This is why cryptographers are developing solutions to replace RSA and attain quantum-safe security, that is, cryptographic protocols that are secure against an enemy who has access to a quantum computer. To do so, there exist two main approaches: post-quantum cryptography and quantum key distribution.
How to encrypt information in a world equipped with quantum computers
Post-quantum cryptography maintains the security paradigm based on complexity. One should look for mathematical problems that remain difficult for quantum computers and use them to construct cryptographic protocols, the idea again is that an enemy can hack them only after a ridiculously large amount of time. Researchers are working hard to develop algorithms for post-quantum cryptography. In fact, the National Institute of Standards and Technology (NIST) initiated a process to solicit and evaluate these algorithms, and the chosen candidates were announced in July 2022.
Post-quantum cryptography presents a very strong advantage: it is based on software. It is, therefore, cheap and, more importantly, its integration with existing infrastructures is straightforward, as one only needs to replace the previous protocol, say RSA, by the new one.
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But post-quantum cryptography also has a clear risk: our confidence in the “hardness” of the chosen algorithms against quantum computers is limited. Here it is important to recall that, strictly speaking, none of the cryptographic protocols based on complexity are proven to be secure. In other words, there is no proof that they cannot be solved efficiently on a classical or quantum computer.
This is the case for factoring: one can’t rule out the discovery of an efficient algorithm for factorization that would enable a classic computer to break down RSA, no quantum computer is required. While unlikely, such a possibility cannot be excluded. In the case of the new algorithms, the evidence of their complexity is much more limited, as they have not yet been intensively tested against smart researchers, much less quantum computers. Indeed, a quantum-safe algorithm proposed in the NIST initiative was later cracked in an hour on a standard PC.