Regular public-key crypto mostly use one kind of mathematical structures (finite fields) who have a known hard problem (finding the discrete logarithm of a number of a finite field) while the reverse problem (calculate the power of n of a given number) is trivial. You can do crypto on every structure for which it exists such a problem.
Latice are different mathematical structures, for which it exists different kinds of problems that can be used for crypto.
secure multiparty computation
Let say you have some confidential data X and I have some confidential data Y. What we want to do is compute f(X,Y) without sharing the X and Y because we don't trust one another (or any third party).
Lattice-based crypto:
Regular public-key crypto mostly use one kind of mathematical structures (finite fields) who have a known hard problem (finding the discrete logarithm of a number of a finite field) while the reverse problem (calculate the power of n of a given number) is trivial. You can do crypto on every structure for which it exists such a problem.
Latice are different mathematical structures, for which it exists different kinds of problems that can be used for crypto.
secure multiparty computation
Let say you have some confidential data X and I have some confidential data Y. What we want to do is compute f(X,Y) without sharing the X and Y because we don't trust one another (or any third party).
I hope it helped.