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Magic Internet Math

Elliptic Curve Cryptography: A Self-Study Guide

By Brian HIrschfield and Rob Hamilton

Aired Feb 16, 2026 · 1h 55m · Last boosted Aug 10, 2026

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Show Notes

The Study guide: https://ecc-study-guide.magicinternetmath.com/guide.pdf In this episode of Magic Internet Math, Rob and Fundamentals discuss the math behind Bitcoin's security, exploring elliptic curve cryptography, modulo arithmetic, and digital signatures. Key Topics: Seed-Phrase Generation Elliptic Curve Cryptography Modulo Arithmetic Securing Bitcoin with Math The Importance of Primes Understanding Finite Fields LibSecP and Its Significance Quantum Computing Deterministic Nonces Summary: The conversation begins with an overview of how Bitcoin secures money, moving from helpful abstractions like seed phrases to the foundational math involving finite fields and elliptic curves...

Nostr Boost Stats

sats
7.5k
boosts
5
boosters
5

Nostr Community

Everyone who has boosted Elliptic Curve Cryptography: A Self-Study Guide on Nostr, ranked by sats sent, all time.

  1. Ape Mithrandir 3.2k sats
  2. UsedToReadALot 2k sats
  3. Boomer 1k sats
  4. Stack Jarrow 1k sats
  5. godsdeth (dr4kdr0u) 237 sats
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Apr 10, 2026
Nostr Boosts:12k
Stack_JarrowApr 10, 2026
10k
Pod keeping it real discussion wise in the #40HPW space. A bitcoin podcast episode that isn’t really a Bitcoin podcast episode. Signal here for being bullish on life! Definitely some real value here.
Stack_JarrowApr 10, 2026
1k
2 @npub1z9hy7a0n8… at 18 min left on the pod
1.2k
Thank you gentlemen
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Apr 26, 2026
The 49th Parallel4 - Union
Nostr Stats:2 boosters4 boosts
Nostr Boosts:10k
BoomerApr 30, 2026
2.1k
Let's get this to #10 on the Fountain Hot Episode Charts... @npub1unmftuzmk… , have you listened yet?
BoomerApr 28, 2026
2.1k
Thanks for all the great feedback. I could talk to Luke all day... about anything.
Stack_JarrowApr 27, 2026
1k
Based discussion here
BoomerApr 26, 2026
5k
"You trust Bitcoin, and she trusts you."
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Jul 29, 2025
UNGOVERNABLERagnarök
Nostr Stats:2 boosters3 boosts
Nostr Boosts:10k
237
To pay or not to pay... My credit card bills?
2.4k
Thank you gentleman. This is a must listen.
Ape MithrandirJul 29, 2025
7.8k
Somehow, I don't think Bitcoin fixes this.
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Jul 15, 2025
Nostr Boosts:8.8k
Stack_JarrowJul 16, 2025
1k
I heard a reflection of myself in the discussion about "lone wolf mentality" and it has led me to Bitcoin, NOSTR, and the Ungovernable Misfits. I've noticed a lot of the victim mentality echoing in the Bitcoin sphere, particularly in podcasts and social media, mentioning blame on centralized banks, inflation, Cantillonaires, and so on. But I think the real issue lies with people's time preferences and their craving for convenience, which the system facilitates more easily. This UGMF podcast was incredibly high in signal, and the segment about the person leading by example and working hard to be better than others, daring to show up 100% was truly inspiring. It's something to mirror oneself after, as it shows the transformation from a lone wolf to becoming part of a team.
Ape MithrandirJul 16, 2025
7.8k
Joel is the Ben Gunn I can understand. So many well spoken points were made. The anarchists will not organize, it's a matter of principle.
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Feb 20, 2025
Nostr Boosts:8.8k
Ape MithrandirMar 9, 2025
7.8k
All you need now are some Scots to join the conversation for us Yanks to get even more lost.
Stack_JarrowFeb 20, 2025
1k
If making your own lightning node do you use sats from a KYC or non KYC stack for the liquidity portion you deposit or at that point does it not matter?
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Jan 30, 2025
Nostr Boosts:8.3k
Ape MithrandirMar 11, 2025
7.8k
∀ n ∈ N, ∃ p1​, p2​,…, pk​ ∈ P, ∃ e1​, e2​,…, ek​ ∈ N such that n=p1^e1​​ x p2^e2​​ x ⋯ x pk^ek​​ Where: N is the set of natural numbers. P is the set of prime numbers. p1​,p2​,…,pk​ are distinct prime numbers. e1​,e2​,…,ek​ are the respective powers (non-negative integers) of those primes.
