{"publication_status":"published","citation":{"ieee":"J. F. Alwen, J. Blocki, and K. Z. Pietrzak, “Depth-robust graphs and their cumulative memory complexity,” presented at the EUROCRYPT: Theory and Applications of Cryptographic Techniques, Paris, France, 2017, vol. 10212, pp. 3–32.","short":"J.F. Alwen, J. Blocki, K.Z. Pietrzak, in:, J.-S. Coron, J. Buus Nielsen (Eds.), Springer, 2017, pp. 3–32.","apa":"Alwen, J. F., Blocki, J., &#38; Pietrzak, K. Z. (2017). Depth-robust graphs and their cumulative memory complexity. In J.-S. Coron &#38; J. Buus Nielsen (Eds.) (Vol. 10212, pp. 3–32). Presented at the EUROCRYPT: Theory and Applications of Cryptographic Techniques, Paris, France: Springer. <a href=\"https://doi.org/10.1007/978-3-319-56617-7_1\">https://doi.org/10.1007/978-3-319-56617-7_1</a>","ama":"Alwen JF, Blocki J, Pietrzak KZ. Depth-robust graphs and their cumulative memory complexity. In: Coron J-S, Buus Nielsen J, eds. Vol 10212. Springer; 2017:3-32. doi:<a href=\"https://doi.org/10.1007/978-3-319-56617-7_1\">10.1007/978-3-319-56617-7_1</a>","chicago":"Alwen, Joel F, Jeremiah Blocki, and Krzysztof Z Pietrzak. “Depth-Robust Graphs and Their Cumulative Memory Complexity.” edited by Jean-Sébastien Coron and Jesper Buus Nielsen, 10212:3–32. Springer, 2017. <a href=\"https://doi.org/10.1007/978-3-319-56617-7_1\">https://doi.org/10.1007/978-3-319-56617-7_1</a>.","mla":"Alwen, Joel F., et al. <i>Depth-Robust Graphs and Their Cumulative Memory Complexity</i>. Edited by Jean-Sébastien Coron and Jesper Buus Nielsen, vol. 10212, Springer, 2017, pp. 3–32, doi:<a href=\"https://doi.org/10.1007/978-3-319-56617-7_1\">10.1007/978-3-319-56617-7_1</a>.","ista":"Alwen JF, Blocki J, Pietrzak KZ. 2017. Depth-robust graphs and their cumulative memory complexity. EUROCRYPT: Theory and Applications of Cryptographic Techniques, LNCS, vol. 10212, 3–32."},"month":"04","scopus_import":1,"main_file_link":[{"url":"https://eprint.iacr.org/2016/875","open_access":"1"}],"volume":10212,"status":"public","date_updated":"2021-01-12T08:07:22Z","author":[{"full_name":"Alwen, Joel F","last_name":"Alwen","id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87","first_name":"Joel F"},{"first_name":"Jeremiah","last_name":"Blocki","full_name":"Blocki, Jeremiah"},{"orcid":"0000-0002-9139-1654","last_name":"Pietrzak","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","first_name":"Krzysztof Z","full_name":"Pietrzak, Krzysztof Z"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","editor":[{"first_name":"Jean-Sébastien","last_name":"Coron","full_name":"Coron, Jean-Sébastien"},{"last_name":"Buus Nielsen","first_name":"Jesper","full_name":"Buus Nielsen, Jesper"}],"_id":"640","year":"2017","alternative_title":["LNCS"],"quality_controlled":"1","doi":"10.1007/978-3-319-56617-7_1","publist_id":"7148","type":"conference","publisher":"Springer","department":[{"_id":"KrPi"}],"oa_version":"Submitted Version","date_published":"2017-04-01T00:00:00Z","conference":{"location":"Paris, France","start_date":"2017-04-30","end_date":"2017-05-04","name":"EUROCRYPT: Theory and Applications of Cryptographic Techniques"},"ec_funded":1,"abstract":[{"lang":"eng","text":"Data-independent Memory Hard Functions (iMHFS) are finding a growing number of applications in security; especially in the domain of password hashing. An important property of a concrete iMHF is specified by fixing a directed acyclic graph (DAG) Gn on n nodes. The quality of that iMHF is then captured by the following two pebbling complexities of Gn: – The parallel cumulative pebbling complexity Π∥cc(Gn) must be as high as possible (to ensure that the amortized cost of computing the function on dedicated hardware is dominated by the cost of memory). – The sequential space-time pebbling complexity Πst(Gn) should be as close as possible to Π∥cc(Gn) (to ensure that using many cores in parallel and amortizing over many instances does not give much of an advantage). In this paper we construct a family of DAGs with best possible parameters in an asymptotic sense, i.e., where Π∥cc(Gn) = Ω(n2/ log(n)) (which matches a known upper bound) and Πst(Gn) is within a constant factor of Π∥cc(Gn). Our analysis relies on a new connection between the pebbling complexity of a DAG and its depth-robustness (DR) – a well studied combinatorial property. We show that high DR is sufficient for high Π∥cc. Alwen and Blocki (CRYPTO’16) showed that high DR is necessary and so, together, these results fully characterize DAGs with high Π∥cc in terms of DR. Complementing these results, we provide new upper and lower bounds on the Π∥cc of several important candidate iMHFs from the literature. We give the first lower bounds on the memory hardness of the Catena and Balloon Hashing functions in a parallel model of computation and we give the first lower bounds of any kind for (a version) of Argon2i. Finally we describe a new class of pebbling attacks improving on those of Alwen and Blocki (CRYPTO’16). By instantiating these attacks we upperbound the Π∥cc of the Password Hashing Competition winner Argon2i and one of the Balloon Hashing functions by O (n1.71). We also show an upper bound of O(n1.625) for the Catena functions and the two remaining Balloon Hashing functions."}],"oa":1,"language":[{"iso":"eng"}],"date_created":"2018-12-11T11:47:39Z","publication_identifier":{"isbn":["978-331956616-0"]},"title":"Depth-robust graphs and their cumulative memory complexity","day":"01","page":"3 - 32","intvolume":"     10212","project":[{"grant_number":"682815","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","name":"Teaching Old Crypto New Tricks","call_identifier":"H2020"}]}