# Forskning

## Erik Mårtensson, Doktorand

**Introduction to my research**

Asymmetric cryptography is based on the difficulty of solving the mathematical problems of factoring integers or finding discrete logarithms. After decades of intense research there are still no efficient algorithms for solving these problems in the general case on a classical computer.

However, having access to a large-scale quantum computer, both of these problems can be solved in polynomial time using Shor's algorithm. Post-quantum cryptography deals with the (potential) future threat of quantum computers by basing asymmetric cryptography on other mathemtical problems.

In lattice-based cryptography one promising mathematical problem to base cryptosystems on is the Learning with Errors problem (LWE).

In code-based cryptography, the underlying mathematical problem is decoding general linear codes. One famous cryptosystem in code-based cryptography is the McEliece system.

My research is about developing better algorithms for solving some of the underlying mathemtical problems in lattice-based and code-based cryptography. For more details about my research see my Publications.

For a quick introduction to post-quantum cryptography in general see Wikipedia. For a longer introduction I recommend this book.

**News 2021**

I defended my PhD thesis in January 2021. The thesis can be found here.

Since March 2021 I am working as a Postdoctoral Research Fellow in applied cryptology at University of Bergen. My current personal page is here.