Memory-hard function: Difference between revisions

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{{short description|Type of cryptographic algorithm}}In [[cryptography]], a '''memory-hard function''' ('''MHF''') is a function that costs a significant amount of [[random-access memory|memory]] to efficiently evaluate.<ref name=":0">{{Cite thesis |title=Memory-Hard Functions: When Theory Meets Practice |url=https://escholarship.org/uc/item/7x4630qv |publisher=UC Santa Barbara |date=2019 |language=en |first=Binyi |last=Chen}}</ref> It differs from a [[memory-bound function]], which incurs cost by slowing down computation through memory latency.<ref>{{Cite journal |last=Dwork |first=Cynthia |last2=Goldberg |first2=Andrew |last3=Naor |first3=Moni |date=2003 |editor-last=Boneh |editor-first=Dan |title=On Memory-Bound Functions for Fighting Spam |url=https://link.springer.com/chapter/10.1007/978-3-540-45146-4_25 |journal=Advances in Cryptology - CRYPTO 2003 |series=Lecture Notes in Computer Science |language=en |___location=Berlin, Heidelberg |publisher=Springer |pages=426–444 |doi=10.1007/978-3-540-45146-4_25 |isbn=978-3-540-45146-4|doi-access=free }}</ref> MHFs have found use in [[key stretching]] and [[proof of work]] as their increased memory requirements significantly reduce the computational efficiency advantage of custom hardware over general-purpose hardware compared to non-MHFs.<ref name=":1">{{Cite web |last=LIU |first=ALEC |date=2013-11-29 |title=Beyond Bitcoin: A Guide to the Most Promising Cryptocurrencies |url=https://www.vice.com/en/article/4x3ywn/beyond-bitcoin-a-guide-to-the-most-promising-cryptocurrencies |access-date=2023-09-30 |website=Vice |language=en}}</ref><ref name=":0" />

== Introduction ==

MHFs are designed to consume large amounts of memory on a computer in order to reduce the effectiveness of [[parallel computing]]. In order to evaluate the function using less memory, a significant time penalty is incurred. As each MHF computation requires a large amount of memory, the number of function computations that can occur simultaneously is limited by the amount of available memory. This reduces the efficiency of specialised hardware, such as [[application-specific integrated circuit]]s and [[Graphics processing unit|graphics processing units]], which utilise parallelisation, in computing a MHF for a large number of inputs, such as when [[Brute-force attack|brute-forcing]] password hashes or [[Cryptocurrency|mining cryptocurrency]].<ref name=":0" /><ref name=":2">{{Cite journal |last=Biryukov |first=Alex |last2=Khovratovich |first2=Dmitry |date=2015 |editor-last=Iwata |editor-first=Tetsu |editor2-last=Cheon |editor2-first=Jung Hee |title=Tradeoff Cryptanalysis of Memory-Hard Functions |url=https://link.springer.com/chapter/10.1007/978-3-662-48800-3_26 |journal=Advances in Cryptology – ASIACRYPT 2015 |series=Lecture Notes in Computer Science |language=en |___location=Berlin, Heidelberg |publisher=Springer |pages=633–657 |doi=10.1007/978-3-662-48800-3_26 |isbn=978-3-662-48800-3|doi-access=free }}</ref>

== Motivation and examples ==