One of the greatest difficulties in the digital age is securing data from hacker attacks, a problem that experts, governments, and businesses throughout the globe are working hard to solve. While there are plans to create a connected and secure future, there is still plenty that can be learned from the past. In less than an hour, a mathematical theorem decrypted a post-quantum encryption technique. One of the most promising post-quantum encryption methods developed by a group of prominent researchers has just been cracked by a decade-old curved math theorem.
Researchers were requested to find flaws in a set of encryption algorithms that the US National Institute of Standards and Technology (NIST) believed would survive the power of quantum computers. A $50,000 reward was also given by Microsoft to anyone who could break the encryption of the SIKE algorithm, as several of their researchers were present on the SIKE team. To tackle the problem, a researcher at Katholieke Universiteit Leuven (KU Leuven) used a single conventional computer and a 1997 mathematical theorem made by Dr. Ernst Kani of Queen’s University in Canada to defeat SIKE in less than an hour.
Ernst Kani has been researching and teaching since the late 1970s—first at the University of Heidelberg, in Germany, and then at Queen’s, where he joined the Department of Mathematics and Statistics in 1986. His main research focus is arithmetic geometry, an area of mathematics that uses the techniques of algebraic geometry to solve problems in number theory.
Mathematicians often refer to mathematics as a beautiful thing. For those who don’t work in the field, it might be challenging to see this beauty, or even to have a high-level understanding of what these research projects are all about—it requires some imagination.
Although cryptographers and computing engineers are not always well-versed in all the high-powered techniques of mathematics, many different skills and forms of knowledge can be combined to advance the way we store and transmit data.
“Cryptography uses a lot of sophisticated mathematics, especially arithmetic geometry. Computing experts and math experts have to work together to advance this field,” says Dr. Kani, who continues to teach undergraduate and graduate courses and to work in arithmetic geometry—particularly on problems involving genus two curves and elliptic curves.
Update: The title and content of the article have been updated to reflect that the algorithm is not currently in use with the U.S. government and the reward was offered by Microsoft and not NIST as stated earlier.