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@ -56,7 +56,7 @@ ECC does not receive much attention in this tutorial. That's because this tutori
**_What is an Elliptic Curve?_** An elliptic curve is a geometric curve that takes the form `y`<sup>`2`</sup> = `x`<sup>`3`</sup>` + ax + b`. A specific elliptic curve is chosen by selecting specific values of `a` and `b`. The curve must then be carefully examined to determine if it works well for cryptography. For example, the secp256k1 curve used by Bitcoin is defined as `a=0` and `b=7`. **_What is an Elliptic Curve?_** An elliptic curve is a geometric curve that takes the form `y`<sup>`2`</sup> = `x`<sup>`3`</sup>` + ax + b`. A specific elliptic curve is chosen by selecting specific values of `a` and `b`. The curve must then be carefully examined to determine if it works well for cryptography. For example, the secp256k1 curve used by Bitcoin is defined as `a=0` and `b=7`.
Any line that intersects an elliptic curve will do so at either 1 or 3 points ... and that's the basis of elliptic-curve cryptography. Any line that intersects an elliptic curve will typically so at 3 points (absent a few cases for infinity and intersections) ... and that's the basis of elliptic-curve cryptography.
**_What are Finite Fields?_** A finite field is a finite set of numbers, where all addition, subtraction, multiplication, and division is defined so that it results in other numbers also in the same finite field. One simple way to create a finite field is through the use of a modulo function. **_What are Finite Fields?_** A finite field is a finite set of numbers, where all addition, subtraction, multiplication, and division is defined so that it results in other numbers also in the same finite field. One simple way to create a finite field is through the use of a modulo function.