CRJ-900 Captain reported encountering wake turbulence on descent into JFK in trail of a B777.

Narrative

We were on NY Center descending through about 18;000 [ft.] for 250 [kts]/12;000 [ft.] at CCC. A 777 was in front of us about 10 miles initially. They were given the same altitude and speed restriction. We tried staying above their descent path. When we were passing FL180 [the 777] did a sudden speed reduction. We went from 10 to 5 [miles] in trail quickly. I told the First Officer (FO) to start slowing asap and keep an eye on the spacing. About 30 seconds later we saw 777's wake about 5 seconds before we hit it. The FO disengaged the autopilot and arrested the descent rate as much as he could. We hit the top portion of the wake. There was an initial roll about 35-40 degrees left then and bank to the right about 30 degrees with a couple smooth oscillations for about 20-30 seconds. Once we had the aircraft fully stabilized I told ATC we needed more spacing after the wake encounter. ATC gave us a turn to the right and kept us about 8-10 miles in trail the rest of the way in. 777 slowing before required from ATC restriction reducing spacing.