I just published a new post on "Elliptic Curves".

Elliptic curves are smooth plane curves defined by cubic polynomials with no repeated roots, and have applications in cryptography, error-correcting codes, and number theory. The group law on elliptic curves allows efficient computation of points and forms the basis of cryptographic algorithms such as Elliptic Curve Cryptography (ECC). Understanding the properties and applications of elliptic curves contributes to a deeper understanding of algebraic structures and opens up avenues for practical and theoretical research.