Fermat Factorization in the Wild

ePrint Report: Fermat Factorization in the Wild

Hanno Böck

We are applying Fermat’s factorization algorithm to sets of public RSA keys. Fermat’s factorization allows efficiently calculating the prime factors of a composite number if the difference between the two primes is small. Knowledge of the prime factors of an RSA public key allows efficiently calculating the private key. A flawed RSA key generation function that produces close primes can therefore be attacked with Fermat’s factorization.
We discovered a small number …

algorithm eprint report fermat function key keys knowledge prime private key public public key report rsa