### Fermat Factorization in the Wild

##### Abstract

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.

Available format(s)
Category
Attacks and cryptanalysis
Publication info
Preprint.
Keywords
rsafactorizationfermat
Contact author(s)
hanno @ hboeck de
History
2023-01-09: approved
See all versions
Short URL
https://ia.cr/2023/026

CC BY

BibTeX

@misc{cryptoeprint:2023/026,
author = {Hanno Böck},
title = {Fermat Factorization in the Wild},
howpublished = {Cryptology ePrint Archive, Paper 2023/026},
year = {2023},
note = {\url{https://eprint.iacr.org/2023/026}},
url = {https://eprint.iacr.org/2023/026}
}

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