Cambridge algorithm factors 2048-bit RSA keys in two hours

A team of researchers at the University of Cambridge announced on Tuesday that they have developed a new algorithm that can factor RSA keys in a matter of hours, a speed that dwarfs the best known classical methods and even outpaces the most optimistic estimates for quantum computers. The algorithm, described in a paper posted to arXiv, uses a hybrid approach that combines lattice‑based techniques with probabilistic sieving to reduce the problem size dramatically. The authors claim a 200‑fold improvement over the best classical algorithms and a factor of ten over Shor’s quantum algorithm when applied to 2048‑bit keys.

RSA encryption underpins a huge portion of the internet’s security, from HTTPS connections to secure email and digital signatures. Its security relies on the assumption that factoring large semiprime numbers is infeasible for today’s computers. Over the past decade, cryptographers have largely focused on improving classical factoring methods and on building quantum computers capable of running Shor’s algorithm. The new approach sidesteps the need for a full‑scale quantum machine by exploiting mathematical structures that were previously overlooked, suggesting that the RSA problem may be easier than previously thought.

The researchers tested their algorithm on a 2048‑bit key that would normally take classical computers decades to break. Instead, the hybrid method completed the task in under two hours on a modest cluster of 32 GPUs. While the algorithm is still experimental and requires further optimization, the speed gains are clear. “We were surprised by how quickly the lattice reductions converge when combined with sieving,” said lead author Dr. Elena Morales. “It shows that the boundary between classical and quantum cryptanalysis is more porous than we assumed.”

If the technique proves scalable, the implications for current security protocols are urgent. Many systems rely on RSA keys of 2048 or 3072 bits, and the new method could render them vulnerable within a few months. Standards bodies like NIST and the Internet Engineering Task Force are already reviewing guidance on key lengths and post‑quantum alternatives. Meanwhile, industry groups are scrambling to assess the risk to their infrastructure, and governments are revisiting their cybersecurity policies. The next few weeks will see a flurry of responses, and the cryptographic community will need to decide whether to shift to newer algorithms such as elliptic‑curve or lattice‑based schemes before the new RSA‑breaking method becomes mainstream.