Side Channels and the Montgomery Reduction Algorithm with Golang
The method I will illustrate is defined here.
A paper presented at the USENIX Security Symposium in 2018 [1] outlined how RSA encryption keys can be cracked from the radio waves emitted by a mobile phone [here]:
The researchers used the EM radiation emitted from the processor is it performs complex RSA calculations, and then used a timing attack to recover the private key. Figure 2 outlines the capture of the signal and the identification of the key parts of the signal which are gathered:
It works without even knowing the actual ciphertext. This type of attack is known as a side-channel attack, and these types of attacks have been well-known in the industry to break encryption. Common side channel attack vectors include monitoring variations in the electrical power signal, and temperature levels, and have even included monitoring the sound emitted from a system.