<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">On Jul 16, 2020, at 10:29 AM, Jerry Leichter <<a href="mailto:leichter@lrw.com" class="">leichter@lrw.com</a>> replied to me:<div><blockquote type="cite" class=""><div class=""><meta http-equiv="Content-Type" content="text/html; charset=utf-8" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""><font color="#5856d6" class=""><span style="caret-color: rgb(88, 86, 214);" class=""><br class=""></span></font></div><blockquote type="cite" class=""><div class=""><font color="#5856d6" class=""><span style="caret-color: rgb(88, 86, 214);" class="">Thanks. An architect proposing a skyscraper with a structural design based on an unproven mathematical theory, would ridiculed. But a large part of the world economy is secured based on mathematical conjectures and no one seems to mind. </span></font></div></blockquote></div></div></blockquote><br class=""><blockquote type="cite" class=""><div class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class="">This is a really bad analogy. A skyscraper isn't built on the basis of mathematical theories. It's based mainly on physical measurements of various properties of materials, combined using mathematical approximations. The measurements and approximations are all validated empirically. Mathematical proof plays a surprising small role.</div></div></div></blockquote><div><br class=""></div></div><div><blockquote type="cite" class=""><div class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class="">Case in point: A story relayed to me …</div></div></div></blockquote><div><br class=""></div><div>This is not the forum to argue about structural engineering, but I remember when the finite element method, extensively used nowadays in analyzing structures, was in its infancy and since then a large amount of theoretical research has gone into establishing its mathematical validity. The full story, about the Citicorp Center in Manhattan, illustrates a critical use of accurate mathematical models, the caveat being the importance of using the model correctly. </div><div><br class=""></div><div>But an analogy is just a rhetorical tool and if it did not work for you, my apologies. I only made it to suggest there is some need for encryption tools that do not depend on the correctness of unproven mathematical statements. Quantum cryptography also attempts to meet that need, but it has its own problems, including very finicky communications requirements. In my paper <a href="https://www.researchgate.net/publication/342697247" class="">https://www.researchgate.net/publication/342697247</a> I argue that Terakey offers comparable security, without many of the drawbacks of QKD. </div><div><br class=""></div><div>If nothing else, a conjecture-free tool for secure communication would be valuable in rebuilding, if some mathematical breakthrough or other broad security beach undermines the existing public key world. The recent breach of VIP Twitter accounts, is only the latest in a very long series of warnings about cracked foundations in our security structures. </div><div><br class=""></div><div>Arnold Reinhold</div><div><br class=""></div><div><br class=""></div><div><br class=""></div><div><br class=""></div><div><br class=""></div><div><br class=""></div><div><br class=""></div><br class=""></div></body></html>