{"id":{"repo_id":"umkc","oai_identifier":"oai:mospace.umsystem.edu:10355/59656"},"canonical_url":"https://search.dev.ndltd.org/etd/umkc/oai:mospace.umsystem.edu:10355/59656","repository":{"repo_id":"umkc","name":"University of Missouri - Kansas City","base_url":"https://mospace.umsystem.edu/oai/request"},"display":{"title":"Protected Secret Sharing and its Application to Threshold Cryptography","abstract":"In the secret reconstruction of Shamir’s (t,n) secret sharing scheme (SS), shares released by shareholders need to be protected otherwise, non-shareholders can also obtain the secret. Key establishment protocol can establish pairwise keys for any pair of shareholders. Then, shareholders can use these pairwise keys to protect shares in the secret reconstruction process. However, adding a key establishment in the secret reconstruction slows down the process significantly. Shamir’s SS is based on a univariate polynomial. Shares generated by a bivariate polynomial enable pairwise keys to be shared between any pair of shareholders. But we proposed a new type of SS, called protected secret sharing scheme (PSS), in which shares of shareholders can not only be used to reconstruct the secret but also be used to protect the secrecy of shares in the secret reconstruction process. Thus, the recovered secret is only available to shareholders but not to non-shareholders. A basic (t,n) PSS based on a bivariate polynomial is proposed. Furthermore, we introduce to use this basic PSS in the applications of threshold cryptography. The PSS is unique since it protects the secrecy of the recovered secret in a very efficient way.","abstract_html":"In the secret reconstruction of Shamir’s (t,n) secret sharing scheme (SS), shares released by shareholders need to be protected otherwise, non-shareholders can also obtain the secret. Key establishment protocol can establish pairwise keys for any pair of shareholders. Then, shareholders can use these pairwise keys to protect shares in the secret reconstruction process. However, adding a key establishment in the secret reconstruction slows down the process significantly. Shamir’s SS is based on a univariate polynomial. Shares generated by a bivariate polynomial enable pairwise keys to be shared between any pair of shareholders. But we proposed a new type of SS, called protected secret sharing scheme (PSS), in which shares of shareholders can not only be used to reconstruct the secret but also be used to protect the secrecy of shares in the secret reconstruction process. Thus, the recovered secret is only available to shareholders but not to non-shareholders. A basic (t,n) PSS based on a bivariate polynomial is proposed. Furthermore, we introduce to use this basic PSS in the applications of threshold cryptography. The PSS is unique since it protects the secrecy of the recovered secret in a very efficient way.","abstract_has_math":false,"creators":["Mannava, Spandan"],"institution":"University of Missouri--Kansas City","degree_name":"M.S.","degree_level":"Masters","degree_discipline":"Computer Science (UMKC)","degree_department":null,"school":null,"contributors":[],"advisors":["Harn, Lein"],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016","date_published":"2016","updated_at":"2026-07-24T05:16:44Z","subjects":[],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10355/59656","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Harn, Lein"]},{"key":"dc:creator","label":"Author","values":["Mannava, Spandan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-04-04T17:39:16Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-04-04T17:39:16Z"]},{"key":"dc:date.issued","label":"Date","values":["2016"]},{"key":"dc:publisher","label":"Institution","values":["University of Missouri--Kansas City"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science (UMKC)"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Missouri--Kansas City"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10355/59656"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Title from PDF of title page, viewed April 19, 2017","Thesis advisor: Lein Harn","Vita","Includes bibliographical references (pages 36-40)","Thesis (M.S.)--School of Computing and Engineering. University of Missouri--Kansas City, 2016"]},{"key":"dc:description.abstract","label":"Abstract","values":["In the secret reconstruction of Shamir’s (t,n) secret sharing scheme (SS), shares released by shareholders need to be protected otherwise, non-shareholders can also obtain the secret. Key establishment protocol can establish pairwise keys for any pair of shareholders. Then, shareholders can use these pairwise keys to protect shares in the secret reconstruction process. However, adding a key establishment in the secret reconstruction slows down the process significantly. Shamir’s SS is based on a univariate polynomial. Shares generated by a bivariate polynomial enable pairwise keys to be shared between any pair of shareholders. But we proposed a new type of SS, called protected secret sharing scheme (PSS), in which shares of shareholders can not only be used to reconstruct the secret but also be used to protect the secrecy of shares in the secret reconstruction process. Thus, the recovered secret is only available to shareholders but not to non-shareholders. A basic (t,n) PSS based on a bivariate polynomial is proposed. Furthermore, we introduce to use this basic PSS in the applications of threshold cryptography. The PSS is unique since it protects the secrecy of the recovered secret in a very efficient way."]},{"key":"dc:title","label":"Title","values":["Protected Secret Sharing and its Application to Threshold Cryptography"]}]}],"canonical_facts":{"dc:contributor.advisor":["Harn, Lein"],"dc:creator":["Mannava, Spandan"],"dc:date.accessioned":["2017-04-04T17:39:16Z"],"dc:date.available":["2017-04-04T17:39:16Z"],"dc:date.issued":["2016"],"dc:description":["Title from PDF of title page, viewed April 19, 2017","Thesis advisor: Lein Harn","Vita","Includes bibliographical references (pages 36-40)","Thesis (M.S.)--School of Computing and Engineering. University of Missouri--Kansas City, 2016"],"dc:description.abstract":["In the secret reconstruction of Shamir’s (t,n) secret sharing scheme (SS), shares released by shareholders need to be protected otherwise, non-shareholders can also obtain the secret. Key establishment protocol can establish pairwise keys for any pair of shareholders. Then, shareholders can use these pairwise keys to protect shares in the secret reconstruction process. However, adding a key establishment in the secret reconstruction slows down the process significantly. Shamir’s SS is based on a univariate polynomial. Shares generated by a bivariate polynomial enable pairwise keys to be shared between any pair of shareholders. But we proposed a new type of SS, called protected secret sharing scheme (PSS), in which shares of shareholders can not only be used to reconstruct the secret but also be used to protect the secrecy of shares in the secret reconstruction process. Thus, the recovered secret is only available to shareholders but not to non-shareholders. A basic (t,n) PSS based on a bivariate polynomial is proposed. Furthermore, we introduce to use this basic PSS in the applications of threshold cryptography. The PSS is unique since it protects the secrecy of the recovered secret in a very efficient way."],"dc:identifier.uri":["https://hdl.handle.net/10355/59656"],"dc:language.iso":["en_US"],"dc:publisher":["University of Missouri--Kansas City"],"dc:title":["Protected Secret Sharing and its Application to Threshold Cryptography"],"dc:type":["Thesis"],"thesis:degree_discipline":["Computer Science (UMKC)"],"thesis:degree_level":["Masters"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Missouri--Kansas City"]},"updated_at":"2026-07-24T05:16:44Z"}