论文标题
碰撞发现的NISQ复杂性
The NISQ Complexity of Collision Finding
论文作者
论文摘要
抗碰撞的哈希是现代密码学中的基本原始性,可确保没有有效的方法可以找到产生相同哈希价值的不同输入。该属性支持了各种加密应用程序的安全性,这对于了解其复杂性至关重要。在经典环境中,该问题的复杂性被很好地理解,并且需要查询$θ(n^{1/2})$查询才能找到碰撞。但是,量子计算的出现引入了新的挑战,因为量子对手$ \ unicode {x2013} $配备了量子查询的力量$ \ unicode {x2013} $可以更有效地发现碰撞。 Brassard,Höyer和Tapp以及Aaronson和Shi确定,全尺寸的量子对手需要$θ(n^{1/3})$查询来查找碰撞,促使需要更长的哈希输出,这会影响安全性所需的关键长度。 本文探讨了量子攻击在嘈杂的中等量表量子(NISQ)时代的含义。在这项工作中,我们研究了NISQ算法的三种不同模型,并为所有这些模型实现了紧密的界限: (1)一种混合算法进行自适应量子或经典查询,但量子查询预算有限或 (2)一种量子算法,可访问嘈杂的甲骨文,但要遵守dephasing或depolarization通道或 (3)一种杂种算法,其最大量子深度具有上限;即,由低深度量子电路帮助的经典算法。 实际上,我们的结果处理NISQ和全尺寸量子计算机之间的所有制度。以前,只有Sun和Zheng,Rosmanis,Chen,Cotler,Huang和Li的模型才知道这些模型的前图搜索问题的结果,而对碰撞发现问题一无所知。
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 $Θ(N^{1/2})$ 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, Höyer and Tapp and Aaronson and Shi established that full-scale quantum adversaries require $Θ(N^{1/3})$ 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.