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Bitcoin Elliptic Curve – Efficiency Or Some Secret Backdoor Entry?

World’s renowned cryptographers believes that Satoshi Nakamoto chose Bitcoin’ [BTC] elliptic curve either for its efficiency or because it’s going to offer some secret backdoor.

A Bitcoin public key is created by employing elliptic-curve cryptography to the private key. One can easily create a public key from the private key, but it’s impossible to travel back in the reverse direction. Unless, of course, Bitcoin’s elliptic curve is compromised.

Several cryptocurrency experts have also noticed that Bitcoin’s choice of secp256k1 elliptic curve was unusual for its time, because it wasn’t yet well researched, including the leading cryptographers, Tatsuaki Okamoto, about this unusual choice. Okamoto is director of the Cryptography & Information Security Lab at NTT Research.

Efficiency Or Some Secret Backdoor Entry

In line with Okamoto, there are considerably 2 alternative explanations for this choice: Either Satoshi picked this as it offers greater efficiency or because it’s going to have serve as some secret backdoor. Of course, Okamoto underlined that these are just two logical hypotheses, as he has no way of knowing what Satoshi was thinking at the time:

1. The Koblitz curve is specifically designed for faster scalar multiplications. Hence the [signing, verifying and key generation] operations on Secp256k1 are faster than those on Secp256r1.

2. Although the Secp256r1 curve was announced to be randomly selected, there could still exist some suspicion that some backdoor could be secretly found out within the curve parameters. In contrast, the Koblitz curve parameters are mathematically determined, and there’s little possibility for setting such a backdoor.”

Okamoto is impressed with the way the Bitcoin creator was successfully able to combine several cryptographic techniques – like hash chains, Merkle trees and elliptic curves – to make the world’s first decentralized currency:

“I think it’s a revolutionary invention, the primary decentralized currency, and its core technology blockchain, is to have an excellent impact on our society.”

Still A Big Confusion Between The Community Renowned Developers

Bitcoin Core developer Wladimir van der Laan also added that he doesn’t know why Satoshi chose this particular curve. He also found that if someone has discovered a vulnerability, they have not progressed to announce it anyways:

“I don’t have any idea why Satoshi chose this particular curve, they have offered no rationale anywhere [it seems, in hindsight, to possess been a reasonably good selection though]. Moreover, if Secp256r1 features a vulnerability, nobody has progressed yet to announce their discovery. While on the hand, keeping this discovery to themselves could yield a multi-billion dollar reward.”

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