Podcasts about galois

En este programa, que coincidió con el Día Mundial del Teatro, os ofrecemos tres dramatizaciones de tres momentos importantes de la historia de la ciencia: escucharemos a Galileo Galilei conversar con Urbano VIII en el día en que se retractó de la teoría heliocéntrica, trataremos junto a Edmund Halley de usar los océanos para averiguar la edad de la Tierra y seguiremos a Évariste Galois en la noche más extraordinaria de la historia de las matemáticas. Para ello contaremos con el inigualable elenco actoral formado por Alberto Aparici, Santi García Cremades, Carlos Alsina y Begoña Gómez de la Fuente. Edmund Halley es un reincidente en esta sección: hablamos ya de él en el episodio s05e16, en el que explicamos que su mayor descubrimiento fue, en realidad, Isaac Newton. Este programa se emitió originalmente el 27 de marzo de 2025. Podéis escuchar el resto de audios de Más de Uno en la app de Onda Cero y en su web, ondacero.es

Nuestros científicos Santi García Cremades y Alberto Aparici, en honor al día Mundial del Teatro, van a explicar algunos episodios de la historia de la ciencia recreándolos. La primera escena trata de Galileo, cuando bajo amenaza de tortura, firmó que se había equivocado y que la Tierra no se movía. La segunda escena habla de Halley, el del cometa, que fue capaz de datar la edad de la Tierra gracias a la sal de los océanos. Terminamos con una escena de Galois, un hombre revolucionario que, antes de morir, anotó la clave para resolver ecuaciones matemáticas: el álgebra.

Nuestros científicos Santi García Cremades y Alberto Aparici, en honor al día Mundial del Teatro, van a explicar algunos episodios de la historia de la ciencia recreándolos. La primera escena trata de Galileo, cuando bajo amenaza de tortura, firmó que se había equivocado y que la Tierra no se movía. La segunda escena habla de Halley, el del cometa, que fue capaz de datar la edad de la Tierra gracias a la sal de los océanos. Terminamos con una escena de Galois, un hombre revolucionario que, antes de morir, anotó la clave para resolver ecuaciones matemáticas: el álgebra.

Wir springen in dieser Folge ins Frankreich des späten 18. und frühen 19. Jahrhunderts. Während die Revolution durchs Land fegt, wächst ein Mädchen heran, das – trotz aller gesellschaftlicher Widerstände gegen Frauen in den Wissenschaften – zu einer der bedeutendsten Mathematikerinnen ihrer Zeit werden wird. Wir sprechen über Sophie Germain, die sich nicht nur in der Zahlentheorie, sondern auch der Mathematischen Physik einen Namen machte – und trotzdem zu Lebzeiten nie die Anerkennung erhielt, die sie verdient hätte. //Erwähnte Folgen - GAG361: Gustave Trouvé - der vergessene Erfinder – https://gadg.fm/361 - GAG408: Das kurze und tragische Leben des Évariste Galois – https://gadg.fm/408 - GAG375: Sofia Kowalewskaja, "Königin der Wissenschaft" – https://gadg.fm/375 Literatur - Dora Musielak. Sophie Germain: Revolutionary Mathematician. Springer Nature, 2020. - Hill, Amy Marie. „Sophie Germain : A Mathematical Biography“. University Of Oregon, 1995. https://hdl.handle.net/1794/8965. Hier die Sternengeschichte zu Sophie Germain: https://sternengeschichten.podigee.io/185-sternengeschichten-folge-185-sophie-germain Das Episodenbild zeigt eine junge Sophie Germain. //Aus unserer Werbung Du möchtest mehr über unsere Werbepartner erfahren? Hier findest du alle Infos & Rabatte: https://linktr.ee/GeschichtenausderGeschichte //Wir haben auch ein Buch geschrieben: Wer es erwerben will, es ist überall im Handel, aber auch direkt über den Verlag zu erwerben: https://www.piper.de/buecher/geschichten-aus-der-geschichte-isbn-978-3-492-06363-0 Wer Becher, T-Shirts oder Hoodies erwerben will: Die gibt's unter https://geschichte.shop Wer unsere Folgen lieber ohne Werbung anhören will, kann das über eine kleine Unterstützung auf Steady oder ein Abo des GeschichteFM-Plus Kanals auf Apple Podcasts tun. Wir freuen uns, wenn ihr den Podcast bei Apple Podcasts oder wo auch immer dies möglich ist rezensiert oder bewertet. Wir freuen uns auch immer, wenn ihr euren Freundinnen und Freunden, Kolleginnen und Kollegen oder sogar Nachbarinnen und Nachbarn von uns erzählt! Du möchtest Werbung in diesem Podcast schalten? Dann erfahre hier mehr über die Werbemöglichkeiten bei Seven.One Audio: https://www.seven.one/portfolio/sevenone-audio

In this episode, we sat down with the CEO of Union, Karel, to discuss Union's architecture, including CometBLS, and Galois. We also covered what makes Union unique, and how modularity in crypto will evolve going forward. Finally, Karel told us what to expect from Union in 2025. Thanks for tuning in! As always, remember this podcast is for informational purposes only, and any views expressed by anyone on the show are solely their opinions, not financial advice. -- Follow Union: https://x.com/union_build Follow Karel: https://x.com/0xkaiserkarel Follow Boccaccio: https://x.com/salveboccaccio Follow Blockworks Research: https://x.com/blockworksres Subscribe on YouTube: https://bit.ly/3foDS38 Subscribe on Apple: https://apple.co/3SNhUEt Subscribe on Spotify: https://spoti.fi/3NlP1hA Get top market insights and the latest in crypto news. Subscribe to Blockworks Daily Newsletter: https://blockworks.co/newsletter/ Join the 0xResearch Telegram group: https://t.me/+z0H6y2bS-dllODVh -- Timestamps: (0:00) Introduction (3:32) Union Architecture (6:44) ZK-powered Consensus (11:43) CometBLS & Galois (16:04) Integrating Other Chains (24:55) What is Unique About Union? (28:24) How Will Modularity Change Over the Years? (31:29) Union's Focus in 2025 -- Check out Blockworks Research today! Research, data, governance, tokenomics, and models – now, all in one place Blockworks Research: https://www.blockworksresearch.com/ Free Daily Newsletter: https://blockworks.co/newsletter -- Disclaimer: Nothing said on 0xResearch is a recommendation to buy or sell securities or tokens. This podcast is for informational purposes only, and any views expressed by anyone on the show are solely our opinions, not financial advice. Boccaccio, Dan, and our guests may hold positions in the companies, funds, or projects discussed.

Dr. Joe Kiniry (Mike's big brother) - is a Principal Scientist at a Portland, Oregon-based technology company called Galois. He’s also the Principled CEO and Chief Scientist of a Galois spin-out company called Free & Fair that works on high-assurance election technologies and services. Prior to joining Galois in 2014, Joe was a Full Professor at the Technical University of Denmark where he headed up the Software Engineering section. He also held a guest appointment at the IT University of Copenhagen, and has held permanent positions at four universities in Denmark, Ireland, and The Netherlands. Joe holds five advanced degrees, including a Ph.D. from Caltech.See omnystudio.com/listener for privacy information.

The Lads are joined by Kevin Zhou (aka @Galois_Capital) for his first podcast appearance in a long while, and they've got a boat-load to chat about. It's the final days before the US election, $GOAT is down—and though it's more fun when the price is going up—we're making our own fun here. In Episode #67 we cover: 00:00 Coming Up on Steady Lads… 01:18 Kevin's Luna Battle 05:38 What's Kevin Been Up To? 09:52 Celestia Unlock 18:51 Blockchain Week In Dubai 22:11 Final Days Before The Election 29:05 ETH Blob Bull Post 38:41 It's More Fun When The Price Is Going Up 43:32 Jadoodoo's ETH Journey 46:03 Pasta of the Week

Megoldott egy 350 éves matematikai problémát, aztán 20 évesen meghalt párbajban Telex     2024-10-25 04:15:01     Életmód Könyvtár A politikával is foglalkozó csodagyerek, Évariste Galois csupán 60 oldalnyi tudományos munkát hagyott maga után, de azzal olyan elméleteket indított útjukra, amiknek ma már könyvtárnyi irodalmuk van. Tavasszal döntenek Magyar Péter mentelmi jogáról 24.hu     2024-10-25 06:38:29     Belföld Magyar Péter Lengyelország Tisza Párt Lengyel baloldali EP-képviselő lehet a jelentéstevő a Tisza Párt elnökének mentelmi ügyében. Lemondott az Mszp pártigazgatója, Molnár Zsolt 444.hu     2024-10-25 06:11:36     Belföld Parkolás MSZP Molnár Zsolt Nemrég emeltek vádat ellene hat másik emberrel együtt a zuglói és az újbudai parkolási rendszer ügyében. Megjelentek az első felvételek az ukrán fegyveres erők visszavonulásáról Magyar Hírlap     2024-10-25 06:19:01     Külföld Ukrajna Nemrégiben a Donyecki Népköztársaság vezetője, Denisz Puszilin azt mondta, hogy minden feltétel adott ahhoz, hogy Szelidove városát fedezzék. Elromlott a magyar emberek gazdasági hangulata Portfolio     2024-10-25 06:20:00     Gazdaság Felmérés GKI Októberben az üzleti szféra összesített várakozása nem változott az előző hónaphoz képest, de a fogyasztók kissé pesszimistábbak lettek - derül ki a GKI felméréséből. A lakossági konjunktúraindex két havi süllyedésével elakadt a lassú javuló tendencia, utoljára februárban láttunk a mostaninál kisebb mutatót. Az üzleti és fogyasztói felmérésből össz Alig pár órára van a világ legjobb síterepe First Class     2024-10-25 05:39:17     Utazás Elismerés Síelés A tapasztalt tesztelők ezúttal sem találtak jobb helyet a világon síelésre, évek óta ugyanaz a terület zsebeli be a legjobbnak járó elismerést a világon. „Gyakran üzennek Orbán Viktornak” – ezt látta az ukrajnai háborúban egy magyar újságíró Privátbankár     2024-10-25 05:51:01     Külföld Ukrajna háború Orbán Viktor Moszkva Telex Az orosz-ukrán háborút relatív kevés magyar újságíró látta testközelből, és még kisebb azok száma, akiknek mindkét oldalról vannak személyes és érdemi tapasztalatai. A kevesek egyike Nyilas Gergely, a Telex újságírója, aki korábban évekig dolgozott moszkvai tudósítóként, az elmúlt években pedig számos alkalommal járt ukrajnai háborús övezetekben, p 840 forint a forralt bor Európa egyik legolcsóbb adventi vásárában Startlap Utazás     2024-10-25 06:03:17     Utazás Lengyelország Olcsó Advent Bor Karácsonyi vásár A lengyelországi Wrocław városa meghitt karácsonyi vásárral várja a látogatókat. Az esemény kedvező árairól is ismert: a forralt bor csupán 840 forintba kerül. Nemes bosszút vett a franciákon a magyar válogatott kapusa Magyar Nemzet     2024-10-24 23:33:05     Olimpia Olimpia Kézilabda A magyar női kézilabda-válogatott 30-27-re nyert a világbajnok, olimpiai ezüstérmes Franciaország vendégeként. Meghalt a 28-szoros válogatott labdarúgó Sportal     2024-10-25 06:14:49     Foci Marokkó Harmincöt éves korában elhunyt Abdelaziz Barrada, korábbi 28-szoros marokkói válogatott labdarúgó - számolt be a szomorú hírről a Marokkói Lbadarúgó-szövetség honlapja. Napsütéses lesz október utolsó hétvégéje is Kiderül     2024-10-25 04:37:52     Időjárás Hétvége A hétvégére már csak kisebb tartósan felhős körzetek maradnak, napközben szinte mindenhol kisüt a nap a köd felbomlása után. A jövő hét elejétől viszont egyre nehezebben akar feloszlani a reggeli pára,több helyen egész nap megmarad a szürkeség. A további adásainkat keresd a podcast.hirstart.hu oldalunkon.

