基于Pebbling的静态记忆困难函数和非线性时空折衷
Static-Memory-Hard Functions and Nonlinear Space-Time Tradeoffs via Pebbling
摘要：
Pebble游戏最初是为了研究计算中的时空权衡而制定的，由有向无环图（DAG）上的游戏建模。卵石和密码学之间的密切联系已经知道了几十年。最近的一系列研究（Alwen和Serbinenko，STOC 2015）加深了我们对密码学中记忆硬度概念的理解--哈希函数用于阻止大规模密码破解攻击的有用属性--并且已经表明记忆硬度与图卵石理论有着错综复杂的联系。在这项工作中，我们改进了现有模型的记忆硬度的两个主要限制。首先，记忆硬度的现有测量仅考虑动态（即，运行时）内存使用，而不考虑静态内存使用。我们提出了一个新的静态内存硬功能（SHF）的定义，它考虑到静态内存的使用，并允许更大的内存需求的形式化高效的功能，比在动态设置（内存的使用是固有的运行时有界）。然后，我们给出了两个SHF结构的基础上卵石;为了证明静态记忆硬度，我们定义了一个新的卵石游戏（“黑魔法卵石游戏”），并在我们提出的措施下，新的图形结构具有最佳的复杂性。其次，现有的记忆硬度模型隐含地考虑时间和空间成本之间的线性权衡。我们提出了一个新的模型来捕捉非线性时空权衡，并证明了非线性权衡实际上可以导致对手采用不同的策略从线性权衡。最后，作为一个独立的利益的额外贡献，我们提出了第一个渐近紧图的建设，实现了最好的空间复杂度高达$\log{\log{n}}$ -现有的记忆硬度措施的因素，称为累积复杂性的顺序卵石模型。
英文摘要：
Pebble games were originally formulated to study time-space tradeoffs in computation, modeled by games played on directed acyclic graphs (DAGs). Close connections between pebbling and cryptography have been known for decades. A series of recent research starting with (Alwen and Serbinenko, STOC 2015) has deepened our understanding of the notion of memory-hardness in cryptography --- a useful property of hash functions for deterring large-scale password-cracking attacks --- and has shown memory-hardness to have intricate connections with the theory of graph pebbling. In this work, we improve upon two main limitations of existing models of memory-hardness. First, existing measures of memory-hardness only account for dynamic (i.e., runtime) memory usage, and do not consider static memory usage. We propose a new definition of static-memory-hard function (SHF) which takes into account static memory usage and allows the formalization of larger memory requirements for efficient functions, than in the dynamic setting (where memory usage is inherently bounded by runtime). We then give two SHF constructions based on pebbling; to prove static-memory-hardness, we define a new pebble game ("black-magic pebble game"), and new graph constructions with optimal complexity under our proposed measure. Secondly, existing memory-hardness models implicitly consider linear tradeoffs between the costs of time and space. We propose a new model to capture nonlinear time-space trade-offs and prove that nonlinear tradeoffs can in fact cause adversaries to employ different strategies from linear tradeoffs. Finally, as an additional contribution of independent interest, we present the first asymptotically tight graph construction that achieves the best possible space complexity up to $\log{\log{n}}$-factors for an existing memory-hardness measure called cumulative complexity in the sequential pebbling model.
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