Christopher Wolf: Using Multivariate Quadratic Polynomials in Public Key Cryptography

In public key cryptography, we ease the key distribution problem by splitting the secret key into one public and one private part. Hence, we do no longer need one secret key for each communication channel but only private key per receiver, i.e., we reduce the overall number of secret information from O(n^2) to O(n) with n the number of participants in the communication network. To derive secure public key systems, we need to base them on a hard problem, e.g., factoring for the RSA system or discret log for elliptic curve systems. In this talk we introduce the use of multivariate quadratic polynomials over (small) finite fields in public key cryptography and give an overview about important constructions in this area.