CL-350 Captain reported encountering wake turbulence on approach into SFO in trail of a B777 that resulted in 70-degree banks in both directions.

Narrative

We were flying the SERFR 4 RNAV arrival into SFO and were cleared for the Tip Toe Visual to Runway 28L after EDDYY. Prior to joining final we were given a heading of 350 and a speed of 210 knots and directed to descend to 4000 ft. Approach Control called out traffic; a B-777 that would be landing on the parallel runway. We visually acquired the traffic when it was turning base to final. We were then given a heading to join final (I believe it was 310 heading) and told to slow to 180 knots and maintain 3;000 ft. and were cleared the visual approach. The flying pilot then requested the flaps be selected from 10 to 20 degrees. We were told to keep the B777 in sight which we acknowledged and were cautioned about wake turbulence. After joining final we began a descent at the appropriate point. At approximately 2;800 ft. we encountered wake turbulence and the aircraft abruptly rolled left to approximately 70 degrees followed by an immediate roll to the right of approximately 70 degrees. The flying pilot countered both roll excursions with opposite aileron and we quickly recovered to level flight. We then continued the approach and landed with no additional wake turbulence encounters. I estimate that the horizontal distance between us and the B777 was 2-3 miles. The aircraft rolled rapidly to the left and right. Both insufficient lateral offset and horizontal spacing. This combined with winds that though reported at a direction that would possibly help keep the wake turbulence vortices away from our flight path (270 degrees reported by ATIS with the runway direction of 284 degrees); their direction was not enough to keep or blow the vortices away from us. Also; the winds on final were likely somewhat different than those reported by the ATIS and thus could have actually been blowing the vortices towards us. The flying pilot countered the left roll with opposite aileron and the right roll with left aileron. Having flown into SFO dozens of times; we frequently are flying approaches with other aircraft flying to the parallel runway. Advisories of wake turbulence are common and the appropriate mitigating techniques are employed. Given the same situation I would direct the flying pilot to slow sooner; offset slightly to the left of runway centerline and fly above the normal PAPI glidepath angle sooner.