Types of Cryptography

RSA Encryption:
A message is encrypted using the intended recipients public key,which the recipient then decrypts with a private key.The difficult of computing the private key from the public key is connected to the hardness of prime factorization.

Code Based Cryptography:
The private key is associated with an error correcting code and the public key with a scrambled and erroneous version of the code.Security is based on the hardness of decoding a general linear code.

Lattice Based Cryptography:
Security is related to the difficulty of finding the nearest point in a lattice with hundred of spatial dimensions(where the lattice point is associated with the private key),given an arbitrary location in space(associated with the public key).

Diffie-Hellmand Key Exchange:
Two parties jointly establish a shared secret key over an insecure channel they can then use for encrypted communication. The security of the secret key relies on the hardness of the discrete logarithm problem.

Multivariate Cryptography:
These schemes rely on the hardness of solving systems of multivariate polynomial equations.

Eliptic Curve Cryptography:
Mathematical properties of elliptic curve are used to generate public and private keys.The difficulty of recovering the private key from the public key is related to the hardness of the elliptic curve discrete logarithm problem.