Paper 2023/026
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.
Metadata
- Available format(s)
-
PDF
- Category
- Attacks and cryptanalysis
- Publication info
- Preprint.
- Keywords
- rsafactorizationfermat
- Contact author(s)
- hanno @ hboeck de
- History
- 2023-01-09: approved
- 2023-01-08: received
- See all versions
- Short URL
- https://ia.cr/2023/026
- License
-
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},
url = {https://eprint.iacr.org/2023/026}
}