Megoldott egy 350 éves matematikai problémát, aztán 20 évesen meghalt párbajban Telex     2024-10-25 04:15:01     Életmód Könyvtár A politikával is foglalkozó csodagyerek, Évariste Galois csupán 60 oldalnyi tudományos munkát hagyott maga után, de azzal olyan elméleteket indított útjukra, amiknek ma már könyvtárnyi irodalmuk van. Tavasszal döntenek Magyar Péter mentelmi jogáról 24.hu     2024-10-25 06:38:29     Belföld Magyar Péter Lengyelország Tisza Párt Lengyel baloldali EP-képviselő lehet a jelentéstevő a Tisza Párt elnökének mentelmi ügyében. Lemondott az Mszp pártigazgatója, Molnár Zsolt 444.hu     2024-10-25 06:11:36     Belföld Parkolás MSZP Molnár Zsolt Nemrég emeltek vádat ellene hat másik emberrel együtt a zuglói és az újbudai parkolási rendszer ügyében. Megjelentek az első felvételek az ukrán fegyveres erők visszavonulásáról Magyar Hírlap     2024-10-25 06:19:01     Külföld Ukrajna Nemrégiben a Donyecki Népköztársaság vezetője, Denisz Puszilin azt mondta, hogy minden feltétel adott ahhoz, hogy Szelidove városát fedezzék. Elromlott a magyar emberek gazdasági hangulata Portfolio     2024-10-25 06:20:00     Gazdaság Felmérés GKI Októberben az üzleti szféra összesített várakozása nem változott az előző hónaphoz képest, de a fogyasztók kissé pesszimistábbak lettek - derül ki a GKI felméréséből. A lakossági konjunktúraindex két havi süllyedésével elakadt a lassú javuló tendencia, utoljára februárban láttunk a mostaninál kisebb mutatót. Az üzleti és fogyasztói felmérésből össz Alig pár órára van a világ legjobb síterepe First Class     2024-10-25 05:39:17     Utazás Elismerés Síelés A tapasztalt tesztelők ezúttal sem találtak jobb helyet a világon síelésre, évek óta ugyanaz a terület zsebeli be a legjobbnak járó elismerést a világon. „Gyakran üzennek Orbán Viktornak” – ezt látta az ukrajnai háborúban egy magyar újságíró Privátbankár     2024-10-25 05:51:01     Külföld Ukrajna háború Orbán Viktor Moszkva Telex Az orosz-ukrán háborút relatív kevés magyar újságíró látta testközelből, és még kisebb azok száma, akiknek mindkét oldalról vannak személyes és érdemi tapasztalatai. A kevesek egyike Nyilas Gergely, a Telex újságírója, aki korábban évekig dolgozott moszkvai tudósítóként, az elmúlt években pedig számos alkalommal járt ukrajnai háborús övezetekben, p 840 forint a forralt bor Európa egyik legolcsóbb adventi vásárában Startlap Utazás     2024-10-25 06:03:17     Utazás Lengyelország Olcsó Advent Bor Karácsonyi vásár A lengyelországi Wrocław városa meghitt karácsonyi vásárral várja a látogatókat. Az esemény kedvező árairól is ismert: a forralt bor csupán 840 forintba kerül. Nemes bosszút vett a franciákon a magyar válogatott kapusa Magyar Nemzet     2024-10-24 23:33:05     Olimpia Olimpia Kézilabda A magyar női kézilabda-válogatott 30-27-re nyert a világbajnok, olimpiai ezüstérmes Franciaország vendégeként. Meghalt a 28-szoros válogatott labdarúgó Sportal     2024-10-25 06:14:49     Foci Marokkó Harmincöt éves korában elhunyt Abdelaziz Barrada, korábbi 28-szoros marokkói válogatott labdarúgó - számolt be a szomorú hírről a Marokkói Lbadarúgó-szövetség honlapja. Napsütéses lesz október utolsó hétvégéje is Kiderül     2024-10-25 04:37:52     Időjárás Hétvége A hétvégére már csak kisebb tartósan felhős körzetek maradnak, napközben szinte mindenhol kisüt a nap a köd felbomlása után. A jövő hét elejétől viszont egyre nehezebben akar feloszlani a reggeli pára,több helyen egész nap megmarad a szürkeség. A további adásainkat keresd a podcast.hirstart.hu oldalunkon.

C'est la guerre en Angleterre. Depuis plusieurs jours, la Grande Bretagne connait de violentes émeutes dans ses rues. La raison ? Trois petite filles ont été tuées au couteau à Southport, quelques jours plus tôt. Elles avaient 6, 7 et 9 ans. Le tueur, Axel Rudakubana, est un Galois d'origine rwandaise, de 17 ans. Le meurtre met le feu aux poudres et laisse place à des affrontements sans précédents partout au Royaume-uni. Curieusement, la séquence ressemble à ce que la France a connu avec Lola ou Crépol, quand le pouvoir en place, et l'espace médiatique ne pointent du doigt que ceux qui réclament l'ordre. On debriefe tout. Les fakes news, et le deux poids deux mesures.

Wir springen in dieser Folge nach London, wo in der ersten Hälfte des 19. Jahrhunderts ein französischer Koch aus einfachsten Verhältnissen zum Starkoch des britischen Adels aufsteigt. Mit Charme und voller Energie prägt der junge Koch Alexis Soyer die viktorianische Küche und avanciert so zu einer der schillerndsten Figuren seiner Zeit. Allerdings ist er weit mehr als das: trotz eigener tragischer Rückschläge wird er sein Geld und seine Innovationskraft auch zur Verbesserung der Lebensumstände der Ärmsten einsetzen und schließlich auch noch die Art und Weise, wie Soldaten im Feld versorgt werden, revolutionieren. //Literatur – Ruth Cowen. 2010. Relish: The Extraordinary Life of Alexis Soyer, Victorian Celebrity Chef. Hachette UK. //Erwähnte Folgen GAG290: Der Angriff der Leichten Brigade – https://gadg.fm/290 GAG301: Mary Seacole – https://gadg.fm/301 GAG431: Auguste Escoffier, Kaiser der Köche – https://gadg.fm/431 GAG418: Das älteste Gewürz der Welt – https://gadg.fm/418 GAG60: Wie das Essengehen erfunden wurde – https://gadg.fm/60 GAG408: Das kurze und tragische Leben des Évariste Galois – https://gadg.fm/408 GAG447: Christina, Hans und Heinrich oder Wie ein Gemälde entsteht – https://gadg.fm/447 GAG345: Suffrajitsu – https://gadg.fm/345 GAG464: Die Entstehung des Central Parks – https://gadg.fm/464 GAG09: Wer den englischen Parlamentsbrand auf dem Kerbholz hat – https://gadg.fm/09 GAG458: Wie wir die Nacht zum Tag machten – https://gadg.fm/458 GAG440: Eine Giraffe für den König – https://gadg.fm/440 GAG443: J.S. Bach oder Wie sich ein Komponist den Lebensunterhalt verdient – https://gadg.fm/443 Das Folgenbild zeigt Soyer in einem Gemälde seiner Frau Emma Jones: https://commons.wikimedia.org/wiki/File:Alexis_Soyer.jpg //Aus unserer Werbung Du möchtest mehr über unsere Werbepartner erfahren? Hier findest du alle Infos & Rabatte: https://linktr.ee/GeschichtenausderGeschichte //Wir haben auch ein Buch geschrieben: Wer es erwerben will, es ist überall im Handel, aber auch direkt über den Verlag zu erwerben: https://www.piper.de/buecher/geschichten-aus-der-geschichte-isbn-978-3-492-06363-0 Wer Becher, T-Shirts oder Hoodies erwerben will: Die gibt's unter https://geschichte.shop Wer unsere Folgen lieber ohne Werbung anhören will, kann das über eine kleine Unterstützung auf Steady oder ein Abo des GeschichteFM-Plus Kanals auf Apple Podcasts tun. Wir freuen uns, wenn ihr den Podcast bei Apple Podcasts oder wo auch immer dies möglich ist rezensiert oder bewertet. Wir freuen uns auch immer, wenn ihr euren Freundinnen und Freunden, Kolleginnen und Kollegen oder sogar Nachbarinnen und Nachbarn von uns erzählt! Du möchtest Werbung in diesem Podcast schalten? Dann erfahre hier mehr über die Werbemöglichkeiten bei Seven.One Audio: https://www.seven.one/portfolio/sevenone-audio

The digital asset fund manager community is up in arms about the SEC's latest shenanigans against Galois Capital, and I'm here to tell you; so am I!The SEC alleged three separate violations, and gave us zero helpful detail/analysis/guidance that might let other asset managers avoid similar acitons.Key Points From This Episode:What violations did the SEC allege Galois Capital committed?What does a settlement mean?Why so much secrecy?Shout out to Laura Shin.A few rays of sunshine.Disclaimer:This show is for informational purposes only. Nothing presented here constitutes legal advice. Tokens of Wisdom is produced by Dave Rothschild, partner at Cole-Frieman & Mallon LLP headquartered in San Francisco, California. For more information, visit https://colefrieman.com/Links Mentioned in Today's Episode:Galois Settlement - https://www.sec.gov/files/litigation/admin/2024/ia-6670.pdfUnchained podcast - https://open.spotify.com/episode/0WLRqpxdDNHcZgygf3MwJvDave Rothschild - https://www.linkedin.com/in/davidcrothschild/Cole-Frieman & Mallon LLP - https://colefrieman.com/Music by Joe Ginsberg - https://www.instagram.com/thejoeginsbergFor any questions or comments, email: tow@colefrieman.com

In this episode Eric Bond and Patrick Lafontaine joins us to talk about the life in industry vs the life in academia. Eric is a PhD student at Michigan University under Max New, he works with some pretty cool esoteric cubical agda stuff. Before starting his PhD he has spent some time at the consultancy companies Two Six Technologies and 47 Degrees doing some cool functional programming and formal methods. Before that we were pals doing an internship at Galois, and even before that he finished his masters with Benjamin Delaware at Purdue, Patrick's current advisor. Patrick has just returned from his internship at AWS in the automated reasoning team. So in this episode we talk about their research, their academic and industry experiences, how's the industry looking like for opportunities in PL and all that.

The SEC and CFTC's recent actions against Uniswap and Galois Capital could mark a turning point in crypto regulation. With both firms settling on relatively low fines, are we witnessing regulators establish precedent for a broader crackdown on the industry?  In this episode, Larry Florio, general counsel at 1kx, delves into the implications of these settlements, the frustrations asset managers face with regulatory compliance, and whether the SEC's approach could push the crypto industry into a corner. Will these actions set a precedent for more aggressive enforcement ahead? Show highlights: Why the SEC's action against Galois Capital highlights a shift in language, focusing on tokens "offered and sold as securities" What a qualified custodian is and why the SEC's action against Galois punishes them for using FTX, which could have fit one definition of a qualified custodian if it hadn't been perpetrating a fraud How the SEC demands crypto fund managers comply with regulations on qualified custodians while also limiting qualified custodians in crypto Whether the SEC is effectively banning crypto funds by requiring compliance with impossible rules How the SEC penalized Galois for giving affiliates better liquidity terms than outside investors How SEC Commissioner Mark Uyeda's call for clarity on "crypto asset securities" reflects the industry's frustration with the lack of clear guidelines from the SEC Why the CFTC's fine against Uniswap for alleged leveraged transactions may set a precedent for future enforcement actions How Commissioner Summer K. Mersinger's dissent highlights the unfairness of punishing Uniswap despite their proactive compliance, according to Larry Whether the New York Attorney General's subpoenas to VCs about Uniswap signal a renewed adversarial approach to regulating DeFi The timing of these actions, along with the SEC's Wells notice to OpenSea Visit our website for breaking news, analysis, op-eds, articles to learn about crypto, and much more: unchainedcrypto.com Thank you to our sponsors! iTrustCapital Polkadot Mantle Gemini Stellar Guest Larry Florio, general counsel at 1kx Timestamps:  ➡️ 01:51 - The SEC using different language to describe tokens as securities ➡️ 04:53 - Qualified custodians & Galois Capital's use of FTX ➡️ 09:04 - Compliance frustrations for crypto asset managers ➡️ 11:58 - The SEC effectively banning crypto funds? ➡️ 18:22 - Penalty for giving some investors undisclosed preferential treatment ➡️ 18:25 - SEC Commissioner Mark Uyeda's call for clarity on crypto assets ➡️ 19:35 - CFTC's fine against Uniswap: A troubling precedent? ➡️ 23:09 -Uniswap's compliance efforts & two CFTC Commissioners' dissents ➡️ 24:56 - NY Attorney General's subpoenas ➡️ 27:04 - OpenSea's Wells notice: NFTs as securities? ➡️ 30:34 - Crypto News Recap Links Galois Capital: The Block: SEC charges and settles with crypto-focused Galois Capital over custody issues Larry Florio's thread Uniswap:  CoinDesk: Uniswap Labs Settles CFTC Charges Over 'Illegal' Margin Products Blockworks: CFTC Commissioners dissent on Uniswap settlement Comments from Uniswap counsel Axios: The SEC has questions for VCs about Uniswap NY Attorney General's Subpoenas CoinDesk: VC Giants a16z, Union Square Ventures Get Subpoenaed by New York About Uniswap: Sources OpenSea's Wells notice: Unchained: If the SEC Sues OpenSea, Here's Why the NFT Platform Could Win Easily Learn more about your ad choices. Visit megaphone.fm/adchoices

Uniswap Labs and Galois Capital have settled with the CFTC and the SEC, respectively, but crypto lawyer Larry Florio says these small settlements could set bad precedents for the rest of the industry.The SEC and CFTC's recent actions against Uniswap and Galois Capital could mark a turning point in crypto regulation. With both firms settling on relatively low fines, are we witnessing regulators establish precedent for a broader crackdown on the industry? In this episode, Larry Florio, general counsel at 1kx, delves into the implications of these settlements, the frustrations asset managers face with regulatory compliance, and whether the SEC's approach could push the crypto industry into a corner. Will these actions set a precedent for more aggressive enforcement ahead?Show highlights:Why the SEC's action against Galois Capital highlights a shift in language, focusing on tokens "offered and sold as securities"What a qualified custodian is and why the SEC's action against Galois punishes them for using FTX, which could have fit one definition of a qualified custodian if it hadn't been perpetrating a fraudHow the SEC demands crypto fund managers comply with regulations on qualified custodians while also limiting qualified custodians in cryptoWhether the SEC is effectively banning crypto funds by requiring compliance with impossible rulesHow the SEC penalized Galois for giving affiliates better liquidity terms than outside investorsHow SEC Commissioner Mark Uyeda's call for clarity on "crypto asset securities" reflects the industry's frustration with the lack of clear guidelines from the SECWhy the CFTC's fine against Uniswap for alleged leveraged transactions may set a precedent for future enforcement actionsHow Commissioner Summer K. Mersinger's dissent highlights the unfairness of punishing Uniswap despite their proactive compliance, according to LarryWhether the New York Attorney General's subpoenas to VCs about Uniswap signal a renewed adversarial approach to regulating DeFiThe timing of these actions, along with the SEC's Wells notice to OpenSeaVisit our website for breaking news, analysis, op-eds, articles to learn about crypto, and much more: unchainedcrypto.comThank you to our sponsors!iTrustCapitalPolkadotMantleGeminiStellarGuestLarry Florio, general counsel at 1kxUnchained Podcast is Produced by Laura Shin Media, LLC. Distributed by CoinDesk.See Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

Matt and Nic are back for another week of news and deals. In this episode: SEC fiscal year ending in September How to get accurate transfer volume figures for stablecoins How much volume do stablecoins really settle? Do SEC rules stop registered venture firms from voting in governance or staking? CFTC settles with Uniswap Robinhood settles with the California DoJ Choke Point 2.0 is still happening What's the latest with World Liberty Financial? John Deaton wins his primary in MA What's the deal with Polymarket versus the polls? Sponsor notes: Withum's Digital Currency and Blockchain Technology Team specializes in crypto-assets, offering accounting, tax and advisory solutions to fortify trust in a dynamic industry. Contact them today to get started. - withum.com/crypto Coin Metrics: An Update on Layer–1 Networks

The SEC and CFTC's recent actions against Uniswap and Galois Capital could mark a turning point in crypto regulation. With both firms settling on relatively low fines, are we witnessing regulators establish precedent for a broader crackdown on the industry?  In this episode, Larry Florio, general counsel at 1kx, delves into the implications of these settlements, the frustrations asset managers face with regulatory compliance, and whether the SEC's approach could push the crypto industry into a corner. Will these actions set a precedent for more aggressive enforcement ahead? Show highlights: Why the SEC's action against Galois Capital highlights a shift in language, focusing on tokens "offered and sold as securities" What a qualified custodian is and why the SEC's action against Galois punishes them for using FTX, which could have fit one definition of a qualified custodian if it hadn't been perpetrating a fraud How the SEC demands crypto fund managers comply with regulations on qualified custodians while also limiting qualified custodians in crypto Whether the SEC is effectively banning crypto funds by requiring compliance with impossible rules How the SEC penalized Galois for giving affiliates better liquidity terms than outside investors How SEC Commissioner Mark Uyeda's call for clarity on "crypto asset securities" reflects the industry's frustration with the lack of clear guidelines from the SEC Why the CFTC's fine against Uniswap for alleged leveraged transactions may set a precedent for future enforcement actions How Commissioner Summer K. Mersinger's dissent highlights the unfairness of punishing Uniswap despite their proactive compliance, according to Larry Whether the New York Attorney General's subpoenas to VCs about Uniswap signal a renewed adversarial approach to regulating DeFi The timing of these actions, along with the SEC's Wells notice to OpenSea Visit our website for breaking news, analysis, op-eds, articles to learn about crypto, and much more: unchainedcrypto.com Thank you to our sponsors! iTrustCapital Polkadot Mantle Gemini Stellar Guest Larry Florio, general counsel at 1kx Timestamps:  ➡️ 01:51 - The SEC using different language to describe tokens as securities ➡️ 04:53 - Qualified custodians & Galois Capital's use of FTX ➡️ 09:04 - Compliance frustrations for crypto asset managers ➡️ 11:58 - The SEC effectively banning crypto funds? ➡️ 18:22 - Penalty for giving some investors undisclosed preferential treatment ➡️ 18:25 - SEC Commissioner Mark Uyeda's call for clarity on crypto assets ➡️ 19:35 - CFTC's fine against Uniswap: A troubling precedent? ➡️ 23:09 -Uniswap's compliance efforts & two CFTC Commissioners' dissents ➡️ 24:56 - NY Attorney General's subpoenas ➡️ 27:04 - OpenSea's Wells notice: NFTs as securities? ➡️ 30:34 - Crypto News Recap Links Galois Capital: The Block: SEC charges and settles with crypto-focused Galois Capital over custody issues Larry Florio's thread Uniswap:  CoinDesk: Uniswap Labs Settles CFTC Charges Over 'Illegal' Margin Products Blockworks: CFTC Commissioners dissent on Uniswap settlement Comments from Uniswap counsel Axios: The SEC has questions for VCs about Uniswap NY Attorney General's Subpoenas CoinDesk: VC Giants a16z, Union Square Ventures Get Subpoenaed by New York About Uniswap: Sources OpenSea's Wells notice: Unchained: If the SEC Sues OpenSea, Here's Why the NFT Platform Could Win Easily Learn more about your ad choices. Visit megaphone.fm/adchoices

In this episode we go into a deep dive into the formal methods side of Voting systems, and for this nobody better than our guest: Joe Kiniry, A Principal Scientist at Galois, Principled CEO and Chief Scientist of Free & Fair, a Galois spin-out focused on high-assurance elections technologies and services. For the past 20 years Joe has worked tiredly in designing, developing, supporting and auditing all kinds of voting systems for different private parties and government parties. Links Broken Ballots Joe Website Galois website SAW

In this episode we continue our conversation with David Christiansen, he wrote the books Functional Programming in Lean and the Little Typer. He has also worked as the Executive Director of the Haskell Foundation, at Galois and did his PhD developing a bunch of cool stuff for Idris. In today's episode we talk about the story behind writing The Little Typer together with Dan Friedman, and we get more technical by talking about Equality, Bidirectional Type Checking, Quotation and Quasi Quotation. Some links: David's Website David's X Lean Zulip Chat Truth of a proposition, evidence of a judgement, validity of a proof

Mit gerade einmal 20 Jahren stirbt der französische Mathematiker Évariste Galois an den Folgen eines Pistolenduells — nicht ohne vorher noch schnell die Algebra zu revolutionieren. Die Idee für diesen Podcast ist am MIP.labor entstanden, der Ideenwerkstatt für Wissenschaftsjournalismus zu Mathematik, Informatik und Physik an der Freien Universität Berlin, ermöglicht durch die Klaus Tschira Stiftung. >> Artikel zum Nachlesen: https://detektor.fm/wissen/geschichten-aus-der-mathematik-evariste-galois

Mit gerade einmal 20 Jahren stirbt der französische Mathematiker Évariste Galois an den Folgen eines Pistolenduells — nicht ohne vorher noch schnell die Algebra zu revolutionieren. Die Idee für diesen Podcast ist am MIP.labor entstanden, der Ideenwerkstatt für Wissenschaftsjournalismus zu Mathematik, Informatik und Physik an der Freien Universität Berlin, ermöglicht durch die Klaus Tschira Stiftung. >> Artikel zum Nachlesen: https://detektor.fm/wissen/geschichten-aus-der-mathematik-evariste-galois

Mit gerade einmal 20 Jahren stirbt der französische Mathematiker Évariste Galois an den Folgen eines Pistolenduells — nicht ohne vorher noch schnell die Algebra zu revolutionieren. Die Idee für diesen Podcast ist am MIP.labor entstanden, der Ideenwerkstatt für Wissenschaftsjournalismus zu Mathematik, Informatik und Physik an der Freien Universität Berlin, ermöglicht durch die Klaus Tschira Stiftung. >> Artikel zum Nachlesen: https://detektor.fm/wissen/geschichten-aus-der-mathematik-evariste-galois

In this episode we talk with David Christiansen, he wrote the books Functional Programming in Lean and the Little Typer. He has also worked as the Executive Director of the Haskell Foundation, at Galois and did his PhD developing a bunch of cool stuff for Idris. David is a super upbeat person and I feel that we could spend hundreds of hours talking about Functional Programming Writing and Dependent Types, and we still wouldn't run out of topics!

Adam Karvonen was my coworker at Galois and is a bright guy doing really interesting stuff in the ML interpretability space. Today he joined us to present his work on Chess-GPT, you guessed it, a GPT model that can play chess. The punchline isn't so much how good the model is as it is how the model "thinks" -- Adam provides compelling evidence that the model internally reasons about an actual board state, and learns to make legal moves. The discussion on this one was great and we really appreciate that Adam took the time to talk to us! Also -- you should hire him! He's doing MATS but will be on the job market at the end of the Summer.

Joshua Brandon Holden, the author of The Mathematics of Secrets, Cryptography from Caesar Ciphers to Digital Encryption, graduated with a degree in pure math and went on to teach at the University of Massachusetts and Duke. He discovered that he was spending most of his time on teaching, so he sought jobs where they would reward teaching. He then worked at the Rose Hulman Institute of Technology, where he did both teaching and research.  Common Misconceptions about Cryptography Joshua discusses common misconceptions about cryptography and its connection to the internet. He explains that people often knew about cryptography in ancient times but don't know about the throughline. Older theories of cryptography were implicitly mathematical but not explicitly, while new theories are very explicitly mathematical. Joshua aims to open up the connection between older forms of cryptography and the new ones, stating that everyone has some ability to do all of it in varying amounts. He talks about the current state of cryptography online, including public key cryptography, which originated in the 70s and gained popularity in the 90s with internet commerce. Public key cryptography allows users to send secret messages through a one-way key, which is only decrypted by the sender who has a different key. This is important for sending credit card information to companies like Amazon or Walmart. However, end-to-end encryption means middlemen are no longer able to decrypt messages, so it's crucial to look carefully at providers' policies to determine if they stay in the loop. Joshua talks about the networks and relationships within the cryptography field, including the opportunities for professionals to work in private camps, government agencies, and academia. He notes that while there is money and space in the field, there is also a lot of space for professionals to stay updated on the latest theories and developments. Quantum Computers in Cryptography The conversation turns to the potential of quantum computers in cryptography and the potential for breaking encryption systems. He believes that quantum computers are expected to be better at breaking the problems used in creating mathematical problems used in special public key systems, such as encryption used by browsers to protect credit card information and communications. He also discusses the development of quantum resistant cryptography, which is a more complex system but the basic principles of quantum resistance systems are still relatively graspable for anyone with high school algebra and a willingness to dig deep. By applying enough computing power to end-to-end encryption systems, it is possible to break them. The only way to achieve perfect secrecy is to have a secret key, which is as long as the conversation. This method was supposedly used for the famous red phone between the White House and the Kremlin during the Cold War. Keeping Your Data Safe In terms of security, Joshua advises people to know their threat model and consider the potential threats they face. Some people may worry about powerful governments trying to break their communications, while others may be concerned about corporate spies, children, or random people passing by. For those worried about corporate espionage, it is recommended to look for end-to-end encryption systems. While quantum computers may not be easy to break, they do not guarantee that someone can't break the system with enough computing power. Class Field Towers Explained Joshua talks about his research in the field of mathematics, specifically in the area of class field towers. He explains why imaginary numbers are not square roots but rather arbitrary choices. He also discusses the concept of Galois groups, which track the number of ways complex numbers can be shuffled around without making a difference. He explains that class field towers consist of rational numbers, real numbers with irrational decimals, and complex numbers on top of them. These towers record the complexity of each jump made in the tower.  Joshua talks about the role of computers in mathematical research, stating that there is more computer usage in this area due to improved software tools and more applications in cryptography. He identifies two traits that are most useful for being successful in mathematical research: perseverance and curiosity. Perseverance is the reason most people persist. In graduate school or postgraduate school, those who stick with their passion and interest in math may be more likely to succeed in mathematical research. He encourages students to not give up on problems that require a different kind of math, even if it's not necessary for their career. He believes that having a sense of curiosity about everything comes from the fact that in mathematics, all one needs is to  just think hard about things and talk to others. This gives one a sense of confidence that they can figure things out without the need for special abilities or tools. Influential Harvard Professors and Courses Joshua mentions Math 25, an honors calculus course. He also enjoyed Professor McConnell, who he still maintains a friendship with. He also shares his experience with changing his name, which was the first of his non-professional wanderings.  Timestamps: 04:33 Cryptography and its applications in online security 11:57 Cryptography, public key systems, and quantum computing 21:07 Encryption, mathematics, and data security 27:49 Mathematical research and talent 33:41 Math education, career choices, and personal growth Links: Website: https://wordpress.rose-hulman.edu/holden/the-mathematics-of-secrets/

Max Ammann is a cybersecurity researcher at Trail of Bits, where he's recently been working on extending his Master's thesis work on fuzzing cryptographic protocols into an industrial-grade fuzzing tool. That work resulted in an S&P publication which is what he joined us to present today. This was a really good talk but also a great discussion, in large part because of the highly engaged audience (with representation from Galois, TwoSix, and academia!).

If you see networking as large meet-ups and one-off coffee dates, it's time to rethink your networking strategy. Find Your Dream Job guest Sophia Wellons stresses the need for building long-term relationships through networking. Networking isn't simply meeting someone and asking them if they have a job for you; it building relationships that will serve both parties for months or years to come. Sophia says you have to go into these settings with clarity on what you need and how you can help others, along with a willingness to do so. About Our Guest: Sophia Wellons (http://linkedin.com/in/srwellons) is a recruiter at Galois (https://lifeatgalois.com/). Her company specializes in the research and development of new technologies. Resources in This Episode: Sophia welcomes connections on LinkedIn. You can find her at (www.linkedin.com/in/srwellons/). From our Sponsor: Find Your Dream Job is brought to you by TopResume.(http://macslist.org/topresume) Top Resume has helped more than 400,000 professionals land more interviews and get hired faster. Get a free review of your resume today from one of Top Resume's expert writers. (http://macslist.org/topresume)

Joe Kiniry is a computer scientist at Galois, specializing in Rigorous Systems and Software Engineering (Model-based Systems Engineering with Digital Twins), Hardware/Firmware Security, Trustworthy and Verifiable Elections, High-assurance Cryptography, and Audits-for-Good. He's also the Chief Scientist at Free & Fair, a Galois spin-off focused specifically on verified elections tech. Today Joe joined us for a Q&A focused specifically on his elections tech work, and it was a fun one! Joe is one of the more pragmatic and charismatic FM evangelists out there and I think this is an enormously compelling use-case for the tech. We really enjoyed the event and hope you do too!

Ever felt stuck trying to find your big idea? In a tale as intense as it is enlightening, Darren Hardy reveals how the pressure of a life-or-death moment propelled mathematician Évariste Galois to unlock groundbreaking ideas. Listen to discover how urgency can unearth your own big idea. Go to https://herosjourney.com/podcast to join the 2024 HERO COMMUNITY COHORT! Get more personal mentoring from Darren each day. Go to DarrenDaily at http://darrendaily.com/join to learn more.

Voltamos com mais um episódio do Escuta Essa, podcast semanal em que Denis e Danilo trocam histórias de cair o queixo e de explodir os miolos. Todas as quartas-feiras, no seu agregador de podcasts favorito, é a vez de um contar um causo para o outro. Neste episódio são duas histórias sobre mortes estranhas: primeiro Denis nos conta sobre um gênio que teve uma vida atribulada e uma morte inesperada; depois é a vez do Danilo falar sobre um homem que ficou azul e acabou morrendo graças a uma decisão absurda. Não deixe de enviar os episódios do Escuta Essa para aquela pessoa com quem você também gosta de compartilhar histórias e aproveite para mandar seus comentários e perguntas no Spotify, nas redes sociais @escutaessapod, ou no e-mail escutaessa@aded.studio. A gente sempre lê mensagens no final de cada episódio! ... NESTE EPISÓDIO Primeira História - Évariste Galois morreu aos 20 anos no dia 31 de maio de 1832. - Leia aqui o tuíte do matemático Jay Cummings que deu origem a esse episódio por desejar a Galois uma morte 84 anos de idade com 456 artigos e 13 livros publicados. - A história de Galois é uma das relatadas no livro "Matemáticos Famosos", de Antônio Carlos Garcia. - O livro "Quando deixamos de entender o mundo", de Benjamín Labatut, aborda a linha tênue entre a ciência, os cientistas e a loucura. - Joseph Fourier, secretário da Academia de Ciências da França, morreu sem entregar à instituição todos os artigos que havia recebido, incluindo o supostamente brilhante artigo de Galois. - Alexandre Dumas, autor de grandes clássicos da literatura francesa como "Os Três Mosqueteiros" e "O Conde de Monte Cristo", escreveu sobre Galois em seu livro de memórias - sem sequer imaginar que ele seria um matemático famoso. - Alexander Hamilton morreu num duelo com seu rival político Aaron Burr depois de inúmeras tentativas frustradas de reconciliação. Segunda História - Paul Karason virou celebridade em 2008 quando percebeu que estava azul. As imagens dele podem ser conferidas aqui. - Ainda em 2008 Paul Karason foi ao programa da Oprah com o dr. Mehmet Oz para contar sua história. - Paul Karason teve um ataque cardíaco e um derrame em 2013 e acabou morrendo durante o tratamento, aos 62 anos. - "O Nariz" é uma crônica de Luís Fernando Veríssimo sobre um dentista que tem a vida destruída quando resolve usar um nariz falso. A história é uma brincadeira com o livro "A Metamorfose", de Franz Kafka, sobre um homem que acorda transformado num inseto gigantesco e tem sua vida arrasada no processo. - O aparelho usado por Paul Karason era um "Colloidal Silver Generator", um gerador de prata coloidal. ... AD&D STUDIO A AD&D produz podcasts e vídeos que divertem e respeitam sua inteligência! Acompanhe todos os episódios em aded.studio para não perder nenhuma novidade. POUCO PIXEL O podcast Pouco Pixel abriu uma campanha de financiamento coletivo para viabilizar sua próxima temporada! Apoie em poucopixel.com/financiamento

Blog: https://medium.com/asecuritysite-when-bob-met-alice/tetra-burst-42773a490b35  Introduction Anyone can create a cipher. Basically, Bob and Alice do some modulo maths and could encrypt their secret messages into ciphertext by multiplying by 10 and adding 5, and then to decrypt back into plaintext, they would just subtract the ciphertext by 5 and divide by 10. The maths involved could then be defined by a Galois Field (GF)— and which is named after Évariste Galois. Bob and Alice could then keep their method secret from Eve (their adversary), and where they believe their method is secure and thus do not ask Trent to evaluate its security. But Eve is sneaky and tries lots of different ways to crack the cipher. Eventually, after trying to crack the ciphertext, she discovers the method, and can then crack all the future (and, possibly, previous) ciphers. Bob and Alice then carry on using the secret cipher method and would then have no way of knowing that Eve now knows their method. This approach is often known as “cooking your own crypto”, and is not recommended in most implementations. Along with this, as Bob and Alice try to hide their method from Eve, the approach is “Security by obfuscation” rather than “Security-by-design”. Cooking your own crypto There are many cases of propriety cryptography methods being used in production. In 2013, for example, researchers at the University of Birmingham found flaws in the key fobs related to the Volkswagen group vehicles. In fact, the encryption used in the Swiss-made Megamos transponder was so weak that an intruder only needed to listen to two transmitted messages from the fob in order to crack the key. The vulnerability related to the poor, proprietary cryptographic methods used by the device, and where the researchers found they could generate the transponder's 96-bit secret key and start the car in less than half an hour. The vulnerability has been well known since 2012, and code to exploit the flaw has circulated online since 2009. Yet, at the time, there was no product recall for the dozens of models that were affected, including Audi, Porsche, Bentley and Lamborghini, Nissan and Volvo. The research team were even stopped from publishing their work through the threat of legal action from Volkswagen. Testing, Evaluation and Standardization Along with the risk of discovering a secret method, the other major problem is that the method used to create a cipher is when it is not rigorously reviewed by experts. This can take years of reviewing and testing — both in the formal theory and in practice. Many companies, too, have bug bounties and which try to discover vulnerabilities in their code. To overcome this, NIST has created open competitions for the standardization of encryption methods. These have included standards related to symmetric key encryption (AES), hashing methods (SHA-3) and post-quantum cryptography (PQC). Once rigorously evaluated, the industry can then follow the standards defined, and where proprietary methods and implementations are often not trusted. With symmetric-key methods (where the same key is used to both encrypt and decrypt), at one time, we used a wide range of methods, such as DES, 3DES, RC2, RC4, Blowfish, and Twofish. To overcome this, NIST set up an operation standardization process for the Advanced Encryption Standard (AES). In the end, and after extensive testing and performance analysis, the Rijndael method was selected. It is now used in most systems, with either a 128-bit, a 192-bit or 256-bit encryption key. Overall, the larger the key size, the more difficult it is to brute force the key. The TETRA standard This week it has been reported that the TETRA (TErrestrial Trunked RAdio) standard [here] has a number of vulnerabilities in its cryptography. Overall, TETRA is used by many police and military forces across the world for encrypted radio. These vulnerabilities have existed for over a decade and could have led to the leakage of sensitive information. These vulnerabilities have been discovered by Midnight Blue and will be presented as “Redacted Telecom Talk” at Black Hat 2023 on 9 August 2023 [here]. As the work is so sensitive, there are many issues related to its disclosure, so the full details of the talk have not been released. But, it has involved over 18 months of responsible disclosure related to the cracking of TETRA-powered radios purchased from eBay. TETRA was first standardised by the European Telecommunications Standards Institute (ETSI) in 1996 and used by many radio manufacturers, such as Motorola and Airbus. It does not have open-source software and relies on cryptography which is secret and proprietary. TEA1 — Intentionally weak crypto Goverments around the world have generally used export controls on cryptography — in order to reduce security levels so that their own law enforcement agents have a good chance to crack encrypted traffic outside their own borders. One of the most famous was related to Netscape and who created the original version of TLS (Transport Layer Security) that created a secure channel for Web pages — the HTTPs that we see on most of our Web accesses now. This, though, had reduced security levels because of export control — with the RSA method used set at only 512 bits (and which is now easily crackable). As this key was used to pass the encryption key that was used in the secure tunnel, it meant that agencies could break the communications channel for HTTPs communications. We have since paid for this weakening —and with vulnerabilities such as Freak and BEAST. The vulnerability in TETRA, too, relates to similar issues and where the cryptography was reduced to comply with export controls. Within TERTA, the TEA1 method reduces the key size down to 80 bits, and, along with other vulnerabilities, allows the encrypted traffic to be cracked within minutes on a standard laptop. Along with this, researchers found other vulnerabilities with TETRA methods that released sensitive information — including within historical communications. The core vulnerability involved a jump-off from the main interface on the radio, and then which followed through with running malicious code execution on the process and then onto the signal processor and wifi hardware. This main chip on the device then contains a secure enclave, which stores the main encryption keys. The team were able to access this chip and discover the cryptography methods used and associated artefacts. For this, they have dubbed the vulnerability TETRA:BURST [here]: The reduced security method of TEA1 was discovered as having an encryption key of just 80 bits (normally, we would use a 128-bit key size, at least). A key size of 80 bits puts it within a range which can be cracked using GPU clusters. But, the research team found a “secret reduction step” which supported lower levels of randomization for the encryption key and which significantly reduced the key strength. Using this, the team were able to crack the communication with consumer-level hardware and with inexpensive radio equipment. Ultimately, the researchers define the attack as fairly trivial to implement. Vulnerabilities discovered A number of CVEs have already been defined for the vulnerabilities. These are [here]: CVE-2022–24401. This involved the Air Interface Encryption (AIE) keystream generator allows for decryption oracle attacks. CVE-2022–24402. This relates to the backdoor of the 80-bit key on the TEA1 algorithm — and which allows a trivial cipher crack. CVE-2022–24404. This involves weaknesses in the AIE for malleability attacks. CVE-2022–24403. This is a weak cryptographic scheme that allows attackers to deanonymize and track users. CVE-2022–24400. This allows attackers to set the Derived Cypher Key (DCK) to 0. On the CVE database [here], these vulnerabilities are marked as “** RESERVED **” and will be populated soon. Conclusions What we have here is “Security by obscurity” and not “Security by design”. It is difficult to keep anything a secret these days, and, as much as possible, methods should be open to assessment. Along with this, the reduction in the security level for TEA1 is causing major problems — just the Netscape restriction on TLS left us with a security legacy that took decades to address.

Related blog post: https://billatnapier.medium.com/cryptography-fundamentals-commutative-encryption-19ba4c4c2173 Introduction What's at the core of cryptography? Well, the simple EX-OR holds a special place, as we can do not lose any information when we apply it. For a bitwise operation of 0 EXOR 0 gives 0, 0 EXOR 1 gives 1, 1 EXOR 0 gives 1, and 1 EXOR 1 gives 0.  And, so, cryptographers dream of the perfect cipher. And that cipher is a one-time pad. Basically, we generate a one-time use key for our plaintext, and then EX-OR them together, and then just EX-OR again with the same key and we will get our plaintext back. Unfortunately, we can only use it once and need to generate another one. So, let's see if we can generate something similar but just use the simple XOR method for our encryption and decryption. In the Tor (The Onion Router) network, data is encrypted with a key from each of the Tor routing nodes. Thus, if we have three nodes of A, B and C, with A as the entry node and C as the exit node. For this, the user will generate a separate key for each node to use and encrypt with the key of A, then the key of B, and then the key of C. The encrypted data is passed to A, and which will decrypt with its key, and pass the encrypted data onto B, and who will decrypt with its key. Finally, C will decrypt with its key, and the data will be decrypted. This protects the data as it is routed. But we have to remove the keys in the reverse order they were applied. One way to do this is with commutative encryption. Using a hasp When I worked as an electrical engineer, we had a hasp to isolate the electric power on a device we were working on: With this, each person who was working on the equipment, would put on their own padlock, and where we could not put the power back on, until all the padlocks had been taken off. The padlocks could be put on in any order, and taken off in any order, but there was no way to putting the power back on, until everyone had taken their padlock off. So how could we do this with data. Let's say that Bob, Alice and Carol want to apply their “data hasp”, so that the data cannot be revealed until they have all taken off their padlock. Well, with symmetric key block ciphers, such as AES, we cannot do this, as we must decrypt in the reverse order of they keys being applied: To encrypt: Bob → Alice → Carol … and then to decrypt: Carol → Alice →Bob There are ways to do it with RSA, such as with SRA [here], but these methods significantly reduce the security of the process. The solution is to use a stream cipher, as we basically just X-OR the data when we are encrypting, and then X-OR again with the same key when we decrypt. We can apply multiple keys to the data, and in any order and it will always decrypt properly once we have applied all the keys. What we need with commutative encryption is to have an encryption string which is the same length as the data string. To make the encryption string, we can use an XOF (eXtendable-Output Functions) and where we can create a hash value of a given size. For this, rather than the fixed hash of SHA-3, we can use the SHAKE. Or with With BLAKE2b we have an XOF of BLAKE2XB, and for BLAKE2s we have an XOF of BLAKE2XS. We can then basically have a secret passphrase, and which generates an output which matches the length of the plaintext. Another method we can use, is to generate an pseudo infinitely long encryption key which is the same length as the plaintext — in the same way that a stream cipher works. A simple application: Booking a ticket With the ever increasing number of breaches, we are moving to a world where companies should not hold any personally sensitive information, as it is just too risky. So how could we create a trustworthy system, where someone can show up with a ticket, and where we can trust it, without actually revealing any personal information about where the person has booked their seat? So how can we generate a receipt of the booking, but not give away your identity, or the details of the booking? Let's take an example of booking a seat in a theatre at the festival, and how your privacy can be respected, but where the theatre will trust the ticket. Let's say there are 100 seats in a theatre, and I want to book one of them, but I don't want the theatre company to know which seat I've booked, or my identity. I also want a receipt of purchase that they can verify my booking. One way would be to get a trusted agent to look after the bookings, but I don't trust them either. So how can we do this? Well it can be done with commutative encryption. The steps would be: Initially the theatre company generates 100 receipts for each of the seats, and then encrypts them with its public key. Next when I want to make a booking they send me the encrypted receipts that they have left, and I select one at random, and then encrypt it with my public key. I send them all back, including the one I've encrypted. The theatre checks to see which one has been changed, and then decrypts it with its private key, and sends it back to me. I decrypt with my private key, and I can now view the receipt for my booking, and the theater company cannot determine which seat I have, but I will have the receipt of my booking. So here is an example where the theatre encrypts all the seats with its key, the person then selects one, and encrypts with their key, and sends them all back again. Then the theater decrypts the one that has changed, and sends it back for the person to decrypt, and we have a booking. The theatre thus does not know who has booked the seat: Commutative encryption using ChaCha20 ChaCha20 is a stream cipher, and where we created pseudo infinitely long encryption key, and the just XOR it with the plain text. With commutative encryption, we can decrypt with the keys in any order. Normally we would encrypt with Bob's key and then encrypt with Alice's key, and then we must decrypt with Alice's key and then Bob's. In commutative encryption, we can decrypt in any order. With a stream cipher, we can automatically apply commutative as we basically just EX-OR with the key stream. In the following we use Go code, and where Bob encrypts, Alice encrypts, Bob decrypts, and then Alice decrypts [here]. And a sample run [here]: Input text: HelloBob passphrase: qwertyAlice passphrase: 123456Input text: HelloBob keygen: 65e84be33532fb784c48129675f9eff3a682b27168c0ea744b2cf58ee02337c5Alice keygen: 8d969eef6ecad3c29a3a629280e686cf0c3f5d5a86aff3ca12020c923adc6c92Cipher after Bob encrypt: d9eef8ecdcCipher after Alice encrypt: 7a5dcd0f43Cipher after Bob decrypt: ebd6598ff0Cipher after Alice decrypt: 48656c6c6fDecrypted text: Hello We can easily extend the method to Carol, Trent, and so on. In my simple example I have used the same nonce for Bob and Alice, but in real life they would use different values, and these would be random for every transaction. Commutative encryption using SHAKE-128 NIST chose Keccak as the standard for SHA-3. But, it's all a bit confusing, as there are two main versions of this: Keccak and SHA-3. Many systems, such as Ethereum have adopted Keccak, while others go for SHA-3. The only real difference between them is a difference in the padding of data. An eXtendable-Output Function (XOF) produces a bit string that can be of any length. In fact, we can create an infinitely long bit string, if required. The main methods are SHAKE128, SHAKE256, BLAKE2XB and BLAKE2XS. With the SHA-3 hashing method, we have four different cryptographic hashing methods (SHA3–224, SHA3–256, SHA3–384, and SHA3–512) and two XOF functions (SHAKE128 and SHAKE256).  With commutative encryption, we can decrypt with the keys in any order. Normally we would encrypt with Bob's key and then encrypt with Alice's key, and then we must decrypt with Alice's key and then Bob's. In commutative encryption, we can decrypt in any order. While our symmetric key block ciphers cannot be made commutative, we can use stream ciphers, as they perform an EX-OR function. In this example we will use the SHAKE128 or SHAKE256, and generate Bob and Alice's key. https://asecuritysite.com/commul/comm_stream Communicative encryption using SRA With maths, operators such as multiplication are commutative, such as: 3 x 5 x 4 = 4 x 5 x 3 In encryption, most operations are non-commutative, so we need to modify the methods. One way is to use RSA, but generate two keys which have shared p, q and N values. So we generate Bob and Alice's keys using the same two prime numbers (p and q), so that they share the same N value (modulus). So let's start with Bob: Let's select: P=7, Q=13 The calculation of n and PHI is: N = 7 x 13 = 91 PHI = (P-1)(Q-1) = 72 We need to make sure that our encryption key (e) does not share any factors with PHI (gcd(PHI,e)=1). We can select e as: e = 5 Next we can calculate d from: (d x 5) mod (72) = 1 The answer is 29 [Solve] d= 29, e=5, N=91Encryption key [91,5]Decryption key [91,29] Now for Alice. We have: N = 7 x 13 = 91PHI = (P-1)(Q-1) = 72 We can select e as (and should not share any factors with PHI): e = 7 Now we must solve: (7 x d) mod (72) = 1 For this we get 31 [Solve] Alice's keys are then: d= 31, e=7, N=91Encryption key [91,7]Decryption key [91,31] An example of this is here: https://asecuritysite.com/commul/comm2 Commutative encryption using Massey-Omura  As we have seen, commutative encryption allows us to decrypt in any order. For this we can use Massey–Omura Cryptosystem and generate encryption keys which share a prime number. One classic patent for commutative encryption was written by James Massey and Jim K. Omura created the Massey–Omura Cryptosystem in 1982 [1]. It took over three years to be assigned and was assigned to Omnet Associates [here]: It uses exponentiation in the Galois field GF(2^n) for both the encryption and decryption functions. In this, if we have a message of M, the encryption is: and This are operated on with the Galois field. For this we define e within: and we make sure that e does not share a factor with 2^n-1 using: The decryption exponent d is defined as: This works because the multiplicative group of the Galois field GF(2^n) has order 2^n−1, and where Lagrange's theorem defines that m^{de}=m for all the values of m in GF(2^n). The coding is here [link]: import libnumimport randomimport sysfrom Crypto.Util.number import getPrimefrom Crypto.Random import get_random_bytesdef chunkstring(string, length): return (string[0+i:length+i] for i in range(0, len(string), length)) def generate_keys(prime): while True: e = random.randint(0, prime-2) if libnum.gcd(e, prime-1) == 1 and e > 2: break d = libnum.invmod(e, prime-1) return e,ddef crypt(chunk, key,prime ): num = 0 for c in chunk: num *= 256 num += ord(c) res = pow(num, key, prime) vect = [] for i in range(0, len(chunk)): vect.append(chr(res%256)) res = res // 256 return "".join(reversed(vect))primebits=64msg = "HellHe"if (len(sys.argv)>1): primebits=int(sys.argv[1])if (len(sys.argv)>2): msg=(sys.argv[2])FRAGMENT_SIZE = primebits//8msg = msg + " "*((FRAGMENT_SIZE - (len(msg)%FRAGMENT_SIZE))%FRAGMENT_SIZE)res=chunkstring(msg,FRAGMENT_SIZE)PRIME = getPrime(primebits, randfunc=get_random_bytes)e,d = generate_keys(PRIME)vect=[]for elem in res: enc=str(crypt(elem, e,PRIME)) vect.append(enc)enc="".join(vect)dec=[]for elem in chunkstring(enc, FRAGMENT_SIZE): dec.append(crypt(elem, d,PRIME))print (f"Msg={msg}")print (f"e={e}, d={d}")print("Decrypted: " + "".join(dec)) A sample run is [link]: Msg=Hello e=16153579288865179167, d=10300837874192230633Decrypted: Hello One of the advantages of the Massey–Omura Cryptosystem is that we can apply commutative encryption. In this way, Bob may have keys of (e_b,d_b) and Alice has keys of (e_a,d_a). We can then apply the keys in any order, such as encrypting with e_a and then encrypting with e_b, and where we can then decrypt with d_a and then decrypt with d_b, or decrypt with d_b first and then decrypt with d_a (as we would normally do). To encrypt: Cipher=E(a_b,E(e_a,M))=E(e_a,E(e_b,M)) To decrypt: E(d_b,E(d_a,Cipher))=E(d_a,E(d_b,Cipher)) Here is an example: https://asecuritysite.com/commul/massey2 Conclusions Communative encryption is a great way of applying multiple keys to encryption data, and then for them to be removed in any order that is required. It is a little like how data is encrypted in the Tor network, but that requires the keys to be removed in the reverse order they were applied. In a future podcast, I will explain how the Tor network works.

I will bet you, that you have a memory of school where you had the “pleasure” or, most likely, the “nightmare” of performing long addition or long subtraction, and where you had carry overs between columns. The units carried over in the tens, the tens into the hundreds, and so on. And, then, you encountered long multiplication with those ever growing list of numbers.  And, please forgive me, you progressed to long division, and you had that divisor dividing into your number and with the bar along the top, and where you put your result, and which those pesky remainders. “Oh, teacher, 61 divided by 9 is 6 remainder 7”. And, didn't you love throwing away that remainder and just making the answer 6. But, in cryptography, the remainder is the bit we like, and we throw away the other bit. So for us, 61 mod 9 is 7.  So, just take a pause now to just calm yourself for those memories. If you want to leave now, please do so, as we will revisit some of these memories, but, hopefully, we will make things a whole lot more simple. To these additions and multiplications in an electronic circuit or some software code can take many operations. But, just imagine a world where you did not need to carry over values from one column to another, and even where all you had to add or multiply was a 0 and 1, life would be so much easier, and these school nightmares would end for you, and life would be so much happier for your kids in learning maths. For example, if we have a binary adder we have 0+0=0, 1+0=1 and 1+1=0. As we see a simple binary adder just throws away that pesky carry. If we add 1+0+1+1+1+0, we see an answer of 0. But in our normal maths, to add 7+4+3+9+8 requires us to add up the units, and carry over in the 10s column. For simplifying things we turn to Évariste Galois. Évariste Galois — who lived from 1811 to 1832 — died of duelling wounds at the age of 20 but left a great legacy. While he was a teenager, he worked on polynomials and laid down the principles of Galois's theory — along with defining the concept of a finite field.  Creating the reverse operation As we have seen from the previous podcasts, we have values in a group, and then can operate on these to get another value in the group. So, if we have a group of 0 to 16, we can constrain our values with a (mod p) operation, and where p is a prime number.  For example, if we use a prime number of 17, and we take a value of 2 and then raise that to the power of 5 and take the mod of 17, to get 15: >>> pow(2,5,17)15 For all of the values from 0 to 16, we should (hopefully) get different mappings for the output. This will then allow us to reverse back by taking the inverse operation to the modulo power. This, as we have seen from a previous podcast, is to subtract one from the prime number (PHI=p-1), and perform an inverse of the base modulo of the prime number minus one. A simple Python program gives us the result for the inverse: >>> pow(5,-1,16)13 If we now multiply our result of 15 by 13 and take (mod 17), we magically get our value back again: >>> pow(15,13,17)2 In this way, we aim to reverse our mathematical operations, and where there is no confusion about the reverse operation.  Simplifying things Up to now, we have seen that we have operated on our normal arithmetic operations for the (mod p) such as add, subtract, multiply and divide, but we can simply things even more if we have a field which has 2^n elements, and where if n is 8, we can have 256 elements. 256 elements, for example, is the number of values we can have for a byte of data in a computer system. If so, we can convert our bit values of our integers into a polynomial, and then operate on them as polynomial operations, such as:  (x²+1)+(x) = x²+x+1 This, as we will see, significantly reduces the complexity of our arithmetic operations, and rather than have complex circuits for adding (with carry overs) and multiplying (and where we end up with a value which has more bits than the inputs values), we constrain the calculation within our finite field. Along with this we then just need simple 1-bit adder or multiplication operation. So from complex adding and subtraction circuits in hardware or with software operations, we end up with simple bit operations. This vastly increases the speed of our cryptographic operation.  This is a Galious field, and defined more generally as GF(p^n), and where p is a prime number. But, in most cases, p will be 2. Arithmetic operations Within a finite field, we limit the number of possible values in a group. As we have seen this can be a prime number and where we get a group from 0 to p-1, and where we can perform our mathematic operations with the (mod p) operation. And, so, even though we have a finite field, we still want our maths to still operate as normal. The rules for every element in the group is: Commutative law. This is where (a+b) equals (b+a), and (a*b) equals (b*a). Associative law. This is where a.(b.c) is equal to b.(a.c). Distributive law. This is where a(b+c) is equal to ab+ac. Additive and Multiplicative Identifies (0 and 1). This means that a+0=a, and a times 1 is equal to a. Additive and Multiplicative Inverses. This means that there is an additive inverse where there is a value of b for a so that a+b=0. For multiplicative inverse, there is a value of b for a so that a.b=0. Within our finite field in cryptography, we want all of these to work, so that we can reverse any operation that we can apply.  A Galois field Within a field, we can operate on values in the field using arithmetic operations. We can thus have an infinite field and where we could include all of the possible integers. A Galois field of GF(p^n) has p^n elements. Typically we use GF(2^n). And so GF(²⁴) has 16 values in the field. Let's say we have GF(2^n) and have a number a∈{0,…,2^n−1}, we can represent it as a vector in the form of a polynomial: a=a0+a_1 x+a_2 x²…a_{n−1} x^{n−1} If we use a_n∈{0,1}, this is exactly the same as representing a binary number modulo 2^n. In this, x^n represents bit position n and a_n is the value of the bit at position x^n. If a bit is a zero at a given position, it will be not included in the polynomial equation. First, let's talk about modulo-2 operations. For this, an addition is: 0+0 = 0, 0+1 = 1, 1+0 = 1, 1+1 =0 (an EX-OR gate) and for multiply we have: 0*0 = 0, 0*1 = 0, 1*0 = 0, 1*1 =1 (an AND gate) So, 1011 can be represented by x³+x+1 and 1010 is represented as x³+x. We can then perform arithmetic operations on these polynomial values. So, to add two values of 1010+1100 we can represent this as (x³+x)+(x³+x²) and which is x²+x as we are using modulo 2 addition, and where x³+x³=0. With modulo 2 addition, 0+0=0, 0+1=1, 1+0=1, and 1+1=1. An example of Galois Fields is within AES (Advanced Encryption Standard) and which uses a finite field GF(²⁸). With AES we operate on bytes (8 bits) in the form of b_7 b_6 b_5 b_4 b_3 b_2 b_1 b_0 and which are operated on a a polynomial of b_7x⁷+b_6x⁶+b_5x⁵+b_4x⁴+b_3x³+b_2x²+b_1x¹+b_0. Oh, and we don't have prime numbers any more, we have irreducible polynomials or primitive polynomial, and which are polynomials that cannot be factorized into polynomial factors. https://asecuritysite.com/gf/gf2 This operatives in a similar way to our (mod p) operation, and where we can reduce a result into the group, and just take the remainder from a division. A few examples Let's take a few examples to illustrate this. Example 1. For a=x²+x+1 (7–111b) and b=x+1 (3–011b) with a primitive of x⁴+x+1 (GF(2⁴)), for addition we get x² (4–100b), and for multiplication we get x3+1(9–1001b): Add=(x²+x+1)+(x+1)=x² Mult=(x²+x+1)×(x+1)=x³+x²+x²+x+x+1=x³+1 As we are using modulo 2 addition, then x+x=0 and x²+x²=0. As the power of the multiplication is not greater than x⁴ and above, there is no need to divide by the primitive polynomial. The following is a sample run: a: 1x^2 + 1x + 1b: 1x + 1b^{-1}: 1x^3 + 1x^2 + 1xp: GF(2^4) [1, 0, 0, 1, 1]Add: 1x^2Subtract: 1x^2Multiply: 1x^3 + 1Divide: 1x^3 + 1x^2 For the division, we determine the inverse of b and then multiply by a. In this case we have a×b^{−1} = (x²+x+1)×(x³+x²+x)=x⁵+x⁴+x³+x⁴+x³+x²+x³+x²+x=x⁵+x³+x. As we have a higher power that the field, we now need to divide by the primitive (x⁴+x+1) and get the remainder: __x______x^4 + x+1 | x^5+ x^3 + x x^5 + x^2 + x -------- x^3+ x^2 This the result of the divide is then the remainder value of x³+x². You can try the example here. Example 2. For a=x³ (8–1000b) and b=x²+1 (5–101b) with a primitive of x⁴+x+1 (GF(²⁴)), for addition we get x³+x²+1 (13–1101b), and for multiplication we get x³+x²+x (14–1110b). Add=(x³)+(x²+1)=x³+x²+1 Mult=(x³)×(x²+1)=x⁵+x³ Now we divide x⁵+x³ by the primitive (x⁴+x+1) and get the remainder: __x______x^4 + x+1 | x^5+x^3 x^5 +x^2+x -------- x^3+x^2+x Thus the result of the multiplication is the remainder of x³+x²+x. a: 1x^3b: 1x^2 + 1b^{-1}: 1x^3 + 1x + 1p: GF(2^4) [1, 0, 0, 1, 1]Add: 1x^3 + 1x^2 + 1Subtract: 1x^3 + 1x^2 + 1Multiply: 1x^3 + 1x^2 + 1xDivide: 1x^2 + 1x + 1 You can try the example here. Example 3. For a=x³+1 (9–1001b) and b=x²+1 (5–101b) with a primitive of x⁴+x+1 (GF(2⁴)), for addition we get x³+x² (12–1100b), and for multiplication we get x³+x+1 (11–1011b). Add=(x³+1)+(x²+1)=x³+x² Mult=(x³+1)×(x²+1)=x⁵+x³+x²+1 Now we divide x⁵+x³+x²+1 by the primitive (x⁴+x+1) and get the remainder: __x______x^4 + x+1 | x^5+ x^3+x^2 +1 x^5 +x^2+x -------- x^3+ x +1 Thus the result of the multiplication is x³+x+1 (11- 1011b). a: 1x^3 + 1b: 1x^2 + 1b^{-1}: 1x^3 + 1x + 1p: GF(2^4) [1, 0, 0, 1, 1]Add: 1x^3 + 1x^2Subtract: 1x^3 + 1x^2Multiply: 1x^3 + 1x + 1Divide: 1x^3 + 1x^2 You can try the example here. Example 4. For a=x²+x+1 (7–0111b) and b=x³+1 (5–1001b) with a primitive of x⁴+x+1 (GF(2⁴)), for addition we get x³+x²+x (14–1110b), and for multiplication we get x³+x (11–1010b). a: 1x^2 + 1x + 1b: 1x^3 + 1b^{-1}: 1xp: GF(2^4) [1, 0, 0, 1, 1]Add: 1x^3 + 1x^2 + 1xSubtract: 1x^3 + 1x^2 + 1xMultiply: 1x^3 + 1xDivide: 1x^3 + 1x^2 + 1x You can try the example here. Example 5. For a=x²+x (6–110b) and b=x⁴+x²+1 (21–10101b) with a primitive of x⁶+x⁵+x⁴+x³+x²+x (GF(2⁸)), for addition we get x⁴+1x+1 (19–10011b), and for multiplication we get x⁶+x⁵+x⁴+x³+x²+x. a: 1x^2 + 1xb: 1x^4 + 1x^2 + 1b^{-1}: 1x^4 + 1x^2 + 1x + 1p: GF(2^7) [1, 0, 0, 1, 1, 1, 0, 1]Add: 1x^4 + 1x + 1Subtract: 1x^4 + 1x + 1Multiply: 1x^6 + 1x^5 + 1x^4 + 1x^3 + 1x^2 + 1xDivide: 1x^6 + 1x^5 + 1x^4 + 1x With addition, there will be no need for the irreducible polynomial. You can try the example here. The code is: from galois_field import GFpn# Generating the field GF(2^4)# irreducible polynomial. (in this case, x^4 + x+1)import sysa=[1,1,0]b=[0,1,0]p=[1,0,0,1,1]if (len(sys.argv)>1): a=eval("["+sys.argv[1].replace(" ","")+"]")if (len(sys.argv)>2): b=eval("["+sys.argv[2].replace(" ","")+"]")if (len(sys.argv)>3): p=eval("["+sys.argv[3].replace(" ","")+"]")try: gf = GFpn(2,p )except Exception as e: print ("Error:" ,e) sys.exit()# Generating an element in GF(2^4)aval = gf.elm(a) # x^2+x+1bval = gf.elm(b) # x# Arithmetic operationsaval + bval # 1x^2 + 1aval - bval # 1x^2 + 1aval * bval # 1x^3 + 1x^2 + 1xaval / bval # 1x^3 + 1xprint ("a:tt",aval)print ("b:tt",bval)print ("b^{-1}: ",bval.inverse())print ("p:t",gf,p)print ("nAdd:tt",aval + bval)print ("Subtract:t",aval - bval)print ("Multiply:t",aval * bval)print ("Divide:tt",aval / bval) Irreducible Polynomials Within polynomials, the prime number equivalents are known as irreducible, as they cannot be factored. I will come back to irreducible polynomials later in this series, but for now, you can read up on them at: https://asecuritysite.com/gf/gf2 Conclusions And, so, you made it to the end of this podcast. If you managed to understand everything here, you deserve a crypto medal. If not — for most — you should try and read over and eventually, it will sink in — slowly at first, and then you will get bits and pieces of knowledge, and eventually, it will make sense. This is one of the reasons I love cryptography — and teach and research the field — as, every day, I learn, but my learning was so much deeper once I really understand why we did all these complex-looking things, and to get behind the maths. I hope I have not given you nightmares of school and with long multiplication and division, but if I have, I can calm you that the maths we use in cryptography is so much simpler, and where you just have to know how to count just a 0 and a 1. Life is so much more relaxed in crypto space. 

Wir springen in dieser Folge ins Frankreich des frühen 19. Jahrhunderts. Dort wird im Jahr 1811 ein Junge geboren, der im Laufe seines kurzen Lebens die moderne Mathematik nachhaltig prägen wird. Die entsprechende Anerkennung wird ihm dafür aber im Laufe seines kurzen und tragischen Lebens nicht zuteil. Wir sprechen in dieser Folge über Évariste Galois, Begründer der später nach ihm benannten Galoistheorie, dessen tragisches Leben unter mysteriösen Umständen viel zu früh endete. Die erwähnten Bücher sind "Évariste Galois: 1811-1832" von Laura Toti Rigatelli und "The equation that couldn't be solved" von Mario Livio. Das Episodenbild zeigt ein Porträt des 15-jährigen Galois. //Aus unserer Werbung Du möchtest mehr über unsere Werbepartner erfahren? Hier findest du alle Infos & Rabatte: https://linktr.ee/GeschichtenausderGeschichte NEU: Wer unsere Folgen lieber ohne Werbung anhören will, kann das über eine kleine Unterstützung auf Steady oder ein Abo des GeschichteFM-Plus Kanals auf Apple Podcasts tun. Wir freuen uns, wenn ihr den Podcast bei Apple Podcasts oder wo auch immer dies möglich ist rezensiert oder bewertet. Wir freuen uns auch immer, wenn ihr euren Freundinnen und Freunden, Kolleginnen und Kollegen oder sogar Nachbarinnen und Nachbarn von uns erzählt!

✨About Galois✨ Galois Capital is a long-standing crypto hedge fund run by a Bitcoin OG, Kevin Zhou. He goes over his highly controversial takes about Ethereum moving to PoS, base layer neutrality, his framework for reasoning about different classes of tokens, and where he believes the space is headed should there be an OFAC chain and permissionless chain paradigm.______________ 

YouTube Link: https://www.youtube.com/watch?v=27zHyw_oHSI Ben Goertzel is a computer scientist, mathematician, and entrepreneur. His work focuses on AGI, which aims to create truly intelligent machines that can learn, reason, and think like humans. This episode has been released early in an ad-free audio version for TOE members at http://theoriesofeverything.org. Sponsors: - Brilliant: https://brilliant.org/TOE for 20% off - *New* TOE Website (early access to episodes): https://theoriesofeverything.org/ - Patreon: https://patreon.com/curtjaimungal - Crypto: https://tinyurl.com/cryptoTOE - PayPal: https://tinyurl.com/paypalTOE - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - iTunes: https://podcasts.apple.com/ca/podcast... - Pandora: https://pdora.co/33b9lfP - Spotify: https://open.spotify.com/show/4gL14b9... - Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeveryt... LINKS MENTIONED: Center for future mind (FAU): https://www.fau.edu/future-mind/ Wolfram talk from Mindfest https://youtu.be/xHPQ_oSsJgg Singularity Net https://singularitynet.io/ TIMESTAMPS: 00:00:00 Introduction 00:02:37 How to make machines that think like people 00:10:03 GPT will make 95% of jobs obsolete 00:18:59 The 5-year Turing test 00:21:37 Definition of "intelligence" doesn't matter 00:26:15 Mathematical definition of self-transcendence 00:30:10 The 3 routes to AGI 00:44:19 Unfolding AI with Galois connections 00:49:32 Neuromorphic chips, hybrid architectures, and future hardware 00:54:05 Super AGI will overshadow humanity 00:56:33 Infinity groupoid 01:01:52 There are no limitations to AI development 01:05:00 Social intelligence is independent in OpenCog Hyperon systems 01:07:33 Embodied collaboration is fundamental to human intelligence 01:08:49 Algorithmic information theory and the Robot College Test Learn more about your ad choices. Visit megaphone.fm/adchoices

Puntata 452, in studio Romina (in Portogallo) e Marco (in Italia). In apertura parliamo di due recenti articoli su Astrophysical Journal che ipotizzano come l'energia oscura possa non essere una proprietà diffusa dello spazio tempo ma sia prodotta nei buchi neri supermassivi. Nella sezione esterna Leonardo intervista Luisa Brunori, giurista e storica del diritto che lavora al CNRS, a Parigi. Con lei parliamo del suo lavoro, e di come il metodo che si applica alle scienze sociali sia diverso da quello che si applica alle scienze cosiddette “dure”. Dopo un'altra terribile barza Romina racconta la storia del gioco del quindici nasconda un profondo segreto matematico legato al povero Galois e di come sia stata trovata per la prima volta una tasselazione aperiodica con una sola tessera.

Heute u.A. mit diesen Themen:Massenentlassung bei Zalando angekündigtVolocopter weitet Series-E-Runde aus„Nachhaltige“ Fonds schichten in Öl und Gas umMicrosoft kooperiert mit AnkrH&M und Remondis starten Joint VentureFintech-Investments steigen nur in AfrikaTencent bringt Meta Quest 2 nach ChinaWeniger chinesische Übernahmen in EuropaKrypto-Hedgefonds Galois Capital aufgelöst

Today's blockchain and cryptocurrency news  Bitcoin is down slightly at $24,848 Ethereum is down slightly at $1,708 Binance Coin is down slightly at $317 Hong Kong regulator to re-think ban on retail crypto trading. FSB addresses G20 saying stablecoins won't meet its high standards. Zipmex to restart customer withdrawals. OKX shows $8.6B in clean assets in their proof of reserves.  Galois capital to shutter its largest fund. Bitmain's BitFuFu to offer mining rig coupons. Learn more about your ad choices. Visit megaphone.fm/adchoices

Grant Sanderson is a mathematician who is the author of the YouTube channel “3Blue1Brown”, viewed by millions for its beautiful blend of visual animation and mathematical pedagogy. His channel covers a wide range of mathematical topics, which to name a few include calculus, quaternions, epidemic modeling, and artificial neural networks. Grant received his bachelor's degree in mathematics from Stanford University and has worked with a variety of mathematics educators and outlets, including Khan Academy, The Art of Problem Solving, MIT OpenCourseWare, Numberphile, and Quanta Magazine.       In this episode, we discuss the famous unsolvability of quintic polynomials: there exists no formula, consisting only of finitely many arithmetic operations and radicals, for expressing the roots of a general fifth degree polynomial in terms of the polynomial's coefficients. The standard proof that is taught in abstract algebra courses uses the machinery of Galois theory. Instead of following that route, Grant and I proceed in barebones style along (somewhat) historical lines by first solving quadratics, cubics, and quartics. Along the way, we present the insights obtained by Lagrange that motivate a very natural combinatorial question, which contains the germs of modern group theory and Galois theory and whose answer suggests that the quintic is unsolvable (later confirmed through the work of Abel and Galois). We end with some informal discussions about Abel's proof and the topological proof due to Vladimir Arnold.   Part I. Introduction 00:00:Introduction 00:52: How did you get interested in math? 06:30: Future of math pedagogy and AI  12:03: Overview. How Grant got interested in unsolvability of the quintic 15:26: Problem formulation 17:42: History of solving polynomial equations 19:50: Po-Shen Loh  Part II. Working Up to the Quintic 28:06: Quadratics 34:38 : Cubics 37:20: Viete's formulas 48:51: Math duels over solving cubics: del Ferro, Fiorre, Tartaglia, Cardano, Ferrari 53:24: Prose poetry of solving cubics 54:30: Cardano's Formula derivation 1:03:22: Resolvent  1:04:10: Why exactly 3 roots from Cardano's formula? Part III. Thinking More Systematically 1:12:25: Takeaways and Lagrange's insight into why quintic might be unsolvable 1:17:20: Origins of group theory? 1:23:29: History's First Whiff of Galois Theory 1:25:24: Fundamental Theorem of Symmetric Polynomials 1:30:18: Solving the quartic from the resolvent 1:40:08: Recap of overall logic Part IV. Unsolvability of the Quintic 1:52:30: S_5 and A_5 group actions 2:01:18: Lagrange's approach fails! 2:04:01: Abel's proof 2:06:16: Arnold's Topological Proof 2:18:22: Closing Remarks Further Reading on Arnold's Topological Proof of Unsolvability of the Quintic: L. Goldmakher. https://web.williams.edu/Mathematics/lg5/394/ArnoldQuintic.pdf B. Katz. https://www.youtube.com/watch?v=RhpVSV6iCko   Twitter: @iamtimnguyen   Webpage: http://www.timothynguyen.org   If you would like to support this series and future such projects:   Paypal: tim@timothynguyen.org Bitcoin: 33thftjoPTHFajj8wJFcCB9sFiyQLFVp8S Ethereum: 0x166a977F411d6f220cF8A56065D16B4FF08a246D

Last week, $60B in value was wiped from crypto in a few days. Not many saw the collapse of Luna coming - even fewer had the guts to bet on it. Since the start of the year, Galois Capital has been openly calling out for the impending fall of Luna and endured the barrage of hate comments until 8th May 2022 - the day that Luna started death spiraling. Kevin Zhou from Galois Capital shares with us: Why he was convinced LUNA would implode How he timed his short trade The 4 high conviction trades Galois has taken How Terra Luna can recover - and why its current plan doesn't work Host: Jason Choi @mrjasonchoi . Not financial advice.   ----------- Sponsors ------------- dYdX is the Leading Decentralized Exchange for trading perpetual contracts. Users enjoy low fees, deep liquidity, up to 20x more buying power and even earn $DYDX from trading. Trade on dYdX today at: https://trade.dydx.exchange   ----------- More Resources --------- Guest Galois Capital's Twitter: https://twitter.com/Galois_Capital   Blockcrunch Blockcrunch VIP: https://blockcrunch.substack.com Blockcrunch Twitter: https://twitter.com/theBlockcrunch Jason Choi's Twitter: https://twitter.com/mrjasonchoi   ------------ Disclosures ------------- Disclaimer: The Blockcrunch Podcast is an educational podcast and newsletter for informational purposes only. The host invest in cryptoassets actively and may hold assets discussed in the newsletter or podcast. All content contained within this podcast is intended for educational purposes only and should not be construed as any form of financial advice. The Blockcrunch Podcast, its associates and affiliates are not liable for any decisions third parties choose to make.    

Joey and Shpat talk with Ankush Desai, a Senior Applied Scientist at AWS and one of the primary developers behind the P language. They dig into uses for P, bug finding, and what it takes for formal methods researchers to build useful tools for applied engineers. Watch all our episodes on the Building Better Systems youtube channel.Ankush Desai: https://www.linkedin.com/in/ankush-desai/ Joey Dodds: https://galois.com/team/joey-dodds/Shpat Morina: https://galois.com/team/shpat-morina/ Galois, Inc.: https://galois.com/ Contact us: podcast@galois.com   

Aurélie Galois is a painter and a writer.While studying literature (at Sorbonne University) and history of art (at theSchool of the Louvre), she learned every traditional technique of painting,drawing, and engraving in a private studio in Paris. As a young editor in chief forseveral magazines and freelance writer, she started to paint the portraits ofthose she was interviewing. Faces and bodies become her favorite landscape,and erotism has also been a frequent inspiration.Christian Lima, is of Portuguese origin and was born in Paris and lived his entire life.As an entrepreneur, he owns two cheese shops called “Fromages et ramage”and is passionate about gastronomy and wines. He plays piano and pétanquefor many years and is renowned for being loud. He's a lover of music, cinema, and human beings.In this episode we discuss:•What are the culture codes in France•Why pleasure is the driving force behind their choices•How the French view love/ romance/ sensuality and why the stereotype isoutdated•Why it's important or true that the French like to show off with nice clothesand nice cars•Why French have a different kind of openness than the American opens•Love is friendship with sex•Why men are just as vulnerable as women in France•What sex means to the them•France is deep in culture- but is it deep in self-awareness•Why real artists are full of doubt and knowingness simultaneously•What other countries could learn from the French culture•Why a good conversation must have good food and good wine•Why French think they are the best and why the men have huge egosConnect with Aurelie:Instagram: @aureliegaloisWebsite: www.aureliegalois.comConnect with Ashley:Instagram: @intothedawnpodcast/ @ashleydrivardWebsite: www.ashleyrivard.com

Programa 02x134. El jove

In episode #18, we chat with Jordan Kyriakidis, co-founder and CEO of QRA Corp. QRA is developing QVScribe, a product that helps engineers write requirements and analyze those requirements to gauge whether they are framed well and capture the writer's intent.We discuss the impact of writing good, early-stage design requirements, how they impact your system, how to write better requirements, the state of natural language processing, and machine learning for this use case. We also talk about applying those in situations where you need explainability and where ambiguity is unacceptable.Watch all our episodes on the Building Better Systems youtube channel.Jordan Kyriakidis: https://www.linkedin.com/in/jordankyriakidis/Joey Dodds: https://galois.com/team/joey-dodds/Shpat Morina: https://galois.com/team/shpat-morina/ Galois, Inc.: https://galois.com/ Contact us: podcast@galois.com

José Calderón  is interviewed by Niki Vazou and Wouter Swierstra .  José has been working on functional programming at Galois and University of Maryland.  He tells us about his research background in many different continents, his experience with teaching compilers, the relation between music and functional programming and the "Recursive Programming Techniques" book that in the  1970s captured the essence of functional programming. 

本期 Feng 哥尽显 nerd 风采，连讲好几个故事：- 数学青年 Galois 20 岁发明群伦；21岁生日前决斗去世。是因为沟通能力不好？- 乔布斯创业合伙人 Woz 是天才工程师，但不善于推销自己 idea- 科学论文的未来：Jupyter Notebook- Feng 哥分享：Demon Under the Microscope - 二战前科学家如何研发抗生素- 大家学习微积分的顺序都错啦- Feng 哥是如何找书找论文的- 【简单心理】正在大规模招聘，特别是熟悉给企业提供服务的 bymmers，发简历到 hr[at]jiandanxinli[dot]com【关于 BYM】BYM 探讨社会、女性、科技的话题。主创 brofeng、简里里，每周更新话题建议、合作邮件发送 bymclub@outlook.com关注微博：简里里、bymbrofengBYM 社区请关注微博话题 #ilovebymmers#

In this episode we dive into Isabelle, the interactive theorem prover based on Higher Order Logic directly from someone who spent quite some time hacking on its internals. Me and Daniel also talk about Mizar, Isar, the seL4, and how it is formalized. Torwards the end of the episode we also talk a little about his current work on the binary analysis of Aarch32 Arm Archtecture at Galois.

In this episode talk with Ashvni Narayanan, a Graduate Student at the London School of Geometry and Number Theory working under the auspice of Prof. Kevin Buzzard. Ashvni studied Galois representations of elliptic curves during her Master's at the University of British Columbia, Vancouver advised by Prof. Sujatha Ramadorai, and completed a Bachelor's in Mathematics at the Indian Statistical Institute, Bangalore. Ashvni currently works on formalizing algebraic number theory in a program called Lean. We converse about her incredible random walks through life and science; her terrific mentors who've inspired her; automating mathematical theorem proving: nature of research and collaborations in a (post) pandemic world; taking care of one's mental, physical, and emotional health in academia; the fantastic Hmm podcast she started during the lockdown; and many more things! Resources to learn about the Xena Project and Lean: https://xenaproject.wordpress.com/useful-links/ https://leanprover-community.github.io/learn.html