Factoring RSA Keys with Many Zeros

Researchers have identified a new class of weak RSA keys, characterized by having many zeros. These keys have been found to exist in the wild. A large dataset of real-world keys was collected from various public sources, including Certificate Transparency logs and internet-wide scans. The dataset was then searched for RSA moduli with unexpectedly sparse patterns, revealing a significant number of keys with these weaknesses. The discovery was made while developing the badkeys project, an open-source tool for checking public keys for known vulnerabilities. The findings indicate that keys with many zeros are more common than expected in real-world usage.