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[Mirror] Zk-SNARKs: Under the Hood

Time Stamp: February 2, 2024 11:10 AM - Modified On: February 2, 2024 - Published By:

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Vitalik Buterin via the Vitalik Buterin Blog This is a mirror of the post at https://medium.com/@VitalikButerin/zk-snarks-under-the-hood-b33151a013f6 This is the third part of a series of articles explaining how the technology behind zk-SNARKs works; the previous articles on quadratic arithmetic programs and elliptic curve pairings are required reading, and this article will assume knowledge of both concepts. Basic knowledge of what zk-SNARKs are and what they do is also assumed. See also Christian Reitwiessner's article here for another technical introduction. In the previous articles, we introduced the quadratic arithmetic program, a

[Mirror] Exploring Elliptic Curve Pairings

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Time Stamp: February 2, 2024 11:01 AM - Modified On: February 2, 2024 - Published By:

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Republished By Plato

Vitalik Buterin via the Vitalik Buterin Blog This is a mirror of the post at https://medium.com/@VitalikButerin/exploring-elliptic-curve-pairings-c73c1864e627 Trigger warning: math. One of the key cryptographic primitives behind various constructions, including deterministic threshold signatures, zk-SNARKs and other simpler forms of zero-knowledge proofs is the elliptic curve pairing. Elliptic curve pairings (or "bilinear maps") are a recent addition to a 30-year-long history of using elliptic curves for cryptographic applications including encryption and digital signatures; pairings introduce a form of "encrypted multiplication", greatly expanding what elliptic curve-based protocols can do. The purpose of this

[Mirror] Quadratic Arithmetic Programs: from Zero to Hero

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Time Stamp: February 2, 2024 10:41 AM - Modified On: February 2, 2024 - Published By:

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Republished By Plato

Vitalik Buterin via the Vitalik Buterin Blog This is a mirror of the post at https://medium.com/@VitalikButerin/quadratic-arithmetic-programs-from-zero-to-hero-f6d558cea649 There has been a lot of interest lately in the technology behind zk-SNARKs, and people are increasingly trying to demystify something that many have come to call "moon math" due to its perceived sheer indecipherable complexity. zk-SNARKs are indeed quite challenging to grasp, especially due to the sheer number of moving parts that need to come together for the whole thing to work, but if we break the technology down piece by piece then

The promise and challenges of crypto + AI applications

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Time Stamp: January 31, 2024 4:49 AM - Modified On: January 31, 2024 - Published By:

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Author: Vitalik Buterin via the Vitalik Buterin Blog Special thanks to the Worldcoin and Modulus Labs teams, Xinyuan Sun, Martin Koeppelmann and Illia Polosukhin for feedback and discussion. Many people over the years have asked me a similar question: what are the intersections between crypto and AI that I consider to be the most fruitful? It's a reasonable question: crypto and AI are the two main deep (software) technology trends of the past decade, and it just feels like there must be some kind of connection between the two. It's

GroundUp Studios Launches Creative Council of Producers to Accelerate Web3 Music and Art in Asia

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Time Stamp: May 17, 2023 5:48 AM - Modified On: May 17, 2023 - Published By:

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Award-winning producers Derrick Sepnio, Fergus Chow and Jae Chong join Creative Council - with more to come Creative Council's main goal is to support member community in their music career development Producers aim to share professional tips on the music industry; provide insights and mentorship on music creation and production; identify and recruit member artists for potential collaborations and more HONG KONG, May 17, 2023 - (ACN Newswire) - GroundUp Studios, a forward-thinking, web3-focused music label today announced its Creative Council of professional veterans in the music industry, to accelerate

Time is Money

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Time Stamp: March 7, 2023 2:55 PM - Modified On: March 7, 2023 - Published By:

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When talking about Central Bank Digital Currencies (CBDCs) most commentators focus on their lack of privacy and ability to be blocked or controlled. Although this dystopian narrative is highly dynamic, in reality that’s not the aspect that central banks are attracted to. They’re interested in CBDCs due to their ability to solve many of the latency issues around cross-border settlements. During a recent discussion with a senior banker in Turkey, the topic of cryptocurrencies naturally arose. Their view was like many in the banking sector who aren’t directly involved with

[Mirror] Zk-SNARKs: Under the Hood

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