

Ask Security/Cryptography Expert Paul Kocher 372
Paul Kocher is unquestionably one of the highest-profile computer and network security experts around. He's president of Cryptography Research, Inc. and one of the architects of SSL 3.0. The floor is now open. Please try not to ask questions that can be answered with a few minutes' worth of online research. We'll post Paul's answers to 10 of the highest-moderated questions soon after he gets them back to us. Update: 03/13 18:18 GMT by M : Let's try this one more time, this time with feeling.
Serious Threats? (Score:5, Interesting)
Re:Serious Threats? (Score:3, Interesting)
Re:Serious Threats? (Score:3, Informative)
The overwhelming majority of security exploits (over 95% iirc-sorry, I don't have a source handy) are due to implementation errors and not cryptanalysis.
Side-channel attacks, technically, *are* attacks against implementations, not the ciphers themselves. They're attacks that exploit the fact that even if the cipher is solid, the execution of the algorithms involves physical effects which can be measured by an attacker with access to the processing device.
Depending on your point of view, you may or may
Re:Serious Threats? (Score:3, Interesting)
Do you think it's valid to rate the severity of a compromise by whether it's being actively exploited right now?
Triple barreled question (Score:5, Interesting)
Re:Triple barreled question (Score:3, Insightful)
The banks have major IT security flaws they do nothing about anyway. *whistles innocently*
Personally I feel if the private individual can afford it then yes - they have access to powerful & secure computers. There
Re:Triple barreled question (Score:3, Funny)
I think you meant to say e-barassment...
fhnlsfdlkm&5nlkd%Bvbcvbc (Score:4, Funny)
Re:fhnlsfdlkm&5nlkd%Bvbcvbc (Score:5, Funny)
Lbh pna ernq guvf? Qnza!
Re:fhnlsfdlkm&5nlkd%Bvbcvbc (Score:3, Funny)
"Be sure to drink your Ovaltine"?!
What the damn? That parent post was just a crummy commercial; aw nuts.
Re:fhnlsfdlkm&5nlkd%Bvbcvbc (Score:2)
uggc://jjj.oyvooyroybooyr.pb.hx/Gbbyