Regression with 0-1 features

Is there a fast strategy for estimating regression when all your features are either 0 or 1?

The OLS solution would be $(X^TX)^{-1} X ^T y$. Given X is a binary matrix, is there a fast way to compute $X^TX$, and a fast way to compute $(X^TX)^{-1}$?. Normally we take advantage of either a SVD or QR decomposition of X, instead of literally inverting. However, I haven't found any special case solver for SVD or QR when X is binary