Quantum inspired factorization up to 100-bit RSA number in polynomial time

• URL: http://arxiv.org/abs/2410.16355v1
• Date: Mon, 21 Oct 2024 18:00:00 GMT
• Title: Quantum inspired factorization up to 100-bit RSA number in polynomial time
• Authors: Marco Tesoro, Ilaria Siloi, Daniel Jaschke, Giuseppe Magnifico, Simone Montangero,
• Abstract summary: We attack the RSA factorization building on Schnorr's mathematical framework. We factorize RSA numbers up to 256 bits encoding the optimization problem in quantum systems. Results do not currently undermine the security of the present communication infrastructure.
• Score: 0.0
• License:
• Abstract: Classical public-key cryptography standards rely on the Rivest-Shamir-Adleman (RSA) encryption protocol. The security of this protocol is based on the exponential computational complexity of the most efficient classical algorithms for factoring large semiprime numbers into their two prime components. Here, we attack RSA factorization building on Schnorr's mathematical framework where factorization translates into a combinatorial optimization problem. We solve the optimization task via tensor network methods, a quantum-inspired classical numerical technique. This tensor network Schnorr's sieving algorithm displays numerical evidence of a polynomial scaling of the resources with the bit-length of the semiprime. We factorize RSA numbers up to 100 bits encoding the optimization problem in quantum systems with up to 256 qubits. Only the high-order polynomial scaling of the required resources limits the factorization of larger numbers. Although these results do not currently undermine the security of the present communication infrastructure, they strongly highlight the urgency of implementing post-quantum cryptography or quantum key distribution.

Related papers

• Sum-of-Squares inspired Quantum Metaheuristic for Polynomial Optimization with the Hadamard Test and Approximate Amplitude Constraints [76.53316706600717]
  Recently proposed quantum algorithm arXiv:2206.14999 is based on semidefinite programming (SDP) We generalize the SDP-inspired quantum algorithm to sum-of-squares. Our results show that our algorithm is suitable for large problems and approximate the best known classicals.
  arXiv  Detail & Related papers  (2024-08-14T19:04:13Z)
• Post-Quantum Security: Origin, Fundamentals, and Adoption [0.29465623430708915]
  We first describe the relation between discrete logarithms and two well-known asymmetric security schemes, RSA and Elliptic Curve Cryptography. Next, we present the foundations of lattice-based cryptography which is the bases of schemes that are considered to be safe against attacks by quantum algorithms. Finally, we describe two such quantum-safe algorithms (Kyber and Dilithium) in more detail.
  arXiv  Detail & Related papers  (2024-05-20T09:05:56Z)
• SOCI^+: An Enhanced Toolkit for Secure OutsourcedComputation on Integers [50.608828039206365]
  We propose SOCI+ which significantly improves the performance of SOCI. SOCI+ employs a novel (2, 2)-threshold Paillier cryptosystem with fast encryption and decryption as its cryptographic primitive. Compared with SOCI, our experimental evaluation shows that SOCI+ is up to 5.4 times more efficient in computation and 40% less in communication overhead.
  arXiv  Detail & Related papers  (2023-09-27T05:19:32Z)
• A comment on "Factoring integers with sublinear resources on a superconducting quantum processor" [0.0]
  We present an open-source implementation of the Schnorr's lattice-based integer factorization algorithm. Our implementation shows that the claimed sublinear lattice dimension for the Hybrid quantum+classical version of Schnorr's successfully factors integers only up to 70 bits. We hope that our implementation serves as a playground for the community to easily test other hybrid quantum + classical integer factorization algorithm ideas.
  arXiv  Detail & Related papers  (2023-07-18T21:46:54Z)
• Revocable Cryptography from Learning with Errors [61.470151825577034]
  We build on the no-cloning principle of quantum mechanics and design cryptographic schemes with key-revocation capabilities. We consider schemes where secret keys are represented as quantum states with the guarantee that, once the secret key is successfully revoked from a user, they no longer have the ability to perform the same functionality as before.
  arXiv  Detail & Related papers  (2023-02-28T18:58:11Z)
• Factoring integers with sublinear resources on a superconducting quantum processor [11.96383198580683]
  Shor's algorithm has seriously challenged information security based on public key cryptosystems. To break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities. We report a universal quantum algorithm for integer factorization by combining the classical lattice reduction with a quantum approximate optimization algorithm.
  arXiv  Detail & Related papers  (2022-12-23T14:45:02Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• Optimizing Tensor Network Contraction Using Reinforcement Learning [86.05566365115729]
  We propose a Reinforcement Learning (RL) approach combined with Graph Neural Networks (GNN) to address the contraction ordering problem. The problem is extremely challenging due to the huge search space, the heavy-tailed reward distribution, and the challenging credit assignment. We show how a carefully implemented RL-agent that uses a GNN as the basic policy construct can address these challenges.
  arXiv  Detail & Related papers  (2022-04-18T21:45:13Z)
• Using Shor's algorithm on near term Quantum computers: a reduced version [0.0]
  We introduce a reduced version of Shor's algorithm that proposes a step forward in increasing the range of numbers that can be factorized on noisy Quantum devices. In particular, we have found noteworthy results in most cases, often being able to factor the given number with only one of the proposed algorithm.
  arXiv  Detail & Related papers  (2021-12-23T15:36:59Z)
• Faster Secure Data Mining via Distributed Homomorphic Encryption [108.77460689459247]
  Homomorphic Encryption (HE) is receiving more and more attention recently for its capability to do computations over the encrypted field. We propose a novel general distributed HE-based data mining framework towards one step of solving the scaling problem. We verify the efficiency and effectiveness of our new framework by testing over various data mining algorithms and benchmark data-sets.
  arXiv  Detail & Related papers  (2020-06-17T18:14:30Z)
• Breaking RSA Security With A Low Noise D-Wave 2000Q Quantum Annealer: Computational Times, Limitations And Prospects [0.0]
  RSA cryptosystem could be easily broken with large scale quantum computers running Shor's factorization algorithm. We analyzed the most promising strategies for RSA hacking via quantum annealing with an extensive study of the low noise D-Wave 2000Q computational times.
  arXiv  Detail & Related papers  (2020-05-05T15:04:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.