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Comput."],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Sidon sets, defined by the property that every sum of any two elements is distinct, play a significant role in areas such as coding theory and cryptography. In this paper, we study two cryptographic functions,\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\boldsymbol{f_q}$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\boldsymbol{g_q}$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , constructed from Bose-type Sidon sets. These functions exhibit three key cryptographic properties: low differential uniformity, uniform output distribution, and low linearity. The first ensures consistent sensitivity to input changes, offering resistance against differential cryptanalysis, as both functions achieve differential\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\boldsymbol{2}$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -uniformity, the lowest non-trivial value possible, thus guaranteeing maximum theoretical resistance. The second maximizes entropy by ensuring a uniform output distribution, thereby avoiding statistical biases that attackers could exploit. The third property exhibits different behavior between the two functions: while\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\boldsymbol{f_p}$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    demonstrates linear growth\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\boldsymbol{\\mathcal{L}(f_p) \\approx 0.637p}$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , the function\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\boldsymbol{g_p}$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    achieves remarkably low linearity, empirically characterized by\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\boldsymbol{\\mathcal{L}(g_p) \\approx 1.89\\sqrt{p}}$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , which is close to the optimal bound\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\sqrt {\\boldsymbol{p}} $$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , providing superior resistance to linear cryptanalysis. This linearity result is supported by extensive computational evidence and is presented as a well-founded conjecture, whose analytical proof remains an open problem. We provide theoretical characterizations of these properties and validate them through comprehensive statistical testing, including lattice tests, Q-Q plots and chi-square tests, demonstrating their suitability for symmetric-key cryptography applications.\n                  <\/jats:p>","DOI":"10.1007\/s12190-026-02828-6","type":"journal-article","created":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T13:27:35Z","timestamp":1781184455000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Design of two cryptographic functions from bose-type Sidon sets with differential 2-uniformity and near-optimal linearity"],"prefix":"10.1007","volume":"72","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7896-2280","authenticated-orcid":false,"given":"Julian","family":"Osorio","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carlos","family":"Trujillo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Diego","family":"Ruiz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,11]]},"reference":[{"key":"2828_CR1","first-page":"1","volume":"6","author":"R.C. 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