The NISQ Complexity of Collision Finding

• URL: http://arxiv.org/abs/2211.12954v2
• Date: Wed, 28 Feb 2024 11:00:06 GMT
• Title: The NISQ Complexity of Collision Finding
• Authors: Yassine Hamoudi, Qipeng Liu, Makrand Sinha
• Abstract summary: A fundamental primitive in modern cryptography, collision-resistant hashing ensures there is no efficient way to find inputs that produce the same hash value. Quantum adversaries now require full-scale computers equipped with the power of NISQ. In this paper, we investigate three different models for NISQ algorithms achieve tight bounds for all of them.
• Score: 2.9405711598281536
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Collision-resistant hashing, a fundamental primitive in modern cryptography, ensures that there is no efficient way to find distinct inputs that produce the same hash value. This property underpins the security of various cryptographic applications, making it crucial to understand its complexity. The complexity of this problem is well-understood in the classical setting and $\Theta(N^{1/2})$ queries are needed to find a collision. However, the advent of quantum computing has introduced new challenges since quantum adversaries $\unicode{x2013}$ equipped with the power of quantum queries $\unicode{x2013}$ can find collisions much more efficiently. Brassard, H\"oyer and Tapp and Aaronson and Shi established that full-scale quantum adversaries require $\Theta(N^{1/3})$ queries to find a collision, prompting a need for longer hash outputs, which impacts efficiency in terms of the key lengths needed for security. This paper explores the implications of quantum attacks in the Noisy-Intermediate Scale Quantum (NISQ) era. In this work, we investigate three different models for NISQ algorithms and achieve tight bounds for all of them: (1) A hybrid algorithm making adaptive quantum or classical queries but with a limited quantum query budget, or (2) A quantum algorithm with access to a noisy oracle, subject to a dephasing or depolarizing channel, or (3) A hybrid algorithm with an upper bound on its maximum quantum depth; i.e., a classical algorithm aided by low-depth quantum circuits. In fact, our results handle all regimes between NISQ and full-scale quantum computers. Previously, only results for the pre-image search problem were known for these models by Sun and Zheng, Rosmanis, Chen, Cotler, Huang and Li while nothing was known about the collision finding problem.

Related papers

• A quantum-classical hybrid algorithm with Ising model for the learning with errors problem [13.06030390635216]
  We propose a quantum-classical hybrid algorithm with Ising model (HAWI) to address the Learning-With-Errors (LWE) problem. We identify the low-energy levels of the Hamiltonian to extract the solution, making it suitable for implementation on current noisy intermediate-scale quantum (NISQ) devices. Our algorithm is iterations, and its time complexity depends on the specific quantum algorithm employed to find the Hamiltonian's low-energy levels.
  arXiv  Detail & Related papers  (2024-08-15T05:11:35Z)
• Discretized Quantum Exhaustive Search for Variational Quantum Algorithms [0.0]
  Currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved accurately with those devices. We propose a novel method that can improve variational quantum algorithms -- discretized quantum exhaustive search''
  arXiv  Detail & Related papers  (2024-07-24T22:06:05Z)
• Generalized Hybrid Search and Applications to Blockchain and Hash Function Security [50.16790546184646]
  We first examine the hardness of solving various search problems by hybrid quantum-classical strategies. We then construct a hybrid quantum-classical search algorithm and analyze its success probability.
  arXiv  Detail & Related papers  (2023-11-07T04:59:02Z)
• Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
  The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• Limitations of Noisy Quantum Devices in Computational and Entangling Power [5.178527492542246]
  We show that noisy quantum devices with a circuit depth of more than $O(log n)$ provide no advantages in any quantum algorithms. We also study the maximal entanglement that noisy quantum devices can produce under one- and two-dimensional qubit connections.
  arXiv  Detail & Related papers  (2023-06-05T12:29:55Z)
• Making the cut: two methods for breaking down a quantum algorithm [0.0]
  It remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy, small-scale quantum hardware. We identify and characterize two methods of breaking down'' quantum algorithms into rounds of lower (query) depth. We show that for the first problem parallelization offers the best performance, while for the second is the better choice.
  arXiv  Detail & Related papers  (2023-05-17T18:00:06Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Iterative Qubits Management for Quantum Index Searching in a Hybrid System [56.39703478198019]
  IQuCS aims at index searching and counting in a quantum-classical hybrid system. We implement IQuCS with Qiskit and conduct intensive experiments. Results demonstrate that it reduces qubits consumption by up to 66.2%.
  arXiv  Detail & Related papers  (2022-09-22T21:54:28Z)
• A single $T$-gate makes distribution learning hard [56.045224655472865]
  This work provides an extensive characterization of the learnability of the output distributions of local quantum circuits. We show that for a wide variety of the most practically relevant learning algorithms -- including hybrid-quantum classical algorithms -- even the generative modelling problem associated with depth $d=omega(log(n))$ Clifford circuits is hard.
  arXiv  Detail & Related papers  (2022-07-07T08:04:15Z)
• 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)
• Hardware Efficient Quantum Search Algorithm [17.74233101199813]
  We propose a novel hardware efficient quantum search algorithm to overcome this challenge. Our key idea is to replace the global diffusion operation with low-cost local diffusions. The circuit cost reduction leads to a remarkable improvement in the system success rates.
  arXiv  Detail & Related papers  (2021-03-26T01:08:50Z)

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.