The world has known for decades that the RSA cryptosystem’s days are numbered. Once quantum computing becomes practical (estimates for that range from 3 to 20 or more years), the foundational security it provides will crumble. New research has revealed a novel method that uses classical computing to reduce the current RSA security level to an unacceptably low threshold.
The finding poses little to no practical threat in the immediate term, except possibly in a few edge cases. Even applying the attack against the deprecated use of 1024-bit keys, the method requires more computation than just about anybody—short of nation-states or companies with massive resources—can achieve. Widely used RSA implementations are also safe.
Nonetheless, the research has taken cryptographers by surprise because it introduces signature forgery, a new way to break RSA keys without factoring. Equally important, this novel method reduces the required computing resources by orders of magnitude.
“If this result holds up under peer review, it would indeed be a conceptual break-through,” Karsten Nohl, a cryptography expert and the head of innovation at Allurity, said in an interview. “RSA is as difficult to break as it is to factor large integers, at least so we thought. The researcher suggests that you can practically break RSA without cracking its key.”
Nadia Heninger, a University of California at San Diego professor and lead author, elaborated:
Cryptographers thought that the only way to compute valid RSA digital signatures was to first compute the private key by factoring, and then use the private key to compute the signatures. For 1024-bit RSA, this was thought to be very expensive, albeit probably doable if you have the computational resources of the large tech companies or the NSA—on the order of tens of millions of dollars of computation time for a single key. For 2048-bit RSA, it was thought to be totally out of reach.
The key forgery attack Heninger and the other researchers devised brings the breakage of 1024-bit RSA into the realm of possibility much sooner than previously estimated. Even for 2048- and 4096-bit keys, the method reduces the security of RSA to unacceptable levels. The National Security Agency, National Institute of Standards and Technology, and European Union Agency for Network and Information Security require that any cryptosystem should provide a level of no less than 128 or more bits, meaning the operations required must exceed 2128.
The forgery attack drops these levels to 265, 290, and 2119 for 1024-, 2048-, and 4096-bit keys respectively. These levels may further drop because Heninger’s team did all the coding by hand and used no AI or GPUs in performing the forgeries. The researcher said these tools will “almost certainly” drop the security levels further.
The attack works only against blind-signature implementations of RSA. The overwhelming majority of RSA in use today provides PKCS or PSS padding, a format that adds data to the plaintext before it’s encrypted. It prevents ciphertext from being deterministic and makes it less vulnerable to side channel and similar attacks. Still, some real-world systems continue to use blind-signature, also known as textbook, RSA. The best-known example, Heninger said, is Privacy Pass, a protocol that allows users to authenticate themselves without revealing their identity. Privacy Pass is used by both Apple and Cloudflare, among many others.
An attack on Privacy Pass would require an attacker to compromise a server belonging to Cloudflare, Apple, or another organization and generate 243 signatures. Heninger said the requirement “sounds [like] a lot, but is on the same order of magnitude of the network traffic that Cloudflare has said publicly it handles in about a day.” Most Privacy Pass implementations rotate keys regularly, a measure that greatly reduces, but doesn’t automatically eliminate, the chances of attacker success.
The technique implements a variant of the number field sieve algorithm that was invented in 2007. This “‘special’ number field sieve” is used against an “oracle,” a weakness in RSA and some other cryptosystems that gives yes-or-no answers to specific queries. By performing a massive number of operations, attackers can gather enough information to decipher the ciphertext. (Again, this technique poses no practical threat against RSA that uses PKCS or PSS padding, because they eliminate the oracle.) While factoring a 1024-bit key requires an estimated 280 operations and 500,000 to 1 million CPU core-years, using the sieve to forge a signature took just (as noted earlier) 265 operations and 1,380 core-years.
The paper’s authors and other researchers stress that the new attack poses little real-world threat. It does, however, drastically lower the estimated security of textbook RSA, and it does so in a way no one knew of previously.
Cryptographers have worked furiously in recent years to devise alternative cryptosystems that aren’t vulnerable to quantum computing attacks. The new attack will further increase the urgency of completely moving away from the cryptosystem. The paper authors provide an easier-to-digest explainer here.
