Countdown to SHA-3 Collisions

[Michael Best]

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.

For comparison, here's the 2012 maths for SHA-1:

https://www.schneier.com/blog/archives/2012/10/when_will_we_se.html

> On a NIST-sponsored hash function mailing list
> <http://csrc.nist.gov/groups/ST/hash/email_list.html>, Jesse Walker (from
> Intel; also a member of the Skein <http://www.schneier.com/skein.html>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.
> According to E-BASH <http://bench.cr.yp.to/ebash.html>, the cost of one
> block of a SHA-1 operation on already deployed commodity microprocessors is
> about 214 cycles. If Stevens' attack
> <http://2012.sharcs.org/slides/stevens.pdf> of 260 SHA-1 operations
> serves as the baseline, then finding a collision costs about 214 * 260 ~ 2
> 74cycles.
> A core today provides about 231 cycles/sec; the state of the art is 8 = 23 cores
> per processor for a total of 23 * 231 = 234 cycles/sec. A server
> typically has 4 processors, increasing the total to 22 * 234 = 236 cycles/sec.
> Since there are about 225 sec/year, this means one server delivers about 2
> 25 * 236 = 261 cycles per year, which we can call a "server year."
> 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:
> 3/1.5 = 2 times by 2015 (3 = 2015 - 2012)
> 6/1.5 = 4 times by 2018 (6 = 2018 - 2012)
> 9/1.5 = 6 times by 2021 (9 = 2021 - 2012)
> So a commodity server year should be about:
> 261 cycles/year in 2012
> 22 * 261 = 263 cycles/year by 2015
> 24 * 261 = 265 cycles/year by 2018
> 26 * 261 = 267 cycles/year by 2021
> Therefore, on commodity hardware, Stevens' attack should cost
> approximately:
> 274 / 261 = 213 server years in 2012
> 274 / 263 = 211 server years by 2015
> 274 / 265 = 29 server years by 2018
> 274 / 267 = 27 server years by 2021
> 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 log2(350) ~ 8.4 the
> cost of the attack will be approximately:
> 213 * 28.4 = 221.4 ~ $2.77M in 2012
> 211 * 28.4 = 219.4 ~ $700K by 2015
> 29 * 28.4 = 217.4 ~ $173K by 2018
> 27 * 28.4 = 215.4 ~ $43K by 2021
> 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.
> 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.
> 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.
> The point is that we in the community need to start the migration away
> from SHA-1 and to SHA-2/SHA-3 now.
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