Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
SQIsign
open-in-new
<h2 id="security">Security</h2> <p>SQIsign's security relies on the hardness of the endomorphism ring problem, which is currently considered hard.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> </p><p>The authors also provide <a href="/facts/Nothing-up-my-sleeve_number/AwqF2wkR">a rationale for the chosen parameters</a> in the last chapter of the specification.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> </p><p>While SQIsign makes use of a similar construction, the weaknesses of <a href="/facts/SIDH/TsGD1l3T">SIDH</a> do not translate to it.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> </p><p>There is a security proof for SQIsign.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> </p> <h2 id="implementations">Implementations</h2> <p>There is a <a href="https://github.com/SQISign/the-sqisign">reference implementation</a> hosted on <a href="/facts/GitHub/n1hNCsc3">GitHub</a>. </p> <h2 id="sqisign-20">SQIsign 2.0</h2> <p>The team behind SQIsign improved the original design in their round 2 submission and incorporated improvements from the SQIsign2D-West variant.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> </p><p>This has improved the signing time by a factor of 20 and the verification time by a factor of 6 while increasing the security level and reducing the signature size by 14%.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a>: 6 </p> <h2 id="variants">Variants</h2> <p>There are a couple of variants based on the original SQIsign:<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> </p> <ul><li>SQIsignHD: New dimensions in cryptography<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a></li> <li>SQIsign2D-West: The fast, the small, and the safer<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a></li> <li>SQIsign2D‑East: A new signature scheme using 2-dimensional isogenies<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a></li> <li>SQIPrime: A dimension 2 variant of SQISignHD with non-smooth challenge isogenies<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>specifically supersingular elliptic curves <a href="/wiki/Supersingular_elliptic_curve" target="_blank">/wiki/Supersingular_elliptic_curve</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Westerbaan, Bas; Larisch, James; Ahmad, Suleman; Fayed, Marwan; Westerbaan, Bas; Valenta, Luke; Krivit, Alex (2021-11-08). "Sizing Up Post-Quantum Signatures". The Cloudflare Blog. Retrieved 2024-11-15. <a href="https://blog.cloudflare.com/sizing-up-post-quantum-signatures/" target="_blank">https://blog.cloudflare.com/sizing-up-post-quantum-signatures/</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Feo, Luca De; Kohel, David; Leroux, Antonin; Petit, Christophe; Wesolowski, Benjamin (2020). "SQISign: compact post-quantum signatures from quaternions and isogenies". Cryptology ePrint Archive. Retrieved 2024-11-18. <a href="https://eprint.iacr.org/2020/1240" target="_blank">https://eprint.iacr.org/2020/1240</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Nakagawa, Kohei; Onuki, Hiroshi (2024). "SQIsign2D-East: A New Signature Scheme Using 2-dimensional Isogenies". Cryptology ePrint Archive. Retrieved 2024-11-15. <a href="https://eprint.iacr.org/2024/771" target="_blank">https://eprint.iacr.org/2024/771</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Page, Aurel; Wesolowski, Benjamin (2023). "The supersingular Endomorphism Ring and One Endomorphism problems are equivalent". Cryptology ePrint Archive. arXiv:2309.10432. Retrieved 2024-11-15. <a href="https://eprint.iacr.org/2023/1399" target="_blank">https://eprint.iacr.org/2023/1399</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>"THE SUPERSINGULAR ENDOMORPHISM RING PROBLEM GIVEN ONE ENDOMORPHISM" (PDF). Retrieved 2024-11-15. <a href="https://eprint.iacr.org/2023/1448.pdf" target="_blank">https://eprint.iacr.org/2023/1448.pdf</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>"SQIsign - Algorithm specifications and supporting documentation - Version 1.0" (PDF). Retrieved 2024-11-15. <a href="https://sqisign.org/spec/sqisign-20230601.pdf" target="_blank">https://sqisign.org/spec/sqisign-20230601.pdf</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>"SQIsign - Algorithm specifications and supporting documentation - Version 1.0" (PDF). Retrieved 2024-11-15. <a href="https://sqisign.org/spec/sqisign-20230601.pdf" target="_blank">https://sqisign.org/spec/sqisign-20230601.pdf</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Aardal, Marius A.; Basso, Andrea; Feo, Luca De; Patranabis, Sikhar; Wesolowski, Benjamin (2025). "A Complete Security Proof of SQIsign". Cryptology ePrint Archive. Retrieved May 16, 2025. <a href="https://eprint.iacr.org/2025/379" target="_blank">https://eprint.iacr.org/2025/379</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>"SQIsign - Algorithm specifications and supporting documentation - Version 2.0" (PDF). Retrieved May 16, 2025. <a href="https://sqisign.org/spec/sqisign-20250205.pdf" target="_blank">https://sqisign.org/spec/sqisign-20250205.pdf</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>"SQIsign - Algorithm specifications and supporting documentation - Version 2.0" (PDF). Retrieved May 16, 2025. <a href="https://sqisign.org/spec/sqisign-20250205.pdf" target="_blank">https://sqisign.org/spec/sqisign-20250205.pdf</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>"SQIsign". SQIsign. 2023-06-01. Retrieved 2024-11-17. <a href="https://sqisign.org/" target="_blank">https://sqisign.org/</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Dartois, Pierrick; Leroux, Antonin; Robert, Damien; Wesolowski, Benjamin (2023). "SQISignHD: New Dimensions in Cryptography". Cryptology ePrint Archive. Retrieved 2024-11-17. <a href="https://eprint.iacr.org/2023/436" target="_blank">https://eprint.iacr.org/2023/436</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Basso, Andrea; Feo, Luca De; Dartois, Pierrick; Leroux, Antonin; Maino, Luciano; Pope, Giacomo; Robert, Damien; Wesolowski, Benjamin (2024). "SQIsign2D-West: The Fast, the Small, and the Safer". Cryptology ePrint Archive. Retrieved 2024-11-17. <a href="https://eprint.iacr.org/2024/760" target="_blank">https://eprint.iacr.org/2024/760</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Nakagawa, Kohei; Onuki, Hiroshi (2024). "SQIsign2D-East: A New Signature Scheme Using 2-dimensional Isogenies". Cryptology ePrint Archive. Retrieved 2024-11-17. <a href="https://eprint.iacr.org/2024/771" target="_blank">https://eprint.iacr.org/2024/771</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>Duparc, Max; Fouotsa, Tako Boris (2024). "SQIPrime: A dimension 2 variant of SQISignHD with non-smooth challenge isogenies". Cryptology ePrint Archive. Retrieved 2024-11-17. <a href="https://eprint.iacr.org/2024/773" target="_blank">https://eprint.iacr.org/2024/773</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> </ol>