In this day and age, encryption is the elemental ingredient of online and offline digital security, keeping sensitive information hidden behind a (supposedly) undecryptable cipher, but it turns out a 380-year-old math trick might be able to crack some of it.
As it happens, in early 2022, information technology security researcher Hanno Böck discovered that it was possible to crack some encryption using a process pioneered by the French scholar Pierre de Fermat in the 17th century, according to a report by Scientific American on April 9.
Specifically, modern encryption follows a padlock-like principle, in which the problem (the lock) is only solvable using additional information (the key). The usual procedure for this is RSA cryptography, which focuses on prime numbers, as decomposing large numbers into a product of prime numbers is difficult, making them useful keys.
The encryption-busting 17th-century math trick
However, in 1643, Fermat discovered a way to factorize even large numbers that are the product of two prime numbers, which computers can only perform fast enough if the two prime factors are not too far apart, and Böck uncovered this vulnerability in a program library deployed by various companies at the time.
Indeed, Fermat’s algorithm revolved around the fact that any odd number can be expressed as the difference between two squares, and when the factors are close to the root of the number, it is easy to calculate them. That said, the method doesn’t work if the factors are truly random and therefore far apart.
But back to Böck – he realized that using Fermat’s Factorization Method can help bypass the encryption used by the printers and Internet of Things (IoT) devices of certain companies, which relied on RSA cryptography for, say, protecting confidential documents sent to the printer through a network. As he explained at the time:
“The problem is that both primes are too similar. So the difference between the two primes is really small.”
Since the discovery, some of these companies, including Fujifilm, issued alerts and fixes to address the problem, but it still stands as a powerful lesson to the vulnerabilities of modern systems against old math tricks and the necessity of introducing super-secure quantum computers.
And by the looks of things, we won’t have to wait much longer for a practical quantum computer, considering that the scientists at the Massachusetts Institute of Technology (MIT) have devised a novel interconnect device that paves the way for scalable, all-to-all communication between superconducting quantum processors.
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