Related papers: The NISQ Complexity of Collision Finding

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.