It is not known whether "quantum supremacy" over conventional computers was achieved during the summer as Google has announced. IBM asserts that no, Google maintains (link) Let's say, for lack of certainty, that the announcement was quantum, in a superposition of half-true and half-untrue state... Nevertheless, the question that arises for cryptography specialists becomes burning. This is reflected in a lecture given by Victoria de Quehen (ISARA) on October 15, 2019 in Montreal. Our correspondent attended.

Cryptography is the basis of computer security. It makes it possible to transmit a message in the public space that can in theory only be understood by the intended recipients. It is therefore ahead of protocols (such as https) and applications, administrators and users (who ultimately manage their passwords). This is so important that in 2005, the NSA launched a process to standardize a robust and efficient method, "elliptic curve cryptography", which has led to RSA encryption, which is now widely used.

Regardless of the encoding system used, current cryptography is based on mathematical problems that are difficult to solve, even with machines. For example, after multiplying two large prime numbers, it is difficult to return to these two prime numbers from the result. And to strengthen the security of a cryptography it is necessary either to increase the number of parameters (for example by increasing the size of the prime numbers), or to change algorithms.

The trick, in post-quantum cryptography, would be to base oneself on very different mathematical domains for each step (encryption, decryption,...). This implies using quantum computers that are known to be much superior (in computing power) to their traditional counterparts for certain very specific tasks that include, since the invention of the Shor link algorithm in 1995, solving the difficult mathematical problems on which current cryptography is based.

Hence three problems identified by Victoria de Quehen: first, anyone (not quite sure...) could store encrypted data today and wait a few decades to decrypt it ('harvert and decrypt').

Secondly, it would take time to rebuild everything on the basis of a new cryptography (the 2005 standardization process is still not completed).

Thirdly, some IT equipment deployed today must be able to last more than a few decades, for example aircraft or autonomous vehicles.

The NIST (National Institute of Standards and Technology) began a process of standardization of post-quantum cryptography in 2017. It is still in progress and aims to recommend a standard by 2022-2024. This process mainly consists in finding the desirable compromise between security (resource-hungry) and efficiency (resource-poor), and therefore choosing the standard accordingly. In the meantime, autonomous aircraft and vehicles could benefit from hybrid solutions combining conventional and post-quantum cryptography, which are less effective than RSA encryption, but more robust to this quantum risk.

Lauriane Gorce, Montreal