Apr 2, 2016 at 11:40 PM
Edited Apr 2, 2016 at 11:41 PM

https://www.sciencedaily.com/releases/2016/04/160401075126.htm
RuhrUniversität Bochum researchers have developed new cryptographic algorithms that are based on particularly hard mathematical problems. They would be virtually unbreakable, say the investigators.
Cryptographic methods are typically created following the adhoc principle: somebody comes up with an algorithm; others attempt to break it  if they don't succeed, it means that the algorithm is secure. The team headed by Prof Dr Eike Kiltz who holds
the Chair for Cryptography at the RuhrUniversität Bochum opted for a different approach. They base their security algorithms on hard mathematical problems.
"If somebody succeeded in breaking those algorithms, he would be able to solve a mathematical problem that the greatest minds in the world have been poring over for 100 or 200 years," compares Kiltz. The mathematicians make the algorithms so efficient
that they can be implemented into microdevices, such as electric garage openers.
The algorithms are based, for example, on the hardness of the following lattice problem: imagine a lattice to have a zero point in one specific location. The challenge is to find the point where two lattice lines intersect and that is closest to zero point.
In a lattice with approx. 500 dimensions, it is impossible to solve this problem efficiently. ...



Asymmetric (read:public key) encryption methods are based on mathematical problems already.
For instance, RSA/PKI is based on number factorization (determining dividers of numbers).
Unfortunately, that makes them slow as well. That's why most hashes and symmetric algorithms rely
more on bit shifts/shuffles.

