Researchers have applied a new computational algorithm to demonstrate that integer factorization can be performed within a subexponential worst-case bound, expanding on a recent breakthrough in theoretical computer science. The result builds upon the work of Anthropic’s internal Claude models, which developed a subexponential algorithm for the 3-SAT problem to disprove the Exponential Time Hypothesis, a foundational theory that previously defined the efficiency limits of certain calculations.
The discovery was made on Oct 16 using 14M output tokens without human intervention, a result that was separately reached by models from OpenAI. While the findings do not immediately compromise existing encryption standards, the breakthrough raises questions about other security assumptions used to protect internet traffic and has prompted reactions of shock from computer scientists whose lifelong research was based on the now-disproven hypothesis.