{"type":"conference","page":"595 - 603","status":"public","project":[{"grant_number":"259668","_id":"258C570E-B435-11E9-9278-68D0E5697425","name":"Provable Security for Physical Cryptography","call_identifier":"FP7"}],"oa":1,"publication":"Proceedings of the 47th annual ACM symposium on Theory of computing","publist_id":"5498","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"01","scopus_import":"1","year":"2015","language":[{"iso":"eng"}],"month":"06","doi":"10.1145/2746539.2746622","date_updated":"2025-09-23T09:17:15Z","isi":1,"quality_controlled":"1","author":[{"first_name":"Joel F","full_name":"Alwen, Joel F","last_name":"Alwen","id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Serbinenko","full_name":"Serbinenko, Vladimir","first_name":"Vladimir"}],"department":[{"_id":"KrPi"}],"oa_version":"Submitted Version","article_processing_charge":"No","publication_status":"published","date_created":"2018-12-11T11:53:16Z","title":"High parallel complexity graphs and memory-hard functions","external_id":{"isi":["000485296600063"]},"abstract":[{"lang":"eng","text":"We develop new theoretical tools for proving lower-bounds on the (amortized) complexity of certain functions in models of parallel computation. We apply the tools to construct a class of functions with high amortized memory complexity in the parallel Random Oracle Model (pROM); a variant of the standard ROM allowing for batches of simultaneous queries. In particular we obtain a new, more robust, type of Memory-Hard Functions (MHF); a security primitive which has recently been gaining acceptance in practice as an effective means of countering brute-force attacks on security relevant functions. Along the way we also demonstrate an important shortcoming of previous definitions of MHFs and give a new definition addressing the problem. The tools we develop represent an adaptation of the powerful pebbling paradigm (initially introduced by Hewitt and Paterson [HP70] and Cook [Coo73]) to a simple and intuitive parallel setting. We define a simple pebbling game Gp over graphs which aims to abstract parallel computation in an intuitive way. As a conceptual contribution we define a measure of pebbling complexity for graphs called cumulative complexity (CC) and show how it overcomes a crucial shortcoming (in the parallel setting) exhibited by more traditional complexity measures used in the past. As a main technical contribution we give an explicit construction of a constant in-degree family of graphs whose CC in Gp approaches maximality to within a polylogarithmic factor for any graph of equal size (analogous to the graphs of Tarjan et. al. [PTC76, LT82] for sequential pebbling games). Finally, for a given graph G and related function fG, we derive a lower-bound on the amortized memory complexity of fG in the pROM in terms of the CC of G in the game Gp."}],"_id":"1652","conference":{"location":"Portland, OR, United States","name":"STOC: Symposium on the Theory of Computing","start_date":"2015-06-14","end_date":"2015-06-17"},"date_published":"2015-06-01T00:00:00Z","publisher":"ACM","main_file_link":[{"url":"http://eprint.iacr.org/2014/238","open_access":"1"}],"ec_funded":1,"citation":{"short":"J.F. Alwen, V. Serbinenko, in:, Proceedings of the 47th Annual ACM Symposium on Theory of Computing, ACM, 2015, pp. 595–603.","ista":"Alwen JF, Serbinenko V. 2015. High parallel complexity graphs and memory-hard functions. Proceedings of the 47th annual ACM symposium on Theory of computing. STOC: Symposium on the Theory of Computing, 595–603.","chicago":"Alwen, Joel F, and Vladimir Serbinenko. “High Parallel Complexity Graphs and Memory-Hard Functions.” In <i>Proceedings of the 47th Annual ACM Symposium on Theory of Computing</i>, 595–603. ACM, 2015. <a href=\"https://doi.org/10.1145/2746539.2746622\">https://doi.org/10.1145/2746539.2746622</a>.","ama":"Alwen JF, Serbinenko V. High parallel complexity graphs and memory-hard functions. In: <i>Proceedings of the 47th Annual ACM Symposium on Theory of Computing</i>. ACM; 2015:595-603. doi:<a href=\"https://doi.org/10.1145/2746539.2746622\">10.1145/2746539.2746622</a>","ieee":"J. F. Alwen and V. Serbinenko, “High parallel complexity graphs and memory-hard functions,” in <i>Proceedings of the 47th annual ACM symposium on Theory of computing</i>, Portland, OR, United States, 2015, pp. 595–603.","mla":"Alwen, Joel F., and Vladimir Serbinenko. “High Parallel Complexity Graphs and Memory-Hard Functions.” <i>Proceedings of the 47th Annual ACM Symposium on Theory of Computing</i>, ACM, 2015, pp. 595–603, doi:<a href=\"https://doi.org/10.1145/2746539.2746622\">10.1145/2746539.2746622</a>.","apa":"Alwen, J. F., &#38; Serbinenko, V. (2015). High parallel complexity graphs and memory-hard functions. In <i>Proceedings of the 47th annual ACM symposium on Theory of computing</i> (pp. 595–603). Portland, OR, United States: ACM. <a href=\"https://doi.org/10.1145/2746539.2746622\">https://doi.org/10.1145/2746539.2746622</a>"},"corr_author":"1"}