The communication on the internet has to be encrypted if you want to be sure that only the sender and receiver can share the information. Today's encryption is based on mathematical problems that are easy to construct but really difficult to solve. If - or when - quantum computers become practically available, today's encryption methods will cease to work. To meet that situation, new types of mathematical problems that will be difficult to solve for both classical binary computers and for quantum computers are researched. Erik Mårtensson's research aims to analyse which of the proposed problems that is good enough. On the 22 January he defends his doctoral dissertation “Some Notes on Post-Quantum Cryptanalysis”.
When you shop online, contact your internet bank or use chat apps, you want to encrypt your data to avoid leaking sensitive information. Encryption as it is used today relies on the assumption that it is hard for computers to factor* large integers and some other similar problems. Despite decades of research no one has been able to efficiently solve these problems on a classical computer.
“On a quantum computer, with enough so called qubits, these problems are quite easy to solve. To prepare for a potential future where today’s encryption is broken, other mathematical problems to base encryption on are studied. This area of study is called post-quantum cryptography”, Erik Mårtensson says.
“I develop algorithms to solve the mathematical problems in post-quantum cryptography as efficiently as possible. In other words, I do cryptanalysis. We can only trust post-quantum encryption methods if considerable efforts at breaking these methods have been made.”
What made you want to pursue a PhD?
“I like math and I like thinking about hard problems. Pursuing a PhD in my area means that I can get payed to do so!”
What’s beautiful about cryptanalysis?
“In many other research areas, a mathematical problem is an approximation of reality. In my research, the mathematical problems I try to solve are constructed precisely, they are not an approximation.”
“Another beautiful aspect of the problems I study is that they are very simple to state and understand, but still very hard to solve. No matter how smart you are and no matter how much computational resources you have access to.”
How will the results come to use?
“When implementing post-quantum encryption schemes in the future, one needs to take into consideration all possible methods for trying to break the schemes, including the methods developed in my research”, Erik Mårtensson concludes.
What are your plans?
“I’m currently applying for a post-doc position.”