This article is poorly written. First, by this time, it's old news: the attack was made public over two months ago. Oddly there doesn't seem to have been a thread about this attack here before, but there was one on Cryptography Stack Exchange which you can read for an introduction to how the attack works.
A second way in which this article is misleading is that this attack does not impact TLS 1.3 in itself. It impacts servers that support TLS 1.3 and older versions, if the attacker manages to downgrade the connection.
“The most common RSA configuration used to encrypt TLS connections” is also misleading. It's technically true, in that it is the only TLS configuration that uses RSA for encryption, but in fact most TLS configurations that use RSA use it for signature, not for encryption.
The attack works only against
TLS_RSA cipher suites, i.e. against cipher suites that have RSA in their name but not DHE or ECDHE. It attacks RSA decryption. Cipher suites that use RSA signature, or that don't use RSA at all, are not affected.
In order to perform the direct attack, the attacker has to convince the victims to use TLS ≤1.2 with an RSA-decryption cipher suite. It can often do that by hijacking the very beginning of the connection (it's a man-in-the-middle attack) and telling the client that it only supports TLS 1.2 (or some earlier version) and only RSA-decryption cipher suites. The client then sends a value encrypted with the server's public key, and the attacker must decrypt it to continue talking to the client. Normally decrypting the value requires the private key, but if the server is vulnerable to the attack, then the attacker is able to trick the server into decrypting that value by making many connections to the server with an RSA-decryption cipher suite, sending carefully-chosen ciphertexts and observing the precise timing of the server's response.
Even if the client refuses to use RSA-decryption cipher suites, or indeed even if the client only supports TLS 1.3, it may still be vulnerable if the server uses the same RSA private key for decryption and for signature. To perform this variant of the attack, the attacker is once again a man-in-the-middle, and it uses an RSA-signature cipher suite to talk to the client. At some point the attacker needs to sign a value with the server's private key, and it does this as above by making many connections to the server with an RSA-decryption cipher suite.
To protect against this attack, you can do any of the following:
- Keep your server up to date. This is the best way to protect against every attack.
- Disable RSA-decryption cipher suites on the server.
- Disable RSA-decryption cipher suites on the client and not use the same RSA private key for decryption and signature on the server.