I am learning Algebraic Geometry(AG) from Shafarevich's book. I know little bit cryptography. I know about RSA algorithm.
Few days back, through some random source, I came to know that AG has lot of application in Cryptography. Can someone explain some basic applications of AG concepts in Cryptography? I want to write a exposition on this topic in future.
There are two areas I can think of: elliptic curves as mentioned in the comments, and error-correcting codes. In the second example, error-correcting codes can be made to correspond to algebraic varieties. In terms of cryptography, one can therefore try to study and use the resulting codes for code-based cryptography.