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E.g. as @CKRaju14 has shown, there is no real proof of "Euclid", and his "proofs" were made up much later.... https://t.co/GB9xPixPYe As Prof....Raju has shown even the notion of "proof" changed completely as the Church theologized math and made...https://t.co/UKLRJFwZfc Here is a good article from Prof. Raju on "axiomatic proofs."...https://t.co/INOFScL7ys As Prof Raju argues, in present-day mathematics, the dogma that deductive proofs
3 years ago
• A zk proof example
• Scalability and Privacy 1. What are zk proofs?...A zk proof is a cryptographic proof that allows someone to prove that they possess specific information...A zk Proof Example
The concept of zk proofs can be hard to wrap you head around....a proof of this computation....That was your intro to zk proofs.
3 years ago
A merkle proof is a cryptographic proof that some key-value pair exists in a data store....We might call it a “proof of inclusion”....A range proof is a proof that some range of keys exist side-by-side in a merkle tree....Hence they succeeded in forging a merkle proof....As part of this, it explicitly *rejected* range proofs. There are no range proofs in ICS23.
3 years ago
(1/13) Cryptography Basics: Zero-Knowledge Proofs
To keep @ethereum decentralized & fair, we keep...(ZK-proof) is a way of proving a statement is valid without revealing it....A ZK-proof relies on verifiable algorithms that take input data and return "true" or "false" without...After processing, that chain can return the results to mainnet with a ZK-proof. (11/13) ZK-technology...Generating proofs is extremely challenging and computationally expensive.
3 years ago
Let's break it all down: (4/17) zkSNARKs are a proof system that anyone can use to prove any statement...https://t.co/6dyjKi6nZ4 (8/17) Non-interactiveness is important because the prover can generate one proof...)
But we can use 'argument' and 'proof' interchangeably for this thread (11/17) Put together, zkSNARK...is a proof system using which a prover (P) can prove the possession of some information to a verifier...is small
- proof fails if V or P are dishonest (12/17) And this proof system unlocks some mind-blowing
3 years ago
Zero-knowledge proofs have a lot of applications beyond blockchains.
🧵👇 Passwordless Authentication...:
Never get passwords leaked again by sending a "proof of password" to a site instead of the password...Identity Verification:
Use a proof of an SSN/ID number instead of trusting the other party to keep it...Voting:
Proofs can enable blind digital voting while retaining security.
3 years ago
With succinct proofs, zkBridge guarantees strong security without external assumptions....generation and low on-chain proof verification cost are required....We use a novel 2-layer distributed recursive proof system to satisfy both properties when proof circuit..., to reduce on-chain verification cost, we use recursive proof in the second layer....Through the 2-layer recursive proof scheme, we perfectly achieve fast proof generation and low verification
3 years ago
'#Allopathy' had ' #scientific' proof that #remdesivir cured vividh.
2....Allopaths published the proof as well.
3....Now Allopathy has scientific proof that remdesivir doesn't cure covid.
4....Allopaths have published those proofs as well.
4 years ago
So let's start..... https://t.co/dcmqlsDW0g Proof 1) Rig Ved 1.84.15 mentions reflection of Sunlight...on the moon. https://t.co/PHfhvo9Ql5 Proof 2) Rig Ved 1.50.4 Speed of Light as per Sayan Bhashya. https...://t.co/JOhd5Da54E Proof 3) Vedant, Chandogya Upanishad of Sam Ved mentions Plants as living beings and...science proved it recently i e 1901, Even Mahabharat has similar proofs (SS attached). https://t.co/...fiqo45FVE2 Proof 4) Rig Ved1.64.13 mentions Rotation of Sun & Sun moves in its orbit.
2 years ago
Take the problem of proof verification....That is, they write their proofs using informal notation, rather than via a proof assistant.
https://.../Odb1w2rCvV This practice is somewhat problematic because it's hard to verify informal mathematical proofs...That means that it may soon become possible to quickly verify whether a controversial proof is valid,...That's because invalid, hallucinated proofs can efficiently be verified as invalid by proof assistants
2 years ago
Worse, it prohibits empirical proofs....Why did europeans prohibit empirical proofs?...Apparently they believed empirical proofs are fallible....Will prohibition of empirical proofs make science superior? No!...Then why does european math prohibit empirical proof?
