{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T02:17:28Z","timestamp":1721960248890},"reference-count":33,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2018,4]]},"abstract":"<jats:p> Universal hashing, discovered by Carter and Wegman in 1979, has many important applications in computer science. MMH[Formula: see text], which was shown to be [Formula: see text]-universal by Halevi and Krawczyk in 1997, is a well-known universal hash function family. We introduce a variant of MMH[Formula: see text], that we call GRDH, where we use an arbitrary integer [Formula: see text] instead of prime [Formula: see text] and let the keys [Formula: see text] satisfy the conditions [Formula: see text] ([Formula: see text]), where [Formula: see text] are given positive divisors of [Formula: see text]. Then via connecting the universal hashing problem to the number of solutions of restricted linear congruences, we prove that the family GRDH is an [Formula: see text]-almost-[Formula: see text]-universal family of hash functions for some [Formula: see text] if and only if [Formula: see text] is odd and [Formula: see text] [Formula: see text]. Furthermore, if these conditions are satisfied then GRDH is [Formula: see text]-almost-[Formula: see text]-universal, where [Formula: see text] is the smallest prime divisor of [Formula: see text]. Finally, as an application of our results, we propose an authentication code with secrecy scheme which strongly generalizes the scheme studied by Alomair et al. [J. Math. Cryptol. 4 (2010) 121\u2013148], and [J.UCS 15 (2009) 2937\u20132956]. <\/jats:p>","DOI":"10.1142\/s0129054118500089","type":"journal-article","created":{"date-parts":[[2018,5,8]],"date-time":"2018-05-08T00:13:37Z","timestamp":1525738417000},"page":"357-375","source":"Crossref","is-referenced-by-count":8,"title":["On an Almost-Universal Hash Function Family with Applications to Authentication and Secrecy Codes"],"prefix":"10.1142","volume":"29","author":[{"given":"Khodakhast","family":"Bibak","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Victoria, Victoria, BC, Canada V8W 3P6, Canada"}]},{"given":"Bruce M.","family":"Kapron","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Victoria, Victoria, BC, Canada V8W 3P6, Canada"}]},{"given":"Venkatesh","family":"Srinivasan","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Victoria, Victoria, BC, Canada V8W 3P6, 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