# Global minimum based cryptography?

When using the Back propagation Algorithm for Machine Learning, it is often said finding the global minimum of a cost function over $\mathbb{R}^n$ is very hard, and as $n$ increases it gets even more complex. I was just wondering if there are any schemes that utilise this property.

If you look at it from the right direction, lattice-based crypto (and the Shortest Vector Problem) can be viewed as a 'global minimization' problem.

• I guess this is the same problem type, however do you think this is a potential problem to base a secure scheme on, as in just minimising or maximising a function globally? – John Miller Sep 20 '18 at 17:05
• @JohnMiller: not really as stated. In crypto, we typically don't rely on things in $\mathbb{R}$ (as there are practical problems with values that cannot be expressed in a finite number of bits). And, approximations to $\mathbb{R}$ (such as floating point) often act subtlety differences (and the differences may be cryptographically important). – poncho Sep 20 '18 at 20:43
• @JohnMiller: it's also not clear how you could make a 'trapdoor' out of a general minimization problem... – poncho Sep 20 '18 at 20:44
• Well you can make the function public, and it's easy to find local minimum points, I'm right now trying to work on a ZKA for revealing the global minimum point such that it can be revealed without giving it away. – John Miller Sep 21 '18 at 12:55