Factoring "short-sleeve" RSA keys with polynomials

What happens when the bits of an RSA private key are heavily biased toward 0 instead of being randomly generated? The public key’s bits could be biased enough for us to detect these incorrectly generated keys in the wild. Together with Hanno Böck of the badkeys project, we found hundreds of unique keys that not only have this property, but can be quickly factored. We also found the bug that led to many of these keys and analyzed historical data to track the issue over time. Surprisingly, the pat