537
Thank you gentlemen. Can you have slides in the thumb nail on fountain showing equations and such as you go thru the epp? Visuals would help me understand a great deal more. Great work
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Jan 23, 2025
Nostr Boosts:8.3k
Ape MithrandirMar 10, 2025
7.8k
Gary needs to lower his time preference and stop jumping ahead, he doesn't even know his homomorphisms from his isomorphisms!
537
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Jan 14, 2025
Nostr Boosts:8.3k
Ape MithrandirMar 9, 2025
7.8k
Wolfram Mathworld was a great resource for us budding self taught mathematicians back in the day.
537
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Nostr Boosts:8k
Ape MithrandirAug 31, 2025
7.8k
5 min in and pausing to boost. You can show using number theory that continued fraction expansions offer the best rational approximations of irrational numbers in terms of increasing numerators and denominators. The first few fractions in the continued fraction expansion of pi are: 3, 22/7, 333/106, 355/113, 103993/33102, 104348/33215, ... To me 355/113 is the most interesting fraction in this list. Using numbers less than 1000 you get an approximation that is accurate to the order of 10^-7. Also it is 11 33 55 split in two, so easy to remember.
237
Thank you gentlemen
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Mar 17, 2025
Nostr Boosts:8k
Ape MithrandirMar 30, 2025
7.8k
🤯
237
Thank you gentleman
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Nostr Boosts:8k
Ape MithrandirMar 17, 2025
7.8k
∀n ∈ ℕ, prove (21n + 4) / (14n + 3) is irreducible. Proof: gcd(21n + 4, 14n + 3) = gcd(2(21n + 4), 3(14n + 3)) = gcd(42n + 8, 42n + 9) = gcd(42n + 8, 1) = 1 ∴ (21n + 4) / (14n + 3) is irreducible. QED
237
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Nostr Boosts:26k
Ape MithrandirDec 20, 2024
7.8k
Epic rant at the end. Craig Raw always worth listening to.
Ape MithrandirDec 19, 2024
18k
(Craig Raw)'s feature request for Broadcast Pool is much needed and we should get more eyes on it. https://github.com/bitcoin/bitcoin/issues/30471
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Jul 28, 2026
Nostr Boosts:7.2k
UsedToReadALotJul 31, 2026
5k
First turning fuel, let's go ⛽
2.2k
Thank you gentlemen
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Jul 13, 2025
Nostr Boosts:7.2k
Stack_JarrowJul 13, 2025
250
First time listening to this early morning. Gives old school radio talk show vibes sort of like the Bob & Tom show. Fun to listen to for sure
7k
Thank you gentlemen
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Jul 20, 2026
Nostr Boosts:7.1k
UsedToReadALotJul 22, 2026
5k
Always a pleasure 🍻
Stack_JarrowJul 21, 2026
2.1k
Kimi K3
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Jun 28, 2026
Nostr Boosts:7.1k
Stack_JarrowJun 30, 2026
2.1k
Weed vs. meditation🤔
BoomerJun 29, 2026
5k
Is this the definitive "weed/leadership" #Bitcoin podcast? @npub1z9hy7a0n8… @npub17934d3gls… @npub1563z6kxmv… @npub153xmex42x… ❤️ J
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Jun 13, 2026
Nostr Boosts:6.2k
1.2k
Thank you gentlemen
BoomerJun 14, 2026
5k
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BoomerJun 8, 2026
5k
Absolutely loved this one. This was my Bitcoin Podcast of the week. Fundy kept it short, with a bunch haymakers on the mindset of Bitcoin/economics. @npub1kqrddzzl6…
1.2k
Thank you sir
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May 31, 2026
Nostr Boosts:6.2k
BoomerJun 7, 2026
5k
I'm boosting for @npub1z9hy7a0n8… . He's the absolute best in the world at making thumbnails. He does ALL the editing and behind the scenes stuff. And he's paying for all the software. He's the absolute best.
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Oct 17, 2024
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Ape MithrandirOct 20, 2024
78k
WHY IS NOT PAYING OUT BOUNTY #9 TO ? Currently, there is a bounty for a FROST Multisig Wallet implementation in the amount of 1 BTC. Stack Wallet started work, in September 2023, on a FROST multisig wallet implementation and has had a compliant version in their app since February of this year. They applied for the bounty and it has been 8 months with no decision from HRF.
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Dec 26, 2024
