http://boolean.wiki.uib.no/index.php?action=history&feed=atom&title=Known_instances_of_APN_functions_over_GF%282%5E8%29Known instances of APN functions over GF(2^8) - Revision history2026-05-28T16:24:43ZRevision history for this page on the wikiMediaWiki 1.39.6http://boolean.wiki.uib.no/index.php?title=Known_instances_of_APN_functions_over_GF(2%5E8)&diff=566&oldid=prevCbeierle: added the two family members of C12 as functions at indices 8191 and 81922021-01-14T14:23:23Z<p>added the two family members of C12 as functions at indices 8191 and 8192</p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The following table lists all currently known APN polynomials over <math>\mathbb{F}_{2^8}</math>. The majority of these were obtained by the matrix method described in <ref name="yuyin">Y. Yu, M. Wang, Y. Li. A matrix approach for constructing quadratic APN functions. Designs, Codes and Cryptography 73, pp. 587-600, 2014. https://doi.org/10.1007/s10623-014-9955-3</ref> and appear there for the first time. The functions at indices 8181 -- 8190 were obtained in <ref>G. Weng, Y. Tan, G. Gong. On quadratic almost perfect nonlinear</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The following table lists all currently known APN polynomials over <math>\mathbb{F}_{2^8}</math>. The majority of these were obtained by the matrix method described in <ref name="yuyin">Y. Yu, M. Wang, Y. Li. A matrix approach for constructing quadratic APN functions. Designs, Codes and Cryptography 73, pp. 587-600, 2014. https://doi.org/10.1007/s10623-014-9955-3</ref> and appear there for the first time. The functions at indices 8181 -- 8190 were obtained in <ref>G. Weng, Y. Tan, G. Gong. On quadratic almost perfect nonlinear</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>functions and their related algebraic object. Workshop on Coding and Cryptography,</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>functions and their related algebraic object. Workshop on Coding and Cryptography,</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>WCC., 2013.</ref>. The representation of function number 8181 was obtained in <ref>L. Budaghyan, M. Calderini, C. Carlet, R. Coulter, I. Villa. Generalized Isotopic Shift Construction for APN Functions. Cryptology ePrint Archive: Report 2020/295</ref>. The table is compiled from Appendix 2 in <ref name="yuyin" />. The symbol "g" in the table is a <del style="font-weight: bold; text-decoration: none;">primitive element </del>of <math>\mathbb{F}_{2^8}</math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>WCC., 2013.<ins style="font-weight: bold; text-decoration: none;"></ref>. The functions at indices 8191 -- 8192 were obtained in <ref>H. Taniguchi. On some quadratic APN functions. Designs, Codes and Cryptography 87, pp. 1973-1983, 2019. https://doi.org/10.1007/s10623-018-00598-2</ins></ref>. The representation of function number 8181 was obtained in <ref>L. Budaghyan, M. Calderini, C. Carlet, R. Coulter, I. Villa. Generalized Isotopic Shift Construction for APN Functions. Cryptology ePrint Archive: Report 2020/295</ref>. The table is compiled from Appendix 2 in <ref name="yuyin" />. The symbol "g" in the table is a <ins style="font-weight: bold; text-decoration: none;">zero </ins>of <ins style="font-weight: bold; text-decoration: none;">X<sup>8</sup> + X<sup>4</sup> + X<sup>3</sup> + X<sup>2</sup> + 1 in </ins><math>\mathbb{F}_{2^8}</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Due to the large number of functions, the table is split into several pages:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Due to the large number of functions, the table is split into several pages:</div></td></tr>
