The basic approach
Find a one-way function, that is, a function that is quick to compute but slow to invert.
Example: Multiplication and factoring - You can multiply two numbers in time proportional to the number of digits. But (as far as anyone knows), the time required to factor a number grows as the size of the number. So, we could quickly multiply a pair of 500 digit numbers. But if we give people the product,it will take them on the order of 10500 times as long to factor the number as it took us to do the multiplication.
A factor of 10500 is a lot more than the difference between a laptop PC and any computer power available to the NSA (we think).