If you don’t know what an elliptic curve is or why it matters in cryptography, let me break it down for you:
An elliptic curve is a mathematical object that looks like this: y2 = x3 + 7 (a = 0, b = 7)
Its basically just a fancy way to draw lines on a graph. But in the world of cryptography, these curves are used for something much more important than doodling they’re used to secure our data and protect our privacy!
Now let me introduce you to secp256k1: this is the specific elliptic curve that Bitcoin uses for its public-key cryptography. It has some pretty cool properties, like being especially efficient to compute on (which is why it’s gaining in popularity). But what really sets it apart from other commonly used curves is how it was constructed secp256k1 wasnt randomly generated; instead, it was carefully crafted with a specific purpose in mind.
So let me break down the parameters of this curve for you:
– Equation y2 = x3 + 7 (a = 0, b = 7) This is just the equation that defines our fancy line on a graph. The values of ‘a’ and ‘b’ are specific to secp256k1.
– Prime Field (p) = 2256 232 977 This refers to the size of the field that were working with, which is a fancy way of saying how many possible values there are for our x and y coordinates on this curve. In secp256k1’s case, there are over 4 billion (that’s right, BILLION) possible points on this curve!
– Base point (G) = (79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798, 483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8) This is the starting point for our curve, which we use to generate all of the other points on it. In secp256k1’s case, this base point has some pretty cool properties that make it especially useful in cryptography (but I wont bore you with those details).
– Order (n) = FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 This is the number of points on our curve that are ‘special’ in some way. In secp256k1, this value is over 7 billion (that’s right, BILLION)!
If you want to learn more about how these curves are used in cryptography or how theyre generated, I highly recommend checking out some of the resources below:
– Standards for Efficient Cryptography (SEC) This is where secp256k1 was first defined and described. It’s a great resource if you want to learn more about elliptic curves in general!
– Bitcoin Wiki The wiki has some great resources on how secp256k1 is used in Bitcoin, as well as other cryptographic concepts that are important for understanding the technology behind this amazing digital currency.
If you want to learn more about how these curves are used in cryptography or how theyre generated, I highly recommend checking out some of the resources below:
– Standards for Efficient Cryptography (SEC) This is where secp256k1 was first defined and described. It’s a great resource if you want to learn more about elliptic curves in general!
Bitcoin Wiki The wiki has some great resources on how secp256k1 is used in Bitcoin, as well as other cryptographic concepts that are important for understanding the technology behind this amazing digital currency.
So if you’re interested in learning more about elliptic curves and their role in cryptography (and who isn’t?!), I highly recommend checking out these resources! And if you have any questions or comments, feel free to leave them below I’d love to hear from you!