Einstein's theory of special relativity contains some very strange ideas such as time dilation (moving clocks run slow), length contraction (moving lengths are shorter), and lack of absolute simultaneity. What is the basis of these ideas?

The uniformity in the speed of light in all frame of references and for all the observers.

Explanation:

The theory of special relativity throws light on the link between space and time in inertial frame.

Time dilation is when the object moves with relativistic speed the time slows down an similar is the case with length contraction, the length is shortened or contracts when the body moves with relativistic speed.

The main idea behind these is that the speed at which the light travels is the same in all the frame of reference and for all the observers.