{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T15:35:57Z","timestamp":1774020957555,"version":"3.50.1"},"reference-count":0,"publisher":"Universitatsbibliothek der Ruhr-Universitat Bochum","license":[{"start":{"date-parts":[[2022,9,9]],"date-time":"2022-09-09T00:00:00Z","timestamp":1662681600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ToSC"],"abstract":"<jats:p>In this paper, we study the gate depth complexity of (vectorial) Boolean functions in the basis of {NAND, NOR, INV} as a new metric, called latency complexity, to mathematically measure the latency of Boolean functions. We present efficient algorithms to find all Boolean functions with low-latency complexity, or to determine the latency complexity of the (vectorial) Boolean functions, and to find all the circuits with the minimum latency complexity for a given Boolean function. Then, we present another algorithm to build bijective S-boxes with low-latency complexity which with respect to the computation cost, this algorithm overcomes the previous methods of building S-boxes.As a result, for latency complexity 3, we present n-bit S-boxes of 3 \u2264 n \u2264 8 with linearity 2n\u22121 and uniformity 2n\u22122 (except for 5-bit S-boxes for whose the minimum achievable uniformity is 6). Besides, for latency complexity 4, we present several n-bit S-boxes of 5 \u2264 n &lt; 8 with linearity 2n\u22122 and uniformity 2n\u22124.<\/jats:p>","DOI":"10.46586\/tosc.v2022.i3.403-447","type":"journal-article","created":{"date-parts":[[2022,9,9]],"date-time":"2022-09-09T18:21:10Z","timestamp":1662747670000},"page":"403-447","source":"Crossref","is-referenced-by-count":11,"title":["Low-Latency Boolean Functions and Bijective S-boxes"],"prefix":"10.46586","author":[{"given":"Shahram","family":"Rasoolzadeh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25480","published-online":{"date-parts":[[2022,9,9]]},"container-title":["IACR Transactions on Symmetric Cryptology"],"original-title":[],"link":[{"URL":"https:\/\/icscm.ub.rub.de\/index.php\/ToSC\/article\/download\/9862\/11607","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/icscm.ub.rub.de\/index.php\/ToSC\/article\/download\/9862\/11707","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/icscm.ub.rub.de\/index.php\/ToSC\/article\/download\/9862\/9361","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,10]],"date-time":"2024-12-10T14:07:08Z","timestamp":1733839628000},"score":1,"resource":{"primary":{"URL":"https:\/\/icscm.ub.rub.de\/index.php\/ToSC\/article\/view\/9862"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,9]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46586\/tosc.v2022.i3.403-447","relation":{},"ISSN":["2519-173X"],"issn-type":[{"value":"2519-173X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,9]]}}}