</table>Cbeierlehttp://boolean.wiki.uib.no/index.php?title=Known_instances_of_APN_functions_over_GF(2%5E8)&diff=549&oldid=prevCbeierle: Added the WCC 2013 paper2020-09-15T08:45:18Z<p>Added the WCC 2013 paper</p>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The following table lists all currently known APN polynomials over <math>\mathbb{F}_{2^8}</math>. The majority of these were obtained by the matrix method described in <ref name="yuyin">Y. Yu, M. Wang, Y. Li. A matrix approach for constructing quadratic APN functions. Designs, Codes and Cryptography 73, pp. 587-600, 2014. https://doi.org/10.1007/s10623-014-9955-3</ref> and appear there for the first time. <del style="font-weight: bold; text-decoration: none;">Function </del>number 8181 <del style="font-weight: bold; text-decoration: none;">is </del>obtained in <ref>L. Budaghyan, M. Calderini, C. Carlet, R. Coulter, I. Villa. Generalized Isotopic Shift Construction for APN Functions. Cryptology ePrint Archive: Report 2020/295</ref>. The table is compiled from Appendix 2 in <ref name="yuyin" />. The symbol "g" in the table is a primitive element of <math>\mathbb{F}_{2^8}</math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The following table lists all currently known APN polynomials over <math>\mathbb{F}_{2^8}</math>. The majority of these were obtained by the matrix method described in <ref name="yuyin">Y. Yu, M. Wang, Y. Li. A matrix approach for constructing quadratic APN functions. Designs, Codes and Cryptography 73, pp. 587-600, 2014. https://doi.org/10.1007/s10623-014-9955-3</ref> and appear there for the first time. <ins style="font-weight: bold; text-decoration: none;">The functions at indices 8181 -- 8190 were obtained in <ref>G. Weng, Y. Tan, G. Gong. On quadratic almost perfect nonlinear</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">functions and their related algebraic object. Workshop on Coding and Cryptography,</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">WCC., 2013.</ref>. The representation of function </ins>number 8181 <ins style="font-weight: bold; text-decoration: none;">was </ins>obtained in <ref>L. Budaghyan, M. Calderini, C. Carlet, R. Coulter, I. Villa. Generalized Isotopic Shift Construction for APN Functions. Cryptology ePrint Archive: Report 2020/295</ref>. The table is compiled from Appendix 2 in <ref name="yuyin" />. The symbol "g" in the table is a primitive element of <math>\mathbb{F}_{2^8}</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Due to the large number of functions, the table is split into several pages:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Due to the large number of functions, the table is split into several pages:</div></td></tr>
</table>Cbeierlehttp://boolean.wiki.uib.no/index.php?title=Known_instances_of_APN_functions_over_GF(2%5E8)&diff=541&oldid=prevNikolay at 17:43, 11 August 20202020-08-11T17:43:45Z<p></p>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The following table lists all currently known APN polynomials over <math>\mathbb{F}_{2^8}</math>. The majority of these were obtained by the matrix method described in <ref name="yuyin">Y. Yu, M. Wang, Y. Li. A matrix approach for constructing quadratic APN functions. Designs, Codes and Cryptography 73, pp. 587-600, 2014. https://doi.org/10.1007/s10623-014-9955-3</ref> and appear there for the first time. The table is compiled from Appendix 2 in <ref name="yuyin" />. The symbol "g" in the table is a primitive element of <math>\mathbb{F}_{2^8}</math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The following table lists all currently known APN polynomials over <math>\mathbb{F}_{2^8}</math>. The majority of these were obtained by the matrix method described in <ref name="yuyin">Y. Yu, M. Wang, Y. Li. A matrix approach for constructing quadratic APN functions. Designs, Codes and Cryptography 73, pp. 587-600, 2014. https://doi.org/10.1007/s10623-014-9955-3</ref> and appear there for the first time<ins style="font-weight: bold; text-decoration: none;">. Function number 8181 is obtained in <ref>L. Budaghyan, M. Calderini, C. Carlet, R. Coulter, I. Villa. Generalized Isotopic Shift Construction for APN Functions. Cryptology ePrint Archive: Report 2020/295</ref></ins>. The table is compiled from Appendix 2 in <ref name="yuyin" />. The symbol "g" in the table is a primitive element of <math>\mathbb{F}_{2^8}</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Due to the large number of functions, the table is split into several pages:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Due to the large number of functions, the table is split into several pages:</div></td></tr>
