5 ms·

Basically, NIST seems to be reasoning that because Keccack's sponge construction has no internal resistance to meet-in-the-middle attacks, the collision and pre

Basically, NIST seems to be reasoning that because Keccack's sponge construction has no internal resistance to meet-in-the-middle attacks, the collision and preimage resistances are the same. An upper bound on the security of Keccack is set by the expression c + r = 1600. 'c' represents the internal bandwidth of the hash that is not directly controllable by an attacker. '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.

throwaway_yy2Di 13y ago
Thanks! This was much clearer than the blog post.
nly 13y ago
> the collision and preimage resistances are the same. > 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.
- marshray 13y ago
  > But does the SHA-3 construction mean a collision attack will further enable a preimage attack? 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.
- afhof 13y ago
  Its deeply troublesome when these kinds of comments come up for two reasons: first and lesser: its wrong; secondly: its inconspicuously wrong. Processor speeds double approximately every generation which we can estimate is once every two years. 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.
  - nullc 13y ago
    > Its deeply troublesome when 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.
rainsford 13y ago
I guess I don't really understand the objection to NIST's reasoning. While a larger capacity (c) would increase pre-image resistance, it wouldn't help generic collision resistance (which would always be limited by the output size). There are certainly contexts where a pre-image attack would be more damaging than a collision, but collisions can be a problem in other situations. Asking the user to figure out which security level applies to their application seems like a source of potential issues. Giving them a generic security level parameter to work with might make things easier. 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.
- marshray 13y ago
  Designing a crypto primitive that generates N bits of output having only N/2 bits of primary preimage security is unprecedented. It's a radical design decision. 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.
  - rainsford 13y ago
    I agree that it's a new design decision, but I think there is reasonable support for making it. Hash function history has pretty well demonstrated that most implementers don't understand the difference between pre-image security, hash output length and collision resistance. And the security margin is far from eliminated entirely. Not only is there significant margin in the round function itself over the full number ofrounds, but the 256-bit security level provided by the proposed SHA-3-512 seems fairly substantial to me. 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.
marshray 13y ago
Minor correction: The final round submission specified c=512 and c=1024 bits for Keccak-256 and Keccak-512 respectively.
realy 13y ago
> I don't think anyone should presume ill intent here on the part of NIST. 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.

throwaway_yy2Di 13y ago

Thanks! This was much clearer than the blog post.

nly 13y ago

> the collision and preimage resistances are the same. > 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.

marshray 13y ago
> But does the SHA-3 construction mean a collision attack will further enable a preimage attack? 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.
afhof 13y ago
Its deeply troublesome when these kinds of comments come up for two reasons: first and lesser: its wrong; secondly: its inconspicuously wrong. Processor speeds double approximately every generation which we can estimate is once every two years. 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.
- nullc 13y ago
  > Its deeply troublesome when 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.

rainsford 13y ago

I guess I don't really understand the objection to NIST's reasoning. While a larger capacity (c) would increase pre-image resistance, it wouldn't help generic collision resistance (which would always be limited by the output size). There are certainly contexts where a pre-image attack would be more damaging than a collision, but collisions can be a problem in other situations. Asking the user to figure out which security level applies to their application seems like a source of potential issues. Giving them a generic security level parameter to work with might make things easier. 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.

marshray 13y ago
Designing a crypto primitive that generates N bits of output having only N/2 bits of primary preimage security is unprecedented. It's a radical design decision. 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.
- rainsford 13y ago
  I agree that it's a new design decision, but I think there is reasonable support for making it. Hash function history has pretty well demonstrated that most implementers don't understand the difference between pre-image security, hash output length and collision resistance. And the security margin is far from eliminated entirely. Not only is there significant margin in the round function itself over the full number ofrounds, but the 256-bit security level provided by the proposed SHA-3-512 seems fairly substantial to me. 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.

marshray 13y ago

Minor correction: The final round submission specified c=512 and c=1024 bits for Keccak-256 and Keccak-512 respectively.

realy 13y ago

> I don't think anyone should presume ill intent here on the part of NIST. 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.