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Codes Cryptogr."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we study the security of the Key-Alternating Feistel (KAF) ciphers, a class of key alternating ciphers with the Feistel structure, where each round of the cipher is instantiated with <jats:italic>n<\/jats:italic>-bit public round permutation <jats:inline-formula><jats:alternatives><jats:tex-math>$$P_i$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>P<\/mml:mi>\n                    <mml:mi>i<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, namely the <jats:italic>i<\/jats:italic>-th round of the cipher maps <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} (X_L, X_R) \\mapsto (X_R, P_i(X_R \\oplus K_i) \\oplus K_i \\oplus X_L). \\end{aligned}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mtable>\n                      <mml:mtr>\n                        <mml:mtd>\n                          <mml:mrow>\n                            <mml:mrow>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:msub>\n                                <mml:mi>X<\/mml:mi>\n                                <mml:mi>L<\/mml:mi>\n                              <\/mml:msub>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:msub>\n                                <mml:mi>X<\/mml:mi>\n                                <mml:mi>R<\/mml:mi>\n                              <\/mml:msub>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mo>\u21a6<\/mml:mo>\n                            <mml:mrow>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:msub>\n                                <mml:mi>X<\/mml:mi>\n                                <mml:mi>R<\/mml:mi>\n                              <\/mml:msub>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:msub>\n                                <mml:mi>P<\/mml:mi>\n                                <mml:mi>i<\/mml:mi>\n                              <\/mml:msub>\n                              <mml:mrow>\n                                <mml:mo>(<\/mml:mo>\n                                <mml:msub>\n                                  <mml:mi>X<\/mml:mi>\n                                  <mml:mi>R<\/mml:mi>\n                                <\/mml:msub>\n                                <mml:mo>\u2295<\/mml:mo>\n                                <mml:msub>\n                                  <mml:mi>K<\/mml:mi>\n                                  <mml:mi>i<\/mml:mi>\n                                <\/mml:msub>\n                                <mml:mo>)<\/mml:mo>\n                              <\/mml:mrow>\n                              <mml:mo>\u2295<\/mml:mo>\n                              <mml:msub>\n                                <mml:mi>K<\/mml:mi>\n                                <mml:mi>i<\/mml:mi>\n                              <\/mml:msub>\n                              <mml:mo>\u2295<\/mml:mo>\n                              <mml:msub>\n                                <mml:mi>X<\/mml:mi>\n                                <mml:mi>L<\/mml:mi>\n                              <\/mml:msub>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mo>.<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:mtd>\n                      <\/mml:mtr>\n                    <\/mml:mtable>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:disp-formula>We have shown that our 5 round construction with independent round permutations and independent round keys achieves 2<jats:italic>n<\/jats:italic>\/3-bit security in the random permutation model, i.e., the setting where the adversary is allowed to make forward and inverse queries to the round permutations in a black box way.<\/jats:p>","DOI":"10.1007\/s10623-023-01288-4","type":"journal-article","created":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T14:05:46Z","timestamp":1696428346000},"page":"13-49","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["BBB security for 5-round even-Mansour-based key-alternating Feistel 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The authors have no conflicts of interest to declare that are relevant to the content of this article. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. The authors have no financial or proprietary interests in any material discussed in this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}