5 years ago
The only way forward is for CEXs to provide PROOF OF SOLVENCY🧵 https://t.co/v44pUiVl6B First, here's...A lot of people are suggesting that the exchanges provide Proof of Reserves
@cz_binance even mentioned...that Binance would soon be providing their Merkle tree proof https://t.co/3tKnH8awvA But proof of reserves...back to the customers Solvency means:
Assets - Liabilities >= 0
Thus, we need CEXs to provide "Proof...3rd party auditors to verify solvency is not enough What we CAN rely on instead, is a cryptographic proof
3 years ago
(Zero-Knowledge Ethereum Virtual Machine):
VM that executes smart contracts through zero-knowledge proof...information itself
The unique design makes it challenging to build EVMs compatible with zero-knowledge proofs...zkEVMs are machines transitioning between states of a program’s operations
zkEVM goes further to define proof..."
/5 zkEVMs initiate zero-knowledge proofs to verify various components in each computation:
• Bytecode...circuit, and the verifier contract
Each section contributes to zkEVM operation from execution and proof
3 years ago
Zero-Knowledge Proofs
STARKs vs SNARKs
A ground-up guide🧵 https://t.co/o7hzapoTdI STARKs and SNARKs...two genius technologies that use different approaches to achieve the same objective:
Zero-Knowledge Proofs...zk proofs enable one party to prove to another party that they know something without revealing the...Setup
SNARKs rely on a trusted party to initially create secret keys that are used for generating proofs...computation = higher gas fees
Is the higher proof size worth it?
3 years ago
At @succinctlabs we believe the future of interoperability is proof-based: https://t.co/grqkKbyFI9....7/ At @succinctlabs we've spent the past few months working on this—we call it "proof of consensus":...using SNARKs to generate succinct validity proofs of consensus....9/ We believe the future of interoperability is proof-based....of consensus + validity proofs of execution make it possible for an on-chain smart contract to verify
3 years ago
your data
But it turns out that there's a magic weapon that destroys all the risk
Zero-Knowledge Proofs...Here's how it works: A zero-knowledge proof (zk proof) is a cryptographic proof that allows someone to...reveal zero spoilers about the show to Vikas In other words, Payal is able to provide a zero-knowledge proof...(of access to HOTD episodes) to Vikas
zk-proofs have 3 essential properties: 1....balance
- proving your identity without sharing personal details like address, phone number, etc zk-proofs
3 years ago
(9/17) If the optimistic rollup transactions were not executed correctly, any user can submit a proof...neat solution, but they mean that the rollup at a particular block isn’t finalized until the fraud proof...(11/17) Zero knowledge rollups (like @zksync and @StarkWareLtd's StarkNet) rely on zero knowledge proofs...(12/17) Rollups sound like a pretty natural application of these proofs, right?...With zero knowledge rollups, a proof is submitted along with the transaction data, the proof is verified
4 years ago
Mina is able to stay a fixed size by using a self-referencing series of cryptographic proofs. https:/...Zero-knowledge proofs are a way to prove something with the verifier learning no information other than...the statement is true. 3/ SNARKs are a type of zero-knowledge proof....MinaProtocol uses a type of zk-SNARK called Pickles that can recursively refer to itself, thus creating proofs...of proofs and keeping the blockchain a fixed size. https://t.co/zKzOrpoEyi 4/ @MinaProtocol has been
3 years ago
(zero-knowledge proof) hardware accelerators, such as GPUs, FPGAs, and ASICs, to speed up the proof generation...Then generated proof for each of the zkEVM circuit
3....Uses proof aggregation to to combine multiple zkEVM circuits to a single proof....blocks, an aggregation task is dispatched to another Roller to combine k block proofs.. 16/ .....(k here signifies the number of blocks) into a single aggregate proof.
2 years ago
In order to withdraw assets, a user submits the Merkle proof for that asset. (8/23) Plasma chains are...The answer: Zero-Knowledge Proofs. https://t.co/Yv9YJmeCOC (17/23) ZK-proofs are a category of mathematical...proofs that allows one party (prover) to prove to another party (verifier) that a statement is true...Here's what you need to know: proof generation is long and hard, but proof verification is quick and...It will then submit the batch and the proof to a verifying contract on-chain.
3 years ago