Is Screen Gems frantically trying to grab the remake rights to the Korean stolen cell-phone thriller “Unlocked?”

If they aren’t, the Hollywood distributor of “Searching” and its somewhat lesser follow-up “Missing” is missing the boat.

“Unlocked” is a crackling, nervy and above all sinister parable that will make any viewer think twice and thrice about letting one’s cell phone out of your sight. And it’ll make ALL of us blush when we recognize the degree to which we’ve folded so much of our lives, our livelihoods, our identity and our fortunes into these pocket-sized modern marvels.

Writer-director Kim Tae-joon — the post-zombie-apocalypse “Peninsula” was his” — pokes at our paranoia, and justifies it in this tight tale that shows just how easy it might be for someone to destroy your life if he has a mind to, and gets hold of your cell phone.

First act montages show us how much plucky Na Mi (Chun Woo-hee) runs her life via her cell.

She’s buying drinks and photographing food, not just by publishing her location via (sometimes drunken) photos on social media. She’s using map applications, doing her banking, making lunch dates, buying baseball tickets, listening to music, running a “hidden” social media identity to help with her marketing job and using her fingerprint to access the damned phone.

And all around her, distractedly zombie-walking down the streets or packed into buses, everybody else is doing the same.

All it takes is one tipsy trip home, one phone left behind on a bus, and one bad actor to blow up her world.

He uses a phrase-reading app to give him a woman’s voice when Ni Ma and a pal call to retrieve her phone. He lies that the phone has been dropped, and has been left with an ace phone repairman, Mr. “Digital Sheriff,” which is this bespectacled nerd’s (Yim Si-wan) alleged business.

Once she’s in his sketchy “shop,” he gets her password from her, copies all the data from her phone and installs spyware that will allow him to hear her calls, see her searches, read her texts and follow her anywhere she goes.

And he starts keeping a long list of her friends, family, “likes” and passions and meticulously writes down ways to use that against her and disrupt her life. She’s cute, so he’ll throw “stalking” into the mix.

But this veteran cop (Kim Hee-won) is on a case where bodies are turning up, usually near plum trees. Det. Ji-man recognizes that M.O. There’s a serial killer on the loose, and we can only assume that he has a thing for cell phones as well as plums.

Kim, adapting a book by Japanese novelist Akira Shiga, serves up three points of view — Ni Ma’s unraveling friendships and ignored warnings from her father (Park Ho-san), the not-frantic-enough police hunt, and the villainous Jun Yeong’s meticulous scheming, contriving ways to meet Ni Ma and meet her “needs” (tickets, buying a CD she advertises online) and even giving himself a makeover when she criticizes his haircut and glasses to a friend while her ever-listening/ever-watching phone is nearby.

“Unlocked” takes a few maddening turns that might prompt a shout or two at the screen and the police, who let one cop dictate that no nationwide “BOLO” be issued for this plum-sucking killer they’ve identified as their one and only suspect.

The film is a bit overly patient in setting up the menace and the obstacles to the mystery being solved and that menace being thwarted before our unsuspecting 20something is snatched and buried “in the mountains” near another plum tree.

But when the third act kicks in, the ticking clock starts and every one of the final minutes on this cell-plan story can be savored for the well-engineered and well-acted thriller it is.

If Netflix isn’t planning a North American/English language remake (it’s in undubbed Korean), Screen Gems certainly should.

Rating: TV-MA, violence

Cast: Chun Woo-hee, Yim Si-wan, Kim Hee-won, Park Ho-san

Credits: Scripted and directed by Kim Tae-joon, based on a novel by Akira Shiga. A Netflix release.

Running time: 1:57