Illustrator EPS gets white lines around the vector art when imported into InDesign

I created a logo in Illustrator and it is fine when in there, and when exported for screens to PNG, but when I import the EPS file into InDesign, I get these white lines all through the artwork. I can't figure out why this is happening or how to get rid of it. Below I've included a screen shot of the artwork. On the left is the Illustrator version (good) and then on the right is how it looks when I put the EPS into InDesign (bad). The lines still show when I export the PDF from InDesign for print. Hopefully you can see it from the screen shot I loaded, it is kind of hard to see in the preview. I'm using CC. Any ideas?