Taylor Swift -- Hackers Threaten to Release Nudes

11:20 AM PT -- Swift just addressed the hack, tweeting, "PS any hackers saying they have 'nudes'? Psssh you'd love that wouldn't you! Have fun photoshopping cause you got NOTHING."

Taylor Swift's social media was taken over by hardcore hackers who are now threatening to release nude pics of Taylor.

Multiple tweets went out from Swift's account this morning ... telling her 51.4 M followers to follow @lizzard and @veriuser -- both of whom claim to have ties to a group of hackers called the Lizard Squad. The messages were also posted on her Instagram account.

The Lizard Squad claims to have hacked major gaming systems -- such as Sony PlayStation and Xbox Live -- last year. They also claim to be behind Monday's Facebook and Instagram outage.

Now, the hackers say they're planning to post naked shots of Taylor.

Swift used her Tumblr page to inform fans she'd been hacked -- and Twitter has shut down the alleged hackers' accounts.

Story developing ...