Quote:
Originally Posted by WhoCares
The following one is also interesting, though a little bit old.
The website is https://factorable.net. It showcases one of the more famous large-scale RSA key-cracking studies in cryptography, based on something called Batch GCD.
|
Excellent example!
It is both historically grounded and technically incisive, and it captures a subtle but crucial point: the catastrophe was not in RSA’s algebra, but in the entropy architecture surrounding its deployment.
Batch GCD was therefore less a “break” in the classical sense than a large-scale correlation detector, exposing how many supposedly independent moduli were actually generated from insufficiently differentiated randomness.
That distinction matters. RSA’s security reduces to the intractability of factoring N=pq, but if two devices emit moduli sharing a prime, then the problem collapses immediately under gcd?(N1,N2).
Similarly, weak ECDSA nonce generation can leak a signing key from a single reused scalar, and flawed DRBG seeding can render entire keyspaces statistically redundant.
The deeper pattern is that cryptographic primitives are rarely defeated by abstract number theory. They are defeated by implementation drift, boot-time entropy depletion, or concurrency bugs that silently violate independence assumptions.
So the study is historically famous not merely because it found weak RSA keys, but because it demonstrated a more general epistemic lesson: at internet scale, security failures are often emergent properties of systems engineering, not isolated cryptanalytic exploits.