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DOI: 10.4230/LIPIcs.ITCS.2020.36
URN: urn:nbn:de:0030-drops-117214
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11721/
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Ameri, Mohammad Hassan ; Blocki, Jeremiah ; Zhou, Samson

Computationally Data-Independent Memory Hard Functions

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LIPIcs-ITCS-2020-36.pdf (0.7 MB)


Abstract

Memory hard functions (MHFs) are an important cryptographic primitive that are used to design egalitarian proofs of work and in the construction of moderately expensive key-derivation functions resistant to brute-force attacks. Broadly speaking, MHFs can be divided into two categories: data-dependent memory hard functions (dMHFs) and data-independent memory hard functions (iMHFs). iMHFs are resistant to certain side-channel attacks as the memory access pattern induced by the honest evaluation algorithm is independent of the potentially sensitive input e.g., password. While dMHFs are potentially vulnerable to side-channel attacks (the induced memory access pattern might leak useful information to a brute-force attacker), they can achieve higher cumulative memory complexity (CMC) in comparison than an iMHF. In particular, any iMHF that can be evaluated in N steps on a sequential machine has CMC at most 𝒪((N^2 log log N)/log N). By contrast, the dMHF scrypt achieves maximal CMC Ω(N^2) - though the CMC of scrypt would be reduced to just 𝒪(N) after a side-channel attack. In this paper, we introduce the notion of computationally data-independent memory hard functions (ciMHFs). Intuitively, we require that memory access pattern induced by the (randomized) ciMHF evaluation algorithm appears to be independent from the standpoint of a computationally bounded eavesdropping attacker - even if the attacker selects the initial input. We then ask whether it is possible to circumvent known upper bound for iMHFs and build a ciMHF with CMC Ω(N^2). Surprisingly, we answer the question in the affirmative when the ciMHF evaluation algorithm is executed on a two-tiered memory architecture (RAM/Cache). We introduce the notion of a k-restricted dynamic graph to quantify the continuum between unrestricted dMHFs (k=n) and iMHFs (k=1). For any ε > 0 we show how to construct a k-restricted dynamic graph with k=Ω(N^(1-ε)) that provably achieves maximum cumulative pebbling cost Ω(N^2). We can use k-restricted dynamic graphs to build a ciMHF provided that cache is large enough to hold k hash outputs and the dynamic graph satisfies a certain property that we call "amenable to shuffling". In particular, we prove that the induced memory access pattern is indistinguishable to a polynomial time attacker who can monitor the locations of read/write requests to RAM, but not cache. We also show that when k=o(N^(1/log log N)) , then any k-restricted graph with constant indegree has cumulative pebbling cost o(N^2). Our results almost completely characterize the spectrum of k-restricted dynamic graphs.

BibTeX - Entry

@InProceedings{ameri_et_al:LIPIcs:2020:11721,
  author =	{Mohammad Hassan Ameri and Jeremiah Blocki and Samson Zhou},
  title =	{{Computationally Data-Independent Memory Hard Functions}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{36:1--36:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Thomas Vidick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11721},
  URN =		{urn:nbn:de:0030-drops-117214},
  doi =		{10.4230/LIPIcs.ITCS.2020.36},
  annote =	{Keywords: Computationally Data-Independent Memory Hard Function, Cumulative Memory Complexity, Dynamic Pebbling Game}
}

Keywords: Computationally Data-Independent Memory Hard Function, Cumulative Memory Complexity, Dynamic Pebbling Game
Seminar: 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Issue Date: 2020
Date of publication: 10.01.2020


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