</table>Nikolayhttp://boolean.wiki.uib.no/index.php?title=Known_instances_of_APN_functions_over_GF(2%5E8)&diff=502&oldid=prevNikolay: Nikolay moved page Known quadratic APN polynomial functions over GF(2^8) to Known instances of APN functions over GF(2^8)2020-07-09T17:49:22Z<p>Nikolay moved page <a href="/Known_quadratic_APN_polynomial_functions_over_GF(2%5E8)" class="mw-redirect" title="Known quadratic APN polynomial functions over GF(2^8)">Known quadratic APN polynomial functions over GF(2^8)</a> to <a href="/Known_instances_of_APN_functions_over_GF(2%5E8)" title="Known instances of APN functions over GF(2^8)">Known instances of APN functions over GF(2^8)</a></p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:49, 9 July 2020</td>
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</td></tr></table>Nikolayhttp://boolean.wiki.uib.no/index.php?title=Known_instances_of_APN_functions_over_GF(2%5E8)&diff=501&oldid=prevNikolay at 17:48, 9 July 20202020-07-09T17:48:40Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:48, 9 July 2020</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The following table lists all currently known APN polynomials over <math>\mathbb{F}_{2^8}</math>. The majority of these were obtained by the matrix method described in <ref name="yuyin">Yu <del style="font-weight: bold; text-decoration: none;">Y</del>, Wang <del style="font-weight: bold; text-decoration: none;">M</del>, Li <del style="font-weight: bold; text-decoration: none;">Y</del>. A matrix approach for constructing quadratic APN functions. Designs, <del style="font-weight: bold; text-decoration: none;">codes </del>and <del style="font-weight: bold; text-decoration: none;">cryptography</del>. <del style="font-weight: bold; text-decoration: none;">2014 Nov 1;73(2):</del>587-600.</ref> and appear there for the first time. The table is compiled from Appendix 2 in <ref name="yuyin" />. The symbol "g" in the table is a primitive element of <math>\mathbb{F}_{2^8}</math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The following table lists all currently known APN polynomials over <math>\mathbb{F}_{2^8}</math>. The majority of these were obtained by the matrix method described in <ref name="yuyin"><ins style="font-weight: bold; text-decoration: none;">Y. </ins>Yu, <ins style="font-weight: bold; text-decoration: none;">M. </ins>Wang, <ins style="font-weight: bold; text-decoration: none;">Y. </ins>Li. A matrix approach for constructing quadratic APN functions. Designs, <ins style="font-weight: bold; text-decoration: none;">Codes </ins>and <ins style="font-weight: bold; text-decoration: none;">Cryptography 73, pp</ins>. 587-600<ins style="font-weight: bold; text-decoration: none;">, 2014</ins>. <ins style="font-weight: bold; text-decoration: none;">https://doi.org/10.1007/s10623-014-9955-3</ins></ref> and appear there for the first time. The table is compiled from Appendix 2 in <ref name="yuyin" />. The symbol "g" in the table is a primitive element of <math>\mathbb{F}_{2^8}</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Due to the large number of functions, the table is split into several pages:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Due to the large number of functions, the table is split into several pages:</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Known quadratic APN polynomial functions over GF(2^8)|1-500]] - [[Known quadratic APN polynomial functions over GF(2^8) 501-1000|501-1000]] - [[Known quadratic APN polynomial functions over GF(2^8) 1001-1500|1001-1500]] - [[Known quadratic APN polynomial functions over GF(2^8) 1501-2000|1501-2000]] - [[Known quadratic APN polynomial functions over GF(2^8) 2001-2500|2001-2500]] - [[Known quadratic APN polynomial functions over GF(2^8) 2501-3000|2501-3000]] - [[Known quadratic APN polynomial functions over GF(2^8) 3001-3500|3001-3500]] - [[Known quadratic APN polynomial functions over GF(2^8) 3501-4000|3501-4000]] - [[Known quadratic APN polynomial functions over GF(2^8) 4001-4500|4001-4500]] - [[Known quadratic APN polynomial functions over GF(2^8) 4501-5000|4501-5000]] - [[Known quadratic APN polynomial functions over GF(2^8) 5001-5500|5001-5500]] - [[Known quadratic APN polynomial functions over GF(2^8) 5501-6000|5501-6000]] - [[Known quadratic APN polynomial functions over GF(2^8) 6001-6500|6001-6500]] - [[Known quadratic APN polynomial functions over GF(2^8) 6501-7000|6501-7000]] - [[Known quadratic APN polynomial functions over GF(2^8) 7001-7500|7001-7500]] - [[Known quadratic APN polynomial functions over GF(2^8) 7501-8000|7501-8000]] - [[Known quadratic APN polynomial functions over GF(2^8) 8001-8500|8001-8500]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Known quadratic APN polynomial functions over GF(2^8)|1-500]] - [[Known quadratic APN polynomial functions over GF(2^8) 501-1000|501-1000]] - [[Known quadratic APN polynomial functions over GF(2^8) 1001-1500|1001-1500]] - [[Known quadratic APN polynomial functions over GF(2^8) 1501-2000|1501-2000]] - [[Known quadratic APN polynomial functions over GF(2^8) 2001-2500|2001-2500]] - [[Known quadratic APN polynomial functions over GF(2^8) 2501-3000|2501-3000]] - [[Known quadratic APN polynomial functions over GF(2^8) 3001-3500|3001-3500]] - [[Known quadratic APN polynomial functions over GF(2^8) 3501-4000|3501-4000]] - [[Known quadratic APN polynomial functions over GF(2^8) 4001-4500|4001-4500]] - [[Known quadratic APN polynomial functions over GF(2^8) 4501-5000|4501-5000]] - [[Known quadratic APN polynomial functions over GF(2^8) 5001-5500|5001-5500]] - [[Known quadratic APN polynomial functions over GF(2^8) 5501-6000|5501-6000]] - [[Known quadratic APN polynomial functions over GF(2^8) 6001-6500|6001-6500]] - [[Known quadratic APN polynomial functions over GF(2^8) 6501-7000|6501-7000]] - [[Known quadratic APN polynomial functions over GF(2^8) 7001-7500|7001-7500]] - [[Known quadratic APN polynomial functions over GF(2^8) 7501-8000|7501-8000]] - [[Known quadratic APN polynomial functions over GF(2^8) 8001-8500|8001-8500]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Source code for <i>Magma</i> which produces a sequence of these functions in the same order as given in the table [[:File:Quadratic_apn_polynomials_8.txt|is available]].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Source code for <i>Magma</i> which produces a sequence of these functions in the same order as given in the table [[:File:Quadratic_apn_polynomials_8.txt|is available <ins style="font-weight: bold; text-decoration: none;">here</ins>]].</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><table></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><table></div></td></tr>
</table>Nikolayhttp://boolean.wiki.uib.no/index.php?title=Known_instances_of_APN_functions_over_GF(2%5E8)&diff=286&oldid=prevNikolay at 10:46, 15 July 20192019-07-15T10:46:04Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:46, 15 July 2019</td>
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<td colspan="2" class="diff-lineno">Line 2:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Due to the large number of functions, the table is split into several pages:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Due to the large number of functions, the table is split into several pages:</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Known quadratic APN polynomial functions over GF(2^8) 501-1000|501-1000]] - [[Known quadratic APN polynomial functions over GF(2^8) 1001-1500|1001-1500]] - [[Known quadratic APN polynomial functions over GF(2^8) 1501-2000|1501-2000]] - [[Known quadratic APN polynomial functions over GF(2^8) 2001-2500|2001-2500]] - [[Known quadratic APN polynomial functions over GF(2^8) 2501-3000|2501-3000]] - [[Known quadratic APN polynomial functions over GF(2^8) 3001-3500|3001-3500]] - [[Known quadratic APN polynomial functions over GF(2^8) 3501-4000|3501-4000]] - [[Known quadratic APN polynomial functions over GF(2^8) 4001-4500|4001-4500]] - [[Known quadratic APN polynomial functions over GF(2^8) 4501-5000|4501-5000]] - [[Known quadratic APN polynomial functions over GF(2^8) 5001-5500|5001-5500]] - [[Known quadratic APN polynomial functions over GF(2^8) 5501-6000|5501-6000]] - [[Known quadratic APN polynomial functions over GF(2^8) 6001-6500|6001-6500]] - [[Known quadratic APN polynomial functions over GF(2^8) 6501-7000|6501-7000]] - [[Known quadratic APN polynomial functions over GF(2^8) 7001-7500|7001-7500]] - [[Known quadratic APN polynomial functions over GF(2^8) 7501-8000|7501-8000]] - [[Known quadratic APN polynomial functions over GF(2^8) 8001-8500|8001-8500<del style="font-weight: bold; text-decoration: none;">]] - [[Known quadratic APN polynomial functions over GF(2^8) 8501-8180|8501-8180</del>]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Known quadratic APN polynomial functions over GF(2^8)|1-500]] - </ins>[[Known quadratic APN polynomial functions over GF(2^8) 501-1000|501-1000]] - [[Known quadratic APN polynomial functions over GF(2^8) 1001-1500|1001-1500]] - [[Known quadratic APN polynomial functions over GF(2^8) 1501-2000|1501-2000]] - [[Known quadratic APN polynomial functions over GF(2^8) 2001-2500|2001-2500]] - [[Known quadratic APN polynomial functions over GF(2^8) 2501-3000|2501-3000]] - [[Known quadratic APN polynomial functions over GF(2^8) 3001-3500|3001-3500]] - [[Known quadratic APN polynomial functions over GF(2^8) 3501-4000|3501-4000]] - [[Known quadratic APN polynomial functions over GF(2^8) 4001-4500|4001-4500]] - [[Known quadratic APN polynomial functions over GF(2^8) 4501-5000|4501-5000]] - [[Known quadratic APN polynomial functions over GF(2^8) 5001-5500|5001-5500]] - [[Known quadratic APN polynomial functions over GF(2^8) 5501-6000|5501-6000]] - [[Known quadratic APN polynomial functions over GF(2^8) 6001-6500|6001-6500]] - [[Known quadratic APN polynomial functions over GF(2^8) 6501-7000|6501-7000]] - [[Known quadratic APN polynomial functions over GF(2^8) 7001-7500|7001-7500]] - [[Known quadratic APN polynomial functions over GF(2^8) 7501-8000|7501-8000]] - [[Known quadratic APN polynomial functions over GF(2^8) 8001-8500|8001-8500]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Source code for <i>Magma</i> which produces a sequence of these functions in the same order as given in the table [[:File:Quadratic_apn_polynomials_8.txt|is available]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Source code for <i>Magma</i> which produces a sequence of these functions in the same order as given in the table [[:File:Quadratic_apn_polynomials_8.txt|is available]].</div></td></tr>
</table>Nikolayhttp://boolean.wiki.uib.no/index.php?title=Known_instances_of_APN_functions_over_GF(2%5E8)&diff=253&oldid=prevNikolay at 10:31, 15 July 20192019-07-15T10:31:42Z<p></p>
<a href="http://boolean.wiki.uib.no/index.php?title=Known_instances_of_APN_functions_over_GF(2%5E8)&diff=253&oldid=252">Show changes</a>Nikolayhttp://boolean.wiki.uib.no/index.php?title=Known_instances_of_APN_functions_over_GF(2%5E8)&diff=252&oldid=prevNikolay: Created page with "The following table lists all currently known APN polynomials over <math>\mathbb{F}_{2^8}</math>. The majority of these were obtained by the matrix method described in <ref na..."2019-07-15T10:15:00Z<p>Created page with "The following table lists all currently known APN polynomials over <math>\mathbb{F}_{2^8}</math>. The majority of these were obtained by the matrix method described in <ref na..."</p>
<p><b>New page</b></p><div>The following table lists all currently known APN polynomials over <math>\mathbb{F}_{2^8}</math>. The majority of these were obtained by the matrix method described in <ref name="yuyin">Yu Y, Wang M, Li Y. A matrix approach for constructing quadratic APN functions. Designs, codes and cryptography. 2014 Nov 1;73(2):587-600.</ref> and appear there for the first time. The table is compiled from Appendix 2 in <ref name="yuyin" />. The symbol "g" in the table is a primitive element of <math>\mathbb{F}_{2^7}</math>.<br />
<br />
Due to the large number of functions, the table is split into several pages:<br />
<br />
Source code for <i>Magma</i> which produces a sequence of these functions in the same order as given in the table [[:File:Quadratic_apn_polynomials_8.txt|is available]].</div>Nikolay