<div dir="ltr">The SHA-3 standard was released by NIST in August of this year. I'm wondering if anyone has done the math on how long until we should no longer consider it pretty secure enough-ish. <div><br></div><div>For comparison, here's the 2012 maths for SHA-1:<div><br></div><div><a href="https://www.schneier.com/blog/archives/2012/10/when_will_we_se.html">https://www.schneier.com/blog/archives/2012/10/when_will_we_se.html</a><br></div><div><blockquote style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex" class="gmail_quote">On a NIST-sponsored hash function <a href="http://csrc.nist.gov/groups/ST/hash/email_list.html" style="margin:0px;padding:0px;border:0px;outline:none;color:black">mailing list</a>, Jesse Walker (from Intel; also a member of the <a href="http://www.schneier.com/skein.html" style="margin:0px;padding:0px;border:0px;outline:none;color:black">Skein</a>team) did some back-of-the-envelope calculations to estimate how long it will be before we see a practical collision attack against SHA-1. I'm reprinting his analysis here, so it reaches a broader audience.<br>According to <a href="http://bench.cr.yp.to/ebash.html" style="margin:0px;padding:0px;border:0px;outline:none;color:black">E-BASH</a>, the cost of one block of a SHA-1 operation on already deployed commodity microprocessors is about 2<sup style="margin:0px;padding:0px;border:0px">14</sup> cycles. If <a href="http://2012.sharcs.org/slides/stevens.pdf" style="margin:0px;padding:0px;border:0px;outline:none;color:black">Stevens' attack</a> of 2<sup style="margin:0px;padding:0px;border:0px">60</sup> SHA-1 operations serves as the baseline, then finding a collision costs about 2<sup style="margin:0px;padding:0px;border:0px">14</sup> * 2<sup style="margin:0px;padding:0px;border:0px">60</sup> ~ 2<sup style="margin:0px;padding:0px;border:0px">74</sup>cycles.<br>A core today provides about 2<sup style="margin:0px;padding:0px;border:0px">31</sup> cycles/sec; the state of the art is 8 = 2<sup style="margin:0px;padding:0px;border:0px">3</sup> cores per processor for a total of 2<sup style="margin:0px;padding:0px;border:0px">3</sup> * 2<sup style="margin:0px;padding:0px;border:0px">31</sup> = 2<sup style="margin:0px;padding:0px;border:0px">34</sup> cycles/sec. A server typically has 4 processors, increasing the total to 2<sup style="margin:0px;padding:0px;border:0px">2</sup> * 2<sup style="margin:0px;padding:0px;border:0px">34</sup> = 2<sup style="margin:0px;padding:0px;border:0px">36</sup> cycles/sec. Since there are about 2<sup style="margin:0px;padding:0px;border:0px">25</sup> sec/year, this means one server delivers about 2<sup style="margin:0px;padding:0px;border:0px">25</sup> * 2<sup style="margin:0px;padding:0px;border:0px">36</sup> = 2<sup style="margin:0px;padding:0px;border:0px">61</sup> cycles per year, which we can call a "server year."<br>There is ample evidence that Moore's law will continue through the mid 2020s. Hence the number of doublings in processor power we can expect between now and 2021 is:<br>3/1.5 = 2 times by 2015 (3 = 2015 - 2012)<br>6/1.5 = 4 times by 2018 (6 = 2018 - 2012)<br>9/1.5 = 6 times by 2021 (9 = 2021 - 2012)<br>So a commodity server year should be about:<br>2<sup style="margin:0px;padding:0px;border:0px">61</sup> cycles/year in 2012<br>2<sup style="margin:0px;padding:0px;border:0px">2</sup> * 2<sup style="margin:0px;padding:0px;border:0px">61</sup> = 2<sup style="margin:0px;padding:0px;border:0px">63</sup> cycles/year by 2015<br>2<sup style="margin:0px;padding:0px;border:0px">4</sup> * 2<sup style="margin:0px;padding:0px;border:0px">61</sup> = 2<sup style="margin:0px;padding:0px;border:0px">65</sup> cycles/year by 2018<br>2<sup style="margin:0px;padding:0px;border:0px">6</sup> * 2<sup style="margin:0px;padding:0px;border:0px">61</sup> = 2<sup style="margin:0px;padding:0px;border:0px">67</sup> cycles/year by 2021<br>Therefore, on commodity hardware, Stevens' attack should cost approximately:<br>2<sup style="margin:0px;padding:0px;border:0px">74</sup> / 2<sup style="margin:0px;padding:0px;border:0px">61</sup> = 2<sup style="margin:0px;padding:0px;border:0px">13</sup> server years in 2012<br>2<sup style="margin:0px;padding:0px;border:0px">74</sup> / 2<sup style="margin:0px;padding:0px;border:0px">63</sup> = 2<sup style="margin:0px;padding:0px;border:0px">11</sup> server years by 2015<br>2<sup style="margin:0px;padding:0px;border:0px">74</sup> / 2<sup style="margin:0px;padding:0px;border:0px">65</sup> = 2<sup style="margin:0px;padding:0px;border:0px">9</sup> server years by 2018<br>2<sup style="margin:0px;padding:0px;border:0px">74</sup> / 2<sup style="margin:0px;padding:0px;border:0px">67</sup> = 2<sup style="margin:0px;padding:0px;border:0px">7</sup> server years by 2021<br>Today Amazon rents compute time on commodity servers for about $0.04 / hour ~ $350 /year. Assume compute rental fees remain fixed while server capacity keeps pace with Moore's law. Then, since log<sub style="margin:0px;padding:0px;border:0px">2</sub>(350) ~ 8.4 the cost of the attack will be approximately:<br>2<sup style="margin:0px;padding:0px;border:0px">13</sup> * 2<sup style="margin:0px;padding:0px;border:0px">8.4</sup> = 2<sup style="margin:0px;padding:0px;border:0px">21.4</sup> ~ $2.77M in 2012<br>2<sup style="margin:0px;padding:0px;border:0px">11</sup> * 2<sup style="margin:0px;padding:0px;border:0px">8.4</sup> = 2<sup style="margin:0px;padding:0px;border:0px">19.4</sup> ~ $700K by 2015<br>2<sup style="margin:0px;padding:0px;border:0px">9</sup> * 2<sup style="margin:0px;padding:0px;border:0px">8.4</sup> = 2<sup style="margin:0px;padding:0px;border:0px">17.4</sup> ~ $173K by 2018<br>2<sup style="margin:0px;padding:0px;border:0px">7</sup> * 2<sup style="margin:0px;padding:0px;border:0px">8.4</sup> = 2<sup style="margin:0px;padding:0px;border:0px">15.4</sup> ~ $43K by 2021<br>A collision attack is therefore well within the range of what an organized crime syndicate can practically budget by 2018, and a university research project by 2021.<br>Since this argument only takes into account commodity hardware and not instruction set improvements (e.g., ARM 8 specifies a SHA-1 instruction), other commodity computing devices with even greater processing power (e.g., GPUs), and custom hardware, the need to transition from SHA-1 for collision resistance functions is probably more urgent than this back-of-the-envelope analysis suggests.<br>Any increase in the number of cores per CPU, or the number of CPUs per server, also affects these calculations. Also, any improvements in cryptanalysis will further reduce the complexity of this attack.<br>The point is that we in the community need to start the migration away from SHA-1 and to SHA-2/SHA-3 now.</blockquote></div></div></div>