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Ape MithrandirDec 27, 2024
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Tell us how much you hate KYC Bitcoin, for the new Bitcoiners who only know how to buy Bitcoin with their IDs!
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Jun 8, 2026
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Thank you again gentlemen
Stack_JarrowJun 9, 2026
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@npub12eml5kmtr… you’re offering a great reality check in the noise of plebslop! What you’re doing is so important right now!! It’s such a great perspective to hear you talk to younger guys like SlyGoomba who’re crashing out or who were all in and putting their lives on hault to stack sats hard AF. The self resentment that becomes apparent during bear cycles when we went all in and what do we have to show for it.. this episode is a good reminder to love that version of ourselves that went all in.
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Stack_JarrowAug 23, 2026
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Inflation narrative is the one to make Bitcoin rise the most quickly… paradoxical we want the price to go up but that generally speaking means that much more inflation has taken place so the want for it to stay at 60K forever is better for everyone… trippy stuff!!!
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Jul 20, 2026
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Stack_JarrowJul 20, 2026
2.1k
2.2k
Thank you gentlemen
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2.2k
Thank you gentlemen
Stack_JarrowJul 1, 2026
2.1k
I like the signal of the end of the bear market being Saylor selling a large chunk of coin. And I’m trying to get in the mindset of this crabwalking downhill market from October last year taking much longer than anticipated. Much like fundamental’s saying that the fiat regime is gonna take a lot longer than we expect to “end the fed” just some pleb trinket the Mary like everything else.
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Jan 1, 2025
Nostr Boosts:18k
Ape MithrandirJan 4, 2025
18k
Forgive me while I shill another Podcast! Citadel Dispatch EP 5 with Max Tannahill and Diverter_NoKYC! We should have Max and Diverter on again! https://fountain.fm/episode/EdngmpelDhHiJAkJ0yFM
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Dec 25, 2024
Nostr Boosts:18k
Ape MithrandirDec 27, 2024
18k
Tell us how much you hate KYC Bitcoin, for the new Bitcoiners who only know how to buy Bitcoin with their IDs!
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Dec 5, 2024
Nostr Boosts:18k
Ape MithrandirDec 11, 2024
18k
As you watch the Bitcoin Price Moon and enjoy your Sats in self-custody, spare a thought for Samourai and TDev, still awaiting trial. Once the US Gov takes down self-custodial privacy tools, they will come for self-custody in general. Get your donation to P2P Rights Samourai Legal Defense Matched by Anon BWEST. Navigate to: https://p2prights.org/donate.html Enter BWEST in any field on the form. Allocate 100% to Samourai Wallet legal defense.
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Nostr Boosts:18k
Ape MithrandirDec 11, 2024
18k
#freesamourai
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Dec 11, 2024
Nostr Boosts:18k
Ape MithrandirDec 11, 2024
18k
#freesamourai
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Episode Boosts

Every boost sent to this episode, as published to Nostr, newest first.

  • 2,000 via Fountain
    I worried I wasn't ready for this before, but it's very accessible so far. Thank you
  • 3,246 via Fountain
    I had to slow down to 1x for some parts here. Well done guys.
  • 1,000 via Fountain
    Great stuff from @Brian Hirschfield & @Rob Hamilton . Bear markets are the time for building, and I bet that 99.9% of Bitcoiners (me included) would benefit from building their knowledge of how the mathematics of #Bitcoin really work. The guys do a great job at making the content easy to follow (although I will have to listen to this one a second time). And check out "Magic Internet Math" on YouTube!
  • 1,000 via Fountain
    Journey down the rabbit hole begins.. Bitcoin is about hype but one must find for themselves beyond the confirmation bias that “well yeah the tech does what people say it does”