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It appears that in order to Break RSA Encryption you just need a Microphone. Yes, that is correct, a microphone and just start listening. Scientists from the Weizmann Institute of Science and Tel Aviv University discovered that they can steal even the most secure RSA 4,096-bit encryption keys nowadays by simply listening to a computer as it decrypts the data. To do the magic, they utilized a microphone to record the noises made by the processor, then process this audio through some filters and isolate the vibrations made by the electronic internals when decrypting With the help of cryptanalysis methods the encryption key was revealed within an hour. It is interesting that one of the researchers involved in the experiment is also a co-inventor of RSA. This is a bad and a good thing – right! It shows that people are actually constantly trying to find ways to Break RSA Encryption and improve it.
This is, of cource, nothing that can be done on a large scale: it’s barely a one target method. In order to reproduce you have to send test emails to a specific computer and then record the sounds as it decrypts the messages. So it’s not something that the NSA tries touse on 500 million people. But can be a useful technique when a computer is seized by the authorities and no one knows what the encryption key is.
You can find the full scientific work here on How to Break RSA Encryption.