The Parallel Reversible Pebbling Game: Analyzing the Post-Quantum Security of iMHFs
Jeremiah Blocki, Blake Holman, Seunghoon Lee

TL;DR
This paper introduces a new parallel reversible pebbling game to analyze the quantum space-time complexity of data-independent memory-hard functions, crucial for understanding post-quantum security of cryptographic schemes.
Contribution
The paper proposes a novel reversible pebbling game that accounts for quantum restrictions, providing new insights into the quantum complexity of cryptographic graph evaluations.
Findings
Reversible pebbling complexity differs from classical pebbling in quantum settings.
Applied to specific graphs, the new game reveals quantum resource requirements.
Provides a framework for assessing post-quantum security of memory-hard functions.
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 with a static data-dependency graph . Of particular interest in the field of cryptography are data-independent memory-hard functions which are defined by a directed acyclic graph (DAG) and a cryptographic hash function . The pebbling complexity of the graph characterizes the amortized cost of evaluating multiple times as well as the total cost to run a brute-force preimage attack over a fixed domain , i.e., given find such that . While a classical attacker will need to evaluate the function at least times a quantum attacker running Grover's algorithm only requires…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Cryptographic Implementations and Security · Cryptography and Data Security
