Kevin Hart Extortion Case Search Warrants Are Being Written

Law enforcement officers have been busy writing multiple search warrants Tuesday as they hone in on the people they believe are the extortionists in the Kevin Hart sex tape investigation ... TMZ has learned.

Law enforcement sources say the declarations in support of the warrants will outline reasons they believe their targets may be the ones who contacted Kevin's people and made 8-figure demands in return for keeping the tape under wraps.

We're told the warrants, which still need to be signed by a judge, will ask permission to seize cell phones, computers and other electronic devices. As we reported, the extortion demands were sent by emails that were encrypted.

Authorities believe the sex video was shot on an iPhone, so authorities are particularly interested in that device.

Montia Sabbag, Kevin's sex partner, maintains she's a victim who had no knowledge she was being recorded in Kevin's Vegas hotel room. As we reported, cops have their suspicions but we don't know if she is one of the search warrant targets.