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over <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <a:msub>\n                           <a:mrow>\n                              <a:mi mathvariant=\"double-struck\">F<\/a:mi>\n                           <\/a:mrow>\n                           <a:mrow>\n                              <a:mn>2<\/a:mn>\n                           <\/a:mrow>\n                        <\/a:msub>\n                     <\/a:math>\n                  <\/jats:inline-formula>. The existing schemes are all constructed based on hash-and-sign lattice-based signature framework, where the implementation of preimage sampling function is Gaussian sampling, and the use of trapdoor basis needs a larger dimension <jats:inline-formula>\n                     <d:math xmlns:d=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <d:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <d:mrow>\n                              <d:mi>m<\/d:mi>\n                              <d:mo>\u2265<\/d:mo>\n                              <d:mn>5<\/d:mn>\n                              <d:mi>n<\/d:mi>\n                              <d:mtext>\u2009<\/d:mtext>\n                              <d:mi mathvariant=\"normal\">log<\/d:mi>\n                              <d:mtext>\u2009<\/d:mtext>\n                              <d:mi>q<\/d:mi>\n                           <\/d:mrow>\n                        <\/d:mfenced>\n                     <\/d:math>\n                  <\/jats:inline-formula>. Hence, they cannot resist potential side-channel attacks and have larger sizes of public key and signature. Under Fiat\u2013Shamir with aborting signature framework and general SIS problem restricted condition <jats:inline-formula>\n                     <j:math xmlns:j=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <j:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <j:mrow>\n                              <j:mi>m<\/j:mi>\n                              <j:mo>\u2265<\/j:mo>\n                              <j:mi>n<\/j:mi>\n                              <j:mtext>\u2009<\/j:mtext>\n                              <j:mi mathvariant=\"normal\">log<\/j:mi>\n                              <j:mtext>\u2009<\/j:mtext>\n                              <j:mi>q<\/j:mi>\n                           <\/j:mrow>\n                        <\/j:mfenced>\n                     <\/j:math>\n                  <\/jats:inline-formula>, we use uniform sampling of filtering technology to design the scheme, and then, our scheme has a smaller public key size and signature size than the existing schemes and it can resist side-channel attacks.<\/jats:p>","DOI":"10.1155\/2020\/8857815","type":"journal-article","created":{"date-parts":[[2020,10,29]],"date-time":"2020-10-29T22:35:08Z","timestamp":1604010908000},"page":"1-7","source":"Crossref","is-referenced-by-count":6,"title":["Lattice-Based Linearly Homomorphic Signature Scheme over <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                     <a:msub>\n                        <a:mrow>\n                           <a:mi mathvariant=\"double-struck\">F<\/a:mi>\n                        <\/a:mrow>\n                        <a:mrow>\n                           <a:mn>2<\/a:mn>\n                        <\/a:mrow>\n                     <\/a:msub>\n                  <\/a:math>"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3151-3963","authenticated-orcid":true,"given":"Jie","family":"Cai","sequence":"first","affiliation":[{"name":"School of Science, Shandong Jianzhu University, Ji\u2019nan, Shandong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4909-367X","authenticated-orcid":true,"given":"Han","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Software, Shandong University, Ji\u2019nan, Shandong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Shandong Normal University, Ji\u2019nan, Shandong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiuliang","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Software, Shandong University, Ji\u2019nan, Shandong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-00468-1_5"},{"key":"2","article-title":"Signatures for network coding","volume":"25","author":"D. 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