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• W4312698707 abstract "The classical (parallel) black pebbling game is a useful abstraction which allows us to analyze the resources (space, space-time, cumulative space) necessary to evaluate a function f with a static data-dependency graph G. Of particular interest in the field of cryptography are data-independent memory-hard functions $$f_{G,H}$$ which are defined by a directed acyclic graph (DAG) G and a cryptographic hash function H. The pebbling complexity of the graph G characterizes the amortized cost of evaluating $$f_{G,H}$$ multiple times as well as the total cost to run a brute-force preimage attack over a fixed domain $$mathcal {X}$$ , i.e., given $$y in {0,1}^*$$ find $$x in mathcal {X}$$ such that $$f_{G,H}(x)=y$$ . While a classical attacker will need to evaluate the function $$f_{G,H}$$ at least $$m=|mathcal {X}|$$ times a quantum attacker running Grover’s algorithm only requires $$mathcal {O}left( sqrt{m}right) $$ blackbox calls to a quantum circuit $$C_{G,H}$$ evaluating the function $$f_{G,H}$$ . Thus, to analyze the cost of a quantum attack it is crucial to understand the space-time cost (equivalently width times depth) of the quantum circuit $$C_{G,H}$$ . We first observe that a legal black pebbling strategy for the graph G does not necessarily imply the existence of a quantum circuit with comparable complexity—in contrast to the classical setting where any efficient pebbling strategy for G corresponds to an algorithm with comparable complexity for evaluating $$f_{G,H}$$ . Motivated by this observation we introduce a new parallel reversible pebbling game which captures additional restrictions imposed by the No-Deletion Theorem in Quantum Computing. We apply our new reversible pebbling game to analyze the reversible space-time complexity of several important graphs: Line Graphs, Argon2i-A, Argon2i-B, and DRSample. Specifically, (1) we show that a line graph of size N has reversible space-time complexity at most $$mathcal {O}left( N^{1+frac{2}{sqrt{log N}}}right) $$ . (2) We show that any (e, d)-reducible DAG has reversible space-time complexity at most $$mathcal {O}left( Ne+dN2^dright) $$ . In particular, this implies that the reversible space-time complexity of Argon2i-A and Argon2i-B are at most $$mathcal {O}left( N^2 log log N/sqrt{log N}right) $$ and $$mathcal {O}left( N^2/root 3 of {log N}right) $$ , respectively. (3) We show that the reversible space-time complexity of DRSample is at most $$mathcal {O}left( N^2 log log N/log Nright) $$ . We also study the cumulative pebbling cost of reversible pebblings extending a (non-reversible) pebbling attack of Alwen and Blocki on depth-reducible graphs." @default.
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• W4312698707 date "2022-01-01" @default.
• W4312698707 modified "2023-09-26" @default.
• W4312698707 title "The Parallel Reversible Pebbling Game: Analyzing the Post-quantum Security of iMHFs" @default.
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• W4312698707 doi "https://doi.org/10.1007/978-3-031-22318-1_3" @default.
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