B737 pilot reported temporary loss of aircraft control due to severe turbulence during cruise.

Narrative

The weather radar tested good on the ground; but at XA25z we experienced severe unexpected turbulence with no indication from radar or the weather app. WiFi was intermittent. Flight attendants were ordered to be seated immediately. Seat belt sign was already on. Duration 45 seconds. Altitude dropped to 34;500 ft; climbed to 35;500; back to 34;500; then back to 35;000. Airspeed varied from .76M to .81M. I used speed brake and reduced power to prevent exceeding Vmo. Once clear of the storm 45 seconds; we returned to light turbulence only. Weather radar failed to display any valid returns on remainder of flight despite visual and weather app indications. Electronic Logbook (ELB) writeups were made for aircraft experiencing severe turbulence; and for inoperative weather radar. No injuries were reported from passengers or crew.