[Resource Topic] 2023/026: Fermat Factorization in the Wild

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Fermat Factorization in the Wild

Authors: 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 of vulnerable devices that generate such flawed RSA keys in the wild. These affect devices from two printer vendors - Canon and Fuji Xerox. Both use an underlying cryptographic module by Rambus.

ePrint: https://eprint.iacr.org/2023/026

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