Paranoid Cryptography: Fermat’s Theorem For Cracking RSA
Someone sent me a great GitHub link from Google. It is named Project Paranoid and allows developers to check for a range of cryptographic weaknesses [here]:
The library is created by two leading cryptographers: Pedro Barbosa and Daniel Bleichenbacher. So, let’s look at one of the examples.
Fermat’s factorization
Pierre de Fermat defined a factorization method which could factor prime number factors if these prime numbers were close to each other. In RSA, we use a modulus (N) and which is the multiplication of two prime numbers (p and q). If these prime numbers are close to each other, then N can be factorized, and the RSA methods can be easily broken.
In March 2022, it was discovered that a Rambus cryptographic module was selecting a prime number and then selecting another which was relatively close. These led to vulnerabilities in a number of printers which used Rambus module [here]:
