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HUBO and QUBO models for prime factorization.

Kyungtaek Jun1,2,3, Hyunju Lee4

  • 1Research center, Qtomo, Busan, South Korea. ktfriends@gmail.com.

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This study introduces a novel quantum computing approach for prime factorization, potentially impacting RSA cryptosystem security. Researchers utilized a D-Wave quantum computer to factor large numbers, demonstrating a new threat to current encryption standards.

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Area of Science:

  • Quantum Computing
  • Cryptography
  • Number Theory

Background:

  • The RSA cryptosystem's security relies on the computational difficulty of factoring large composite numbers into their prime factors.
  • Current factorization methods are vulnerable to advances in quantum computing.

Purpose of the Study:

  • To present a quantum computing-based method for prime factorization.
  • To explore the potential threat of quantum computers to the RSA cryptosystem.

Main Methods:

  • Representing prime numbers as qubits.
  • Defining a cost function based on the difference between the product of qubit-represented primes and the target number N.
  • Minimizing the cost function using D-Wave's quantum annealer and a hybrid solver from the D-Wave Ocean SDK.
  • Employing the range-dependent Hamiltonian algorithm for factorization.

Main Results:

  • Successfully factorized the number 102,454,763 using 26 logical qubits.
  • Successfully factorized the number 1,000,070,001,221.

Conclusions:

  • Quantum computing, specifically using D-Wave's annealer, offers a viable method for prime factorization.
  • This quantum approach poses a future threat to the security of the RSA cryptosystem.