It comes amid increasing concerns about how social media websites and messaging apps are storing users' data, which could be vulnerable and accessed by hackers.
In October, hundreds of thousands of pictures from Snapchat – which allows users to send images that disappear in 10 seconds - were uploaded to the internet after a third-party app was hacked.
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Kevin Abosch, founder of the OneOne app, said that while many messaging platforms claim to keep users' data secure, his service goes one step further and makes people untraceable.
"Everyone is busy with the buzzword 'anonymity' but aren't certain what it means," Abosch, told CNBC by phone. "What really matters is traceability. You can be anonymous or not, but the bottom line is that you can trace a message back to a device. We believe we have done a thorough job making sure this can't happen."
Lawyers, CEOs on board
OneOne is aimed at business executives, lawyers and even doctors, according to Abosch, who said professionals could use the app to send sensitive documents and messages to each other.
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"I have been doing a small road-show speaking to lawyers, execs, because I think they will be our early adopters," Abosch said. "A couple of big CEOs said they are using it when they wanted to talk to somebody on the board about terminating someone else's employment. That is a touchy area."
OneOne users send a web link to another person in order to start a conversation. This link opens up an anonymous communication method, which only those two people can be involved in.
A third party cannot use the link to enter the conversation and the message chain can be deleted at any time, or it will self-destruct in 24 hours. Users don't even have to create an account to use the app.
Abosch admitted that links could potentially be intercepted, but stressed that users can avoid this by using a code word.
OneOne is not the only app in its space. A close competitor is Telegram, another anonymous messaging service, which allows users to send secure messages. Device makers have also identified the appetite for more secure communication. Blackphone, which claims to be the most secure smartphone maker, recently told CNBC it is launching a tablet.
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But while many of these services user strong encryption to protect users' data, Abosch said OneOne was different because it does not allow any messages to be traced back to a user's device, keeping them anonymous.
"Every other service is encrypted but with us there is nothing that can trace the message back to the user," Abosch said.