You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has 2 very powerful applications: Perhaps the most powerful cryptographic technology to come out of the last decade is general-purpose succinct zero knowledge proofs, usually called zk-SNARKs ("zero knowledge succinct arguments of knowledge"). A zk-SNARK allows you to generate a proof that some computation has some particular output, in such a way that the proof can be verified extremely quickly even if the underlying computation takes a very long time to run. The "ZK" part adds an additional feature: the proof can keep some of the inputs to the computation hidden.

You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has two very powerful applications:

1. Scalability: if a block takes a long time to verify, one person can verify it and generate a proof, and everyone else can just quickly verify the proof instead
2. Privacy: you can prove that you have the right to transfer some asset (you received it, and you didn't already transfer it) without revealing the link to which asset you received. This ensures security without unduly leaking information about who is transacting with whom to the public.

But zk-SNARKs are quite complex; indeed, as recently as in 2014-17 they were still frequently called "moon math". The good news is that since then, the protocols have become simpler and our understanding of them has become much better. This post will try to explain how ZK-SNARKs work, in a way that should be understandable to someone with a medium level of understanding of mathematics.

Why ZK-SNARKs "should" be hard

Let us take the example that we started with: we have a number (we can encode "cow" followed by the secret input as an integer), we take the SHA256 hash of that number, then we do that again another 99,999,999 times, we get the output, and we check what its starting digits are. This is a huge computation.

A "succinct" proof is one where both the size of the proof and the time required to verify it grow much more slowly than the computation to be verified. If we want a "succinct" proof, we cannot require the verifier to do some work per round of hashing (because then the verification time would be proportional to the computation). Instead, the verifier must somehow check the whole computation without peeking into each individual piece of the computation.

One natural technique is random sampling: how about we just have the verifier peek into the computation in 500 different places, check that those parts are correct, and if all 500 checks pass then assume that the rest of the computation must with high probability be fine, too?

Such a procedure could even be turned into a non-interactive proof using the Fiat-Shamir heuristic: the prover computes a Merkle root of the computation, uses the Merkle root to pseudorandomly choose 500 indices, and provides the 500 corresponding Merkle branches of the data. The key idea is that the prover does not know which branches they will need to reveal until they have already "committed to" the data. If a malicious prover tries to fudge the data after learning which indices are going to be checked, that would change the Merkle root, which would result in a new set of random indices, which would require fudging the data again... trapping the malicious prover in an endless cycle.

But unfortunately there is a fatal flaw in naively applying random sampling to spot-check a computation in this way: computation is inherently fragile. If a malicious prover flips one bit somewhere in the middle of a computation, they can make it give a completely different result, and a random sampling verifier would almost never find out.

It only takes one deliberately inserted error, that a random check would almost never catch, to make a computation give a completely incorrect result.

If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? There is a clever solution.

The attack began around 10:30 PM +UTC on January 8th.

Peckshield spotted it first, then an official announcement came shortly after.

We’ve said it before; if established companies holding millions of dollars of users’ funds can’t manage their own hot wallet security, what purpose do they serve?

The Unique Selling Proposition (USP) of centralised finance grows smaller by the day.

The official incident report states that 7.94M USD were stolen in total, and that deposits and withdrawals to the platform have been paused.

LCX hot wallet: 0x4631018f63d5e31680fb53c11c9e1b11f1503e6f

Hacker’s wallet: 0x165402279f2c081c54b00f0e08812f3fd4560a05

Stolen funds:

• 162.68 ETH (502,671 USD)
• 3,437,783.23 USDC (3,437,783 USD)
• 761,236.94 EURe (864,840 USD)
• 101,249.71 SAND Token (485,995 USD)
• 1,847.65 LINK (48,557 USD)
• 17,251,192.30 LCX Token (2,466,558 USD)
• 669.00 QNT (115,609 USD)
• 4,819.74 ENJ (10,890 USD)
• 4.76 MKR (9,885 USD)

**~$1M worth of $LCX remains in the address, along with 611k EURe which has been frozen by Monerium.

The rest, a total of 1891 ETH (~$6M) was sent to Tornado Cash.**

Why can’t they keep private keys private?

Is it really that difficult for a traditional corporate structure to maintain good practice?

CeFi hacks leave us with little to say - we can only go on what the team chooses to tell us.

Next time, they can write this article themselves.

See below for a template.

Giving through a donor-advised fund can be tax-efficient. Using a donor-advised fund can reduce your tax liability while increasing your charitable impact.

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Avoid a Windfall Tax Year.

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Make a contribution to reduce or eliminate capital gains.

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Using Appreciated Stock as a Gift

Donating appreciated stock directly to a DAF rather than liquidating it and donating the proceeds reduces philanthropists' tax liability by eliminating capital gains tax and lowering marginal income tax.

In the example below, a donor has $100,000 in long-term appreciated stock with a cost basis of $10,000:

Using a DAF would allow this donor to give more to charity while paying less taxes. This strategy often allows donors to give more than 20% more to their favorite causes.

The information provided here is general and educational in nature. It is not intended to be, nor should it be construed as, legal or tax advice. NPT does not provide legal or tax advice. Furthermore, the content provided here is related to taxation at the federal level only. NPT strongly encourages you to consult with your tax advisor or attorney before making charitable contributions.