RSA IS NOT ALREADY SAFE. IT IS EXTREMELY IMPORTANT!
Here is a slide from the NIST presentation on 04-11-2018. We can see that RSA - 2048 has been hacked already. Furthermore,Elliptic-curve cryptography is also based on RSA and is used in almost every messenger
There are many popular messegers using such algorithms to protect your messages. Have a look here. As you can see, no one can be 100% sure that this security and privacy is real
Several groups are working on designing and building a quantum computer, which is fundamentally different from a classical computer. If one were built - and we're talking science fiction here - then it could factor numbers and solve discrete-logarithm problems very quickly. In other words, it could break all of our commonly used public-key algorithms.
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NIST Post Quantum Project
In recent years, there has been a substantial amount of research on quantum computers – machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the Internet and elsewhere.
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NSA Preps Quantum-Resistant Algorithms to Head Off Crypto-Apocalypse
The National Security Agency is advising US agencies and businesses to prepare for a time in the not-too-distant future when the cryptography protecting virtually all e-mail, medical and financial records, and online transactions is rendered obsolete by quantum computing. Quantum computers have capabilities that can lay to ruin all of the public-key cryptographic systems currently in use.
The National Security Agency, too, has sounded the alarm on the risks to cybersecurity in the quantum computing age. The NSA's "Commercial National Security Algorithm Suite and Quantum Computing FAQ" says that "many experts predict a quantum computer capable of effectively breaking public key cryptography" within "a few decades," and that the time to come up with solutions is now.
According to many experts, the NSA is far too conservative in its prediction; many experts believe that the timeline is more like a decade to a decade and a half, while others believe that it could happen even sooner.