Tensor Network Techniques Reveal Polynomial Scaling in Simulated RSA Factoring

Global: Tensor Network Techniques Reveal Polynomial Scaling in Simulated RSA Factoring

A recent study posted on arXiv demonstrates that a quantum‑inspired tensor network algorithm can factor RSA semiprimes with resource requirements that grow polynomially with key size, at least through simulated instances of up to 130 bits. The research, which builds on Schnorr’s mathematical framework, reports successful factorization of actual RSA numbers up to 100 bits and numerical simulations extending to larger instances.

Background on RSA Security

RSA encryption underpins most modern public‑key infrastructures, and its security traditionally relies on the exponential difficulty of factoring large semiprime numbers using classical algorithms. This difficulty has long been considered a barrier to breaking RSA keys in practical settings.

Tensor Network Methodology

The authors reformulate the factorization problem as a combinatorial optimization task and apply tensor network methods—a technique originally developed for simulating quantum many‑body systems—to solve it on classical hardware. By integrating Schnorr’s sieving approach with tensor network contractions, the algorithm exploits structural patterns in the factorization search space.

Simulation Results

Empirical testing confirms that the algorithm can factor RSA numbers of 100‑bit length directly. In addition, numerical simulations were carried out for key sizes up to 130 bits, with the underlying optimization encoded in quantum‑system analogues requiring up to 256 qubits. Across these experiments, the measured computational resources (memory and runtime) displayed a high‑order polynomial relationship to the bit length of the semiprime.

Resource Scaling and Limitations

Although the observed polynomial scaling marks a departure from the expected exponential growth, the authors note that the high‑order nature of the polynomial still imposes practical limits. Scaling beyond the simulated 130‑bit range would demand resources that grow rapidly, thereby constraining the method’s applicability to larger, industry‑standard RSA keys.

Implications for Cryptographic Practice

The findings do not immediately compromise existing communication systems, but they underscore the accelerating need for post‑quantum cryptographic schemes or quantum key distribution. By illustrating a pathway to more efficient factorization, the work adds weight to ongoing efforts to transition away from RSA‑based security.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.