What is going on with NIST’s SHA-3?
cdt.org
cdt.org
An upper bound on the security of Keccack is set by the expression
c + r = 1600.
'r' is the rate (bits per expensive f() function invocation) at which the message input can be processed.
Due to some basic and well-understood attacks, we know that Keccak cannot be more secure than c/2 bits.
NIST was planning to assign SHA-3-256 and SHA-3-512 having 128 and 256 bits of security respectively. On one hand, this sounds like a nice conservative overall security rating based on the (lower) collision resistance.
But NIST plans to re-tune these internal constants downwards, setting c to 256 or 512. Whereas the competition final round submission specified c = 448 and 1024 bits. The resulting speed boost is 24% and 89%.
I don't think anyone should presume ill intent here on the part of NIST. But it sure doesn't seem like a good time to propose cutting security margins down to the limit of publicly-known attacks. The idea of a hash function which outputs 256 bits having only 128 bits of preimage resistance is unprecedented.
> The idea of a hash function which outputs 256 bits having only 128 bits of preimage resistance is unprecedented.
But does the SHA-3 construction mean a collision attack will further enable a preimage attack? Most breaks in recent cryptographic hashes have been confined to collision attacks. Even MD5 (publicly) hasn't been shown to be vulnerable to a viable preimage attack.
It's worth remembering that just to count to 2^128 it'll take a 3 GHz core with a single cycle increment instruction, along with a billion of its friends, over 3 and a half trillion years.
Also, even if a 128 bit meet in the middle could be computed, it'd require an unfathomable amount of memory.
Yes! This is a well-known feature of the sponge construction. Sponges generally handle this challenge by having a huge internal bandwidth, 1600 bits in the case of Keccack. No one is going to collide that!
However, this internal bandwidth effectively narrows at the points where the message input gets mixed in. Which is why the choice of c (representing the minimum width in bits) is so security critical.
But remember c/2 just represents an upper bound! If algorithmic attacks against the 24 rounds of Keccack's f() function are discovered in the future, it seems very plausible that having a little bit of safety margin in the choice of c could make the difference between it being exploitable or not.
What do we have to count to: 2^128 = 3.402823669209385e+38
How many times can we count in a year with a 3GHz core: 3e9 * 3600 * 24 * 365.24 = 9.4670208e+16
In two years, when processing speeds have doubled? 9.4670208e+16 * 2 = 1.89340416e+17
How many years until a core can complete count to 2^128 in a year? log(3.4028e+38 / 9.467e+16) / log(2) * 2 = 143.21
So, in 143 years a single computer will be able to count to 2^128 in a single year. That's still a long time, but its WAY WAY less than the trillions of years people quote. Add in as many extra cores/machines/datacenters/planets of extra processors and you aren't really indefinitely secure. You are secure for a limited number of years and that's it.
People just assume exponential growth goes on forever. You're giving a counter argument to moores law. Moore's law is not physical law, and physical law says otherwise here.
The amount of energy needed to update a counter 2^128 times on a non-reversible computer with the highest efficiency permitted by understood physics requires the energetic equivalent of something like 2 megatonns of TNT.
The additional state that brings security against brute force preimage attacks also tends to increase security against analytical attacks, as well as speculative QC attacks. So it's not worthless, at all— but your moore's law argument is not credible.
Do you have any sources to back up this claim? Max processor speed has stalled to ~4GHz since 2005. If you're referring to Moore's law, it concerns the amount of transistors in ICs, and will eventually hit a limit (not before 10 years, but not after 140 years).
If the world had access to that kind of energy, I'm sure it'd be used for far more interesting things than finding a single hash collision.
[1] http://en.wikipedia.org/wiki/Landauer_limit [2] http://en.wikipedia.org/wiki/Brute-force_attack#Theoretical_...
Edit: and while we're on the subject of inappropriately extrapolating Moore's law, if current performance-per-watt continues to double every 18 months I'd be interested in how long it'd take to even reach the Landauer limit. I can't seem to find out how much energy it takes to do a single bit flip in a modern processor online, so I can't do the calculation.
On top of that, Keccak's software performance is nothing to write home about and SHA-256 and SHA-512 look a lot safer now than they did when the SHA3 competition was started. The reasonably large performance boost the capacity changes could bring about might help SHA-3's case a bit for software developers who have barely started moving away from SHA-1 (if they're not still hanging on to MD5).
While 512 vs 256 bits of pre-image security for SHA-3-512 (which the author seems to think is an unacceptable security downgrade) is interesting to discuss in an academic sense, it seems ludicrous to suggest the change would actually benefit someone trying to break SHA-3. Any adversary able to perform 2^256 operations is so far beyond modern cryptanalysis that everyone might as well just give up.
The competition Keccak proposals specified a healthy safety margin, NIST proposes to eliminate it entirely. Why? Is it worth being able to hash messages 24-89% faster if in return you have to make your MACs twice as large? For example, if you currently use SHA-1 and want to move to SHA-3 without losing any preimage security, instead of 20 bytes you'll need to send 48 bytes over the wire with every message.
Attacks only ever get better and c/2 is an upper bound. If weaknesses are found in other parts of the function, we may wish there had been at least some safety margin built in.
I don't quite understand your MAC output length math. As far as I can tell, at least HMAC-SHA1 security could be achieved with SHA-3-512 truncated to 20 bytes of output. From what I understand of sponge functions, pre-image security is based on capacity (more specifically, half the capacity) and that truncated output up to the desired security level is valid. The Keccak page parameter calculator claims 160-bit security can be achieved with a capacity of 320 bits and 160 bits of output.
But I will admit that changing the pre-image security level association with output length does seem like it could create some confusion among people who do understand the current hash security situation. To be honest, I would be OK with NIST making the capacity for both be 512 bits (or 576 as DJB suggested). SHA-3-512 performance doesn't suffer much, since it has the most to lose there, security levels are reasonable and implementation is simpler. I would still like a higher performing version of Keccak given that there is already little enough reason to switch to it, but the 512/576 universal capacity might be a reasonable compromise since it wouldn't make SHA-3-256 THAT much slower from NIST's proposed parameters.
At this point, your fellow software developers are pointing and laughing at you for "inventing your own cryptography". Your function doesn't come standard in any library. Every single 3rd party audit of your architecture raises a red flag about this and you have trouble finding any official documentation to back you up. (Ask me how I know about this :-)
I'm not trying to say you don't know what you're doing or that that wouldn't meet the security properties, I'm just saying that the whole point of NIST defining these standards is to save us from having to come up with this kind of thing on our own.
NIST actually does define truncated versions of SHA-2, e.g., SHA-2-512/256. But they specify a different IV so that the functions are distinct.
> some confusion among people who do understand the current hash security situation
Right. I totally agree that most of the time we should assume that collision resistance is the relevant figure, whether we can see the attack or not. But still, SHA-2-256 has has 256 bits of preimage resistance just like a 256 bit random oracle. But SHA-3-256 will have 128? Can we use SHA-3-256 to derive an AES-256 key?
But it's a) unwieldy to specify, and b) reveals the output of NIST-SHAKE512-[0 <= bit < 128] unlike other truncated hash standards.
Note: I am definitely not saying this is the end of the world.
As another mentioned further down, no one is simply going around busting up 256bit keys, and when it finally happens, it will be with a computational paradigm that will require a defense built to an entirely different set of requirements: out of the scope of this competition.
We should assume a federal agency will keep the best interest of our privacy at heart, because they would never do anything to undermine our trust.
Sounds like a good idea.
This sounds pretty prudent. It avoids any security gotchas, and will also make life easier for implementers because the hash will consume a nice round 1024 bits of data at a time for all hash sizes.
This config would have slightly greater anticipated security at 256 bits than the submission, somewhat worse at 512 bit output— but in both cases be better than NIST's proposed parameters... and the performance impact would be relatively modest.
Wasn't that shoe-horned in at the end? There were no requirements that it not be e.g. ARX based, or AES based, etc. It wasn't until the final round that any choices were made based on being as alien as possible, where BLAKE's equal security margin and B+/A+ hardware/software performance was tossed out for Keccak's A+/D-.
Also of interest is that DJB's CubeHash was widely panned during the competition for having the exact same "weakened preimage in exchange for performance" tradeoff that is now being made for Keccak.
This does of course not mean that he made backdoors in AES and Keccak for the NSA. If that were the case he probably would not be allowed to speak about it, and he did talk about it very non-chalantly.
For instance, HMAC over SHA-2-256 or SHA-2-512/256 with a 256-bit key is expected to attain 256-bit security (i.e. the MAC size equals the security level).
Yet SHA-3-256 would not reach anything above 128-bit security, even though the MAC is 256 bits long; to attain 256-bit security one would have to scale the MAC size up to 512 bits instead.
Go impl here, from yours truly: https://github.com/steakknife/echo
Refs:
[0] http://c2.com/cgi/wiki?PrematureOptimization
Making your hash function twice as slow means you've halved the number of hash operations you can perform with fixed computational power. On the other hand, in many situations the resultant doubling of your security margin makes absolutely no practical difference since the existing margin is many, many order of magnitude away from any attacker's capabilities. Making things twice as hard on an attacker sounds impressive, until you think of it like asking someone to travel 2 billion light years instead of only 1 billion. Both are ridiculously outside of our current capabilities, but anyone able to travel 1 billion light years is likely going to be able to travel 2 billion as well.
In more specific terms, making a function with 256 bit security 10x slower has a pretty dramatic impact on performance with a resulting security increase to about 259 bits of security. You have a fairly marginal security increase for making your function 10 times slower. Modern cryptography is fast, but it's not yet fast enough that running at 1/10th the speed won't be noticeable in many situations.
The criteria for SHA-3 is not "as secure as possible". An application that needs as secure a hash as possible should use a protocol that combines multiple hashes of different families.
I know I wasn't the only one who was a little bit surprised when NIST said "Keccak is SHA-3, now let's see how to standardize a hash function and other applications out of it".
'encryption' -> 'hash function' for those that dont grok sed
The title was fixed.
The blog post I linked is titled "What the heck is going on with NIST’s cryptographic standard, SHA-3?" and that's the title I went with, saving the trouble of someone rewriting it without notification. But they rewrote it anyway. The title I would have chosen is "NIST's ability to do crypto work compromised by NSA", fwiw.
.../2409what-heck-going-nist%E2%80%99s-encryption-standard-sha-3