wouldn't work. I wasn't right
The Manston crisis / borders closing changed something too
5/12
A short 🧵
1/
Public health is not my thing
But Brexit is
And throughout 2019 and 2020 I have been trying to make predictions as to what will happen in that story. Lives do not depend on this, only my professional reputation (marginally) does
2/12
The three series of #BrexitDiagram I made in 2019 were extraordinarily accurate
Series 1/2
https://t.co/wOSzIXxJ2M
Series 3
https://t.co/E4fKeGoa5n
Series 4
https://t.co/yRsQ8mLGj1
Each series got that stage of Brexit right
3/12
The 2020 series was nowhere near as good - at one stage I had No Deal Brexit at 78% chance in early December - and that was not what
I own this error - I was wrong
I know *why* I was wrong - I thought the European Parliament would fight more on Provisional Application, and I thought agreeing everything in a week wouldn't work. I wasn't right
The Manston crisis / borders closing changed something too
5/12
Now a £35M cap, a fortnight on
It's one of those small UK if-it-were-listed-in-the-US companies. Bidstack #BIDS and it puts advertising into major online games
It's rocketing - and there are some grounds to think that in quite short order it may be about to turn into a firework
"May" and also:
- history of over promising and disappointing
- very much a AIM small cap
- burns cash
- will place and dilute
- has share price on homepage
- Glassdoor is not great
- emoji issues when discussed
*But* it may now be delivering for real. If so it may also be extremely cheap. How cheap?
20H1 was 2x sequentially and 10x YoY
It may be about to report H1-H2 sequential growth of 5x.
If so, FY20: 10x YoY.
Fwd 21 rev multiple? Perhaps half that number, perhaps even less.
I need to explain in some detail what they do because it's necessary to understand it to gauge not only the opportunity but also the risk - and also to be able to translate aspects of what the company put out in their releases. The juicy stuff comes after.
As simply as I can: Bidstack provide a SDK (software developer kit) to games companies: so far Sega and Codemasters
The SDK allows companies to create areas in their games where adverts can be placed by Bidstack.
The ads appear within the fabric of the game, natively
It's one of those small UK if-it-were-listed-in-the-US companies. Bidstack #BIDS and it puts advertising into major online games
It's rocketing - and there are some grounds to think that in quite short order it may be about to turn into a firework
Not Boku and not for widows & orphans but looking around here, it has the kind of following where rival factions of the warmer kind of bulletin board gang members gun each other down on twitter with rocket emojis but if the Swedes or Americans discover it, can it stay a \xa322M cap? https://t.co/Fa2r6JgTTq
— HRouge (@hareng_rouge) December 17, 2020
"May" and also:
- history of over promising and disappointing
- very much a AIM small cap
- burns cash
- will place and dilute
- has share price on homepage
- Glassdoor is not great
- emoji issues when discussed
*But* it may now be delivering for real. If so it may also be extremely cheap. How cheap?
20H1 was 2x sequentially and 10x YoY
It may be about to report H1-H2 sequential growth of 5x.
If so, FY20: 10x YoY.
Fwd 21 rev multiple? Perhaps half that number, perhaps even less.
I need to explain in some detail what they do because it's necessary to understand it to gauge not only the opportunity but also the risk - and also to be able to translate aspects of what the company put out in their releases. The juicy stuff comes after.
As simply as I can: Bidstack provide a SDK (software developer kit) to games companies: so far Sega and Codemasters
The SDK allows companies to create areas in their games where adverts can be placed by Bidstack.
The ads appear within the fabric of the game, natively
Lot of teachers are back at their computers this morning, facing the task of engaging young people online for the next few weeks. I'm definitely no expert, just been teaching my university students online since September and I've picked up a few tips if they are any use to you👇
Online teaching gives you the opportunity to easily pull in videos, music, images in a way we might not have done had we been in the classroom. Google Classroom, Zoom, Skype all allow you to share your screen and break up your lesson every 15 minutes or so. Lean on your media
Always show your face on video. Students don't engage with just a voice in the ether. Create a home classroom with interesting pictures/posters in the background. God, these are tough times, but be animated and passionate about your subject if you can. Enthusiasm is infectious
One silver lining of this pandemic is that online teaching tools have exploded. Some are fabulous, such as Flipgrid - https://t.co/k55lt2Hi2d - which allow you to engage with young people on a social platform they can relate to. The app also has a Discovery Library. Amazing!
More 👇 It has also opened up a whole world of possibilities for our students here in NI, from helping with learning languages - https://t.co/geLpXa3Ptp - to using flashcards to help students with history on https://t.co/aFfMbsPUvG, the world is our oyster at the present time
Online teaching gives you the opportunity to easily pull in videos, music, images in a way we might not have done had we been in the classroom. Google Classroom, Zoom, Skype all allow you to share your screen and break up your lesson every 15 minutes or so. Lean on your media
Always show your face on video. Students don't engage with just a voice in the ether. Create a home classroom with interesting pictures/posters in the background. God, these are tough times, but be animated and passionate about your subject if you can. Enthusiasm is infectious
One silver lining of this pandemic is that online teaching tools have exploded. Some are fabulous, such as Flipgrid - https://t.co/k55lt2Hi2d - which allow you to engage with young people on a social platform they can relate to. The app also has a Discovery Library. Amazing!
More 👇 It has also opened up a whole world of possibilities for our students here in NI, from helping with learning languages - https://t.co/geLpXa3Ptp - to using flashcards to help students with history on https://t.co/aFfMbsPUvG, the world is our oyster at the present time