For anyone curious about elliptic curves, i wrote a simple thread back in 2023 exploring the K1 vs R1 problem through RIP-7212 (ex EIP-7212 proposal)
HOLY SHIT.
For crypto, this is one of the most insane posts of the year, but I'm guessing most people don't understand it.
Let me explain...
Bitcoin's accounts, and subsequently Ethereum's (and therefore every other EVM chain's), are built on a specific elliptic curve called secp256k1.
secp256k1 is a different elliptic curve from the one used across nearly every modern hardware device, including iPhones.
Modern devices mostly use a different curve called secp256r1, which is usually referred to as P-256 - one of the curves investigated in the article.
This mismatch has made it sooo difficult in the past to integrate crypto accounts natively into the security systems of modern hardware.
For example, Apple's Secure Enclave natively supports P-256, not secp256k1.
This has prevented crypto accounts from being able to use the same hardware protection as things like Apple Pay.
Same goes for the web with passkeys - WebAuthn uses P-256 signatures, which means Ethereum accounts using secp256k1 can't use them natively either.
But why did Satoshi do this?
The main theory for choosing secp256k1 was distrust of the P-256 curve - i.e. he thought there was an NSA backdoor.
A "backdoor" here basically means a secret, intentional weakness in the curve that would allow the NSA to exploit it and access private keys.
This was because P-256 was created with involvement from the NSA...
And the NSA provided a mysterious "seed" used to generate one of the curve's parameters without explaining where that seed came from.
This eventually transformed into a ~25-year-old mystery with a 5-figure reward for finding where this seed came from.
Claude figured it out in less than 30 mins.
And the best part is its internal thinking was: "Hmm wait... is it suspicious that such an obvious thing wasnโt discovered in 25 years?"
The solution was stupidly simple - just the time the curve was created, put into a specific random number generator function.
This doesn't 100% prove there's no backdoor yet, but it provides strong evidence that this seed wasn't secretly engineered by the NSA.
And Claude did this with "just a simple prompt" in under 30 minutes.