What is secp256r1?

A tale of two elliptic curves This curve has a sibling, secp256r1. Both are elliptic curves over a field zp where p is a 256-bit prime (though different primes for each curve). The “k” in sepc256k1 stands for Koblitz and the “r” in sepc256r1 stands for random.

What is the difference between secp256k1 and secp256r1?

The main difference between secp256k1 and secp256r1 is that secp256k1 is a Koblitz curve, while secp256r1 is a prime field curve. Koblitz curves are generally known to be a few bits weaker than prime field curves, but when talking about 256-bit curves, it has little impact.

What is NIST p256?

ECDSA P-256, a prime curve that has been used extensively in critical infrastructure projects, is being used as the Elliptical Curve Digital Signature Algorithm for AS-path signing and verification in the BGPSEC protocol [10].

What is secp256k1?

Secp256k1 is the name of the elliptic curve used by Bitcoin to implement its public key cryptography. When a user wishes to generate a public key using their private key, they multiply their private key, a large number, by the Generator Point, a defined point on the secp256k1 curve.

What’s the difference between secp256k1 and SECP 256R1?

The other difference is how the parameters have been chosen. In secp256r1 they are supposedly from random numbers, however, it is impossible to prove that’s really the case.

Why does secp256k1 have an additional automorphism?

secp256k1 have an additional automorphism because it belongs to a special class of elliptic curves, sometimes referred to as Koblitz (although this has lead to some confusion, and some people have mistakenly called it a binary curve), which have an additional automorphism.

Can a quantum computer backdoor the secp256r1 curve?

The few extra bits of security secp256r1 has won’t matter unless you happen to own e.g. a moderately sized quantum computer that can just manage one but not the other. It would have been easier to backdoor the secp256r1 curve, but on the other hand, Koblitz curves as a class could be completely weak in some way not currently known.

Is the secp256k1 curve more secure than the Koblitz curve?

I would like to take it away from Bitcoin and into the general cryptographic question: is secp256r1 indeed more secure in some sense than secp256k1? The main difference is that secp256k1 is a Koblitz curve, while secp256r1 is not.