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 journalbook |lastlast1=Dwork |firstfirst1=Cynthia |last2=Goldberg |first2=Andrew |last3=Naor |first3=Moni |date=2003 |editor-last=Boneh |editor-first=Dan |titlechapter=On Memory-Bound Functions for Fighting Spam |url=https://link.springer.com/chapter/10.1007/978-3-540-45146-4_25 |journaltitle=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 journalbook |lastlast1=Biryukov |firstfirst1=Alex |last2=Khovratovich |first2=Dmitry |date=2015 |editor-last=Iwata |editor-first=Tetsu |editor2-last=Cheon |editor2-first=Jung Hee |titlechapter=Tradeoff Cryptanalysis of Memory-Hard Functions |url=https://link.springer.com/chapter/10.1007/978-3-662-48800-3_26 |journaltitle=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 ==

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== Variants ==

MHFs can be categorized into two different groups based on their evaluation patterns: data-dependent memory-hard functions (dMHF) and data-independent memory-hard functions (iMHF). As opposed to iMHFs, the memory access pattern of a dMHF depends on the function input, such as the password provided to a key derivation function.<ref>{{Cite journalbook |lastlast1=Blocki |firstfirst1=Jeremiah |last2=Harsha |first2=Ben |last3=Kang |first3=Siteng |last4=Lee |first4=Seunghoon |last5=Xing |first5=Lu |last6=Zhou |first6=Samson |date=2019 |editor-last=Boldyreva |editor-first=Alexandra |editor2-last=Micciancio |editor2-first=Daniele |titlechapter=Data-Independent Memory Hard Functions: New Attacks and Stronger Constructions |chapter-url=https://link.springer.com/chapter/10.1007/978-3-030-26951-7_20 |journaltitle=Advances in Cryptology – CRYPTO 2019 |series=Lecture Notes in Computer Science |language=en |___location=Cham |publisher=Springer International Publishing |pages=573–607 |doi=10.1007/978-3-030-26951-7_20 |isbn=978-3-030-26951-7}}</ref> Examples of dMHFs are [[scrypt]] and [[Argon2]]d, while examples of iMHFs are [[Argon2]]i and [[catena (cryptography)|catena]]. Many of these MHFs have been designed to be used as [[key derivation function|password hashing function]]s because of their memory hardness.

A notable problem with dMHFs is that they are prone to [[side-channel attack]]s such as cache timing. This has resulted in a preference for using iMHFs when hashing passwords. However, iMHFs have been mathematically proven to have weaker memory hardness properties than dMHFs.<ref>Alwen, J., Blocki, J. (2016). [https://doi.org/10.1007/978-3-662-53008-5_9''Efficiently Computing Data-Independent Memory-Hard Functions.'']</ref>