Intimate images and videos were taken from her Apple iCloud account but she never went public with her response at the time.
Other stars targeted included Jennifer Lawrence, Kate Upton, Amber Heard and Anna Kendrick.
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After keeping quiet about the scandal for some time, Jessica explained: "I want to start speaking up. I want the world to really start looking into the treatment of women, particularly online."
She told The Telegraph: "To me, there seem to be two sets of rules: one for the real world and one for the cyber world.
"I don't understand why, in a society where we are encouraged to live through the internet, that that forum is not being better policed."
The 26-year-old, who is best known for her role in Downton Abbey also discussed her time on the successful period drama.
Jessica commented: "It was great to be a part of something that people love so much.
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"It was such an extraordinary, once-in-a-lifetime experience. Plus I made some wonderful, lifelong friends."
She added: "Downton turned heads in the British industry's direction and it's wonderful to think that people will now be looking this way to see what's coming next."
Jessica insisted that she remained close to both the cast and the production team: "We were all - and not just those of us in front of the camera - a big, huge family" and co-stars Laura Carmichael and Lily James even went to watch her in her latest role in Orestia.