{"id":{"repo_id":"cuny-grad","oai_identifier":"oai:academicworks.cuny.edu:gc_etds-1885"},"canonical_url":"https://search.dev.ndltd.org/etd/cuny-grad/oai:academicworks.cuny.edu:gc_etds-1885","repository":{"repo_id":"cuny-grad","name":"City University of New York - Graduate Center","base_url":"https://academicworks.cuny.edu/do/oai/"},"display":{"title":"Some applications of noncommutative groups and semigroups to information security","abstract":"<p>We present evidence why the Burnside groups of exponent 3 could be a good candidate for a platform group for the HKKS semidirect product key exchange protocol. We also explore hashing with matrices over SL<sub>2</sub>(F<sub>p</sub>), and compute bounds on the girth of the Cayley graph of the subgroup of SL<sub>2</sub>(F<sub>p</sub>) for specific generators <em>A</em>, <em>B</em>. We demonstrate that even without optimization, these hashes have comparable performance to hashes in the SHA family.</p>","abstract_html":"&lt;p&gt;We present evidence why the Burnside groups of exponent 3 could be a good candidate for a platform group for the HKKS semidirect product key exchange protocol. We also explore hashing with matrices over SL&lt;sub&gt;2&lt;/sub&gt;(F&lt;sub&gt;p&lt;/sub&gt;), and compute bounds on the girth of the Cayley graph of the subgroup of SL&lt;sub&gt;2&lt;/sub&gt;(F&lt;sub&gt;p&lt;/sub&gt;) for specific generators &lt;em&gt;A&lt;/em&gt;, &lt;em&gt;B&lt;/em&gt;. We demonstrate that even without optimization, these hashes have comparable performance to hashes in the SHA family.&lt;/p&gt;","abstract_has_math":false,"creators":["Bromberg, Lisa"],"institution":"The Graduate School and University Center of The City University of New York","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Vladimir Shpilrain"],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-05-27T07:00:00Z","date_published":"2015-05-27T07:00:00Z","updated_at":"2026-07-24T02:00:26Z","subjects":["Mathematics","cryptography; hash functions; information security"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://academicworks.cuny.edu/gc_etds/871","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Vladimir Shpilrain"]},{"key":"dc:creator","label":"Author","values":["Bromberg, Lisa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-03-29T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The Graduate School and University Center of The City University of New York"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","cryptography; hash functions; information security"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://academicworks.cuny.edu/gc_etds/871"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>We present evidence why the Burnside groups of exponent 3 could be a good candidate for a platform group for the HKKS semidirect product key exchange protocol. We also explore hashing with matrices over SL<sub>2</sub>(F<sub>p</sub>), and compute bounds on the girth of the Cayley graph of the subgroup of SL<sub>2</sub>(F<sub>p</sub>) for specific generators <em>A</em>, <em>B</em>. We demonstrate that even without optimization, these hashes have comparable performance to hashes in the SHA family.</p>"]},{"key":"dc:title","label":"Title","values":["Some applications of noncommutative groups and semigroups to information security"]}]}],"canonical_facts":{"dc:contributor.advisor":["Vladimir Shpilrain"],"dc:creator":["Bromberg, Lisa"],"dc:date.available":["2016-03-29T07:00:00Z"],"dc:description.abstract":["<p>We present evidence why the Burnside groups of exponent 3 could be a good candidate for a platform group for the HKKS semidirect product key exchange protocol. We also explore hashing with matrices over SL<sub>2</sub>(F<sub>p</sub>), and compute bounds on the girth of the Cayley graph of the subgroup of SL<sub>2</sub>(F<sub>p</sub>) for specific generators <em>A</em>, <em>B</em>. We demonstrate that even without optimization, these hashes have comparable performance to hashes in the SHA family.</p>"],"dc:identifier":["https://academicworks.cuny.edu/gc_etds/871"],"dc:subject":["Mathematics","cryptography; hash functions; information security"],"dc:title":["Some applications of noncommutative groups and semigroups to information security"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The Graduate School and University Center of The City University of New York"]},"updated_at":"2026-07-24T02:00:26Z"}