Friday, October 5, 2012

Estimating possible collisions of SHA-1

In a recent post, bruce schneier reprinted an analysis made by Jesse Walker (Skein team member) about the time needed to see a practical collision for SHA-1. It was interesting for me the way the writer goes through the calculations:

According to E-BASH, the cost of one block of a SHA-1 operation on already deployed commodity microprocessors is about 214 cycles. If Stevens' attack of 260 SHA-1 operations serves as the baseline, then finding a collision costs about 214 * 260 ~ 274 cycles.
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 225 * 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.

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