ArticleScientific reports2023
HUBO and QUBO models for prime factorization.
Article in Scientific reports, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Quantum annealing for inverse kinematics in robotics.Scientific reports · 2025Article
- Range dependent Hamiltonian algorithms for numerical QUBO formulation.Scientific reports · 2025Article
- A quantum-inspired probabilistic prime factorization based on virtually connected Boltzmann machine and probabilistic annealing.Scientific reports · 2023Article
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Authors and funding
2 authors.
Funding
Abstract
The security of the RSA cryptosystem is based on the difficulty of factoring a large number N into prime numbers [Formula: see text] and [Formula: see text] satisfying [Formula: see text]. This paper presents a prime factorization method using a D-Wave quantum computer that could threaten the RSA cryptosystem in the future. The starting point for this method is very simple, representing two prime numbers as qubits. Then, we set the difference between the product of the two prime numbers expressed in qubits and N as a cost function, and we find the solution when the cost function is minimized. D-Wave's quantum annealer can find the minimum value of any quadratic problem. However, the cost function must be a higher-order unconstrained optimization (HUBO) model because it contains second- or higher-order terms. We used a hybrid solver accessible via Leap, D-Wave's real-time quantum cloud service, and the dimod package provided by the D-Wave Ocean software development kit (SDK) to solve the HUBO problem. We also successfully factorized 102,454,763 with 26 logical qubits. In addition, we factorized 1,000,070,001,221 using the range-dependent Hamiltonian algorithm.
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