In the digital era and moving towards quantum computing, protecting data against hack attacks is one of our biggest challenges 카지노 게임 컬렉션� and one that experts, governments, and industries worldwide work hard to address. While this is an effort to build a more connected and safe future, it can certainly learn from the past.

In July, the US National Institute of Standards and Technology (NIST) . Part of the latter group was , a candidate algorithm for post-quantum cryptography standard. for whomever managed to break it. : SIKE was hacked with a single personal computer. The attack did not rely on a powerful machine, but on powerful mathematics based on a theorem developed by a Queen카지노 게임 컬렉션�s professor decades ago.

Ernst Kani has been researching and teaching since the late 1970s 카지노 게임 컬렉션� first at the 카지노게임사이트 of Heidelberg, in Germany, and then at Queen카지노 게임 컬렉션�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.

The problems Dr. Kani works to solve stretch back to ancient times. His specific field of research was pioneered by Diophantus of Alexandria around 1,800 years ago and is a set of problems known as Diophantine questions. One of the most famous questions in the field is Fermat카지노 게임 컬렉션�s Last Theorem, posed by Pierre Fermat in 1637 and which took the math community 350 years to prove 카지노 게임 컬렉션� . Wiles received many prizes and honours for this work, including an honourary doctorate from Queen카지노 게임 컬렉션�s in 1997.

Neither Diophantus nor Fermat dreamt of quantum computers, but Dr. Kani카지노 게임 컬렉션�s work on Diophantine questions resurfaced during the NIST round of tests. The successful hackers 카지노 게임 컬렉션� Wouter Castryck and Thomas Decru, both researchers at the Katholieke Universiteit Leuven, in Belgium 카지노 게임 컬렉션� based on the 카지노 게임 컬렉션�glue and split카지노 게임 컬렉션� .

As a matter of fact, Dr. Kani was not concerned about cryptographic algorithms when he developed the theorem. That work kicked-off in the 1980s, in collaboration with another German mathematician, Gerhard Frey 카지노 게임 컬렉션� whose work was crucial in solving Fermat카지노 게임 컬렉션�s last theorem. Drs. Kani and Frey wanted to advance research on elliptic curves, a particular kind of equation that would later be used for cryptographic purposes.

Both researchers카지노 게임 컬렉션� goals at that time were purely theoretical. They were interested in manipulating mathematical objects to learn more about their own properties. 카지노 게임 컬렉션�Doing pure mathematics is an end by itself, so we don카지노 게임 컬렉션�t think of real-world applications,카지노 게임 컬렉션� Dr. Kani explains. 카지노 게임 컬렉션�But, later, many of those studies are useful for different purposes. When Fermat proposed his theorem hundreds of years ago, his intent was to be able to factor certain large numbers. The application to cryptography came only much later in 1978. Basically, all the methods we use today for data encryption are based on mathematics.카지노 게임 컬렉션�

Doughnuts and curves

Mathematicians often refer to mathematics as a beautiful thing. For those who don카지노 게임 컬렉션�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 카지노 게임 컬렉션� it requires some imagination.

Imagine an object shaped like a doughnut, with a hole in the middle: that카지노 게임 컬렉션�s a visual model of an elliptic curve, also known as a genus one curve. Drs. Kani and Frey wanted to combine two genus one curves to form a new object 카지노 게임 컬렉션� a genus two curve, something we can imagine like two doughnuts stuck solidly together side by side. They aimed to use some properties of the constructed genus two curve to deduce certain properties of the two original genus one curves, which were 카지노 게임 컬렉션�glued카지노 게임 컬렉션� together.

In his 1997 paper, Dr. Kani generalized the original construction by gluing together an arbitrary pair of elliptic curves. But in that case the construction sometimes fails 카지노 게임 컬렉션� it might construct an object in which the two doughnuts only touch each other in a single point. The paper analyzes the precise conditions for when this happens (i.e., when the construction fails or 카지노 게임 컬렉션�splits카지노 게임 컬렉션�). Castryck and Decru used this characterization of the failure in their method of attacking the proposed encryption scheme SIKE.

카지노 게임 컬렉션�Our problem had nothing to do with cryptography, which is why I was surprised when I heard of the algorithm attack. It was quite ingenious, what they did there!카지노 게임 컬렉션� says Dr. Kani. 카지노 게임 컬렉션�One of the co-authors of the SIKE algorithm expressed surprise in the fact that genus two curves could be used to gain information about elliptic curves. But this was precisely our original strategy in the 1980카지노 게임 컬렉션�s and 1990카지노 게임 컬렉션�s (and afterwards).카지노 게임 컬렉션�

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.

카지노 게임 컬렉션�Cryptography uses a lot of sophisticated mathematics, especially arithmetic geometry. Computing experts and math experts have to work together to advance this field,카지노 게임 컬렉션� says Dr. Kani, who continues to teach undergraduate and graduate courses and to work in arithmetic geometry 카지노 게임 컬렉션� particularly on problems involving genus two curves and elliptic curves.

Update (12/20/2022): The second paragraph of this article has been updated for clarity.