The method used was first introduced by a French mathematician in the 1600’s.

Cryptographic keys generated with older software now owned by technology company Rambus are weak enough to be broken instantly using commodity hardware, according to a report in Ars Technica. The revelation was made by a researcher on Monday. The discovery is part of an investigation that also uncovered a handful of weak keys in the wild, the report says.

The software comes from a basic version of the SafeZone Crypto Libraries, which were developed by a company called Inside Secure and acquired by Rambus as part of its 2019 acquisition of Verimatrix, a Rambus representative said. That version was deprecated prior to the acquisition and is distinct from a FIPS-certified version that the company now sells under the Rambus FIPS Security Toolkit brand.

TIP: If you’re interested in security, and the role it plays inside organizations, you might also like our recent story about how the security industry is fundamentally broken.

The weak spot: insufficient randomization

Researcher Hanno Böck said that the vulnerable SafeZone library doesn’t sufficiently randomize the two prime numbers it used to generate RSA keys. (These keys can be used to secure Web traffic, shells, and other online connections.) Instead, after the SafeZone tool selects one prime number, it chooses a prime in close proximity as the second one needed to form the key.

“The problem is that both primes are too similar,” Böck said in an interview. “So the difference between the two primes is really small.” The SafeZone vulnerability is tracked as CVE-2022-26320.

Cryptographers have long known that RSA keys that are generated with primes that are too close together can be trivially broken with Fermat’s factorization method. French mathematician Pierre de Fermat first described this method in 1643.

Fermat’s algorithm was based on the fact that any odd number can be expressed as the difference between two squares. When the factors are near the root of the number, they can be calculated easily and quickly. The method isn’t feasible when factors are truly random and hence far apart.