Statistical mechanical models of integer factorization problem

Chihiro H. Nakajima, Masayuki Ohzeki

Research output: Contribution to journalArticlepeer-review


We formulate the integer factorization problem via a formulation of the searching problem for the ground state of a statistical mechanical Hamiltonian. The first passage time required to find a correct divisor of a composite number signifies the exponential computational hardness. The analysis of the density of states of two macroscopic quantities, i.e., the energy and the Hamming distance from the correct solutions, leads to the conclusion that the ground state (correct solution) is completely isolated from the other low-energy states, with the distance being proportional to the system size. In addition, the profile of the microcanonical entropy of the model has two peculiar features that are each related to two marked changes in the energy region sampled via Monte Carlo simulation or simulated annealing. Hence, we find a peculiar first-order phase transition in our model.

Original languageEnglish
Article number014001
Journaljournal of the physical society of japan
Issue number1
Publication statusPublished - 2017 Jan 15

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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