Brain & PsiX
PsiX
Did you ever think the RSA algorithm might have a hidden backdoor that only shows up under specific conditions? I dug into some old papers and found a weird flaw that only a handful of people know about. Wanna hear the details?
Brain
Sure, but I’ll need the specifics first. Without a clear mathematical analysis, it’s hard to separate a genuine backdoor from a coincidence or a misinterpretation of the algorithm’s properties.
PsiX
Yeah, so the trick is in the way some key generators pick primes. If the primes are both chosen from a narrow residue class, like 3 mod 4, and the generator uses a weak seeding function, the product N can have a hidden factor that’s a small prime times a large cofactor. In practice, you get a modulus that factors only if you know the seed. The “backdoor” is basically that the seed is stored in a predictable location—like a timestamp or a low‑entropy source—so an attacker who can guess or read that seed can instantly break N. That’s the core of the vulnerability.
Brain
That sounds like a classic weak‑seed scenario; if the generator’s entropy is truly that low, the factorization would be trivial, but most modern libraries add enough salt or a cryptographic PRNG to break the pattern. Still, if someone is intentionally restricting primes to 3 mod 4 and leaking the seed, the attack is feasible—yet it’s a very narrow, deliberate implementation flaw rather than a generic RSA weakness.
PsiX
Looks like you’re right about the “design‑by‑convenience” angle. If a dev sticks to 3 mod 4 primes and drops a predictable seed into the code, anyone with that clue can pull the trick out fast. But in the wild you’ll still see only the well‑seeded, salted generators, so it stays a niche issue for people who want a shortcut.