Elliptic Curve Cryptography: finite fields and discrete logarithms
Great reading for Crypto assignments
This post is the second in the series ECC: a gentle introduction.
In the previous post, we have seen how elliptic curves over the real numbers can be used to define a group. Specifically, we have defined a rule for point addition: given three aligned points, their sum is zero (P + Q + R =…). We have derived a geometric method and an algebraic method for computing point additions.
Now we will restrict our elliptic curves to finite fields, rather than the set of real numbers, and see how things change.
The field of integers modulo p
A finite field is, first of all, a set with a finite number of elements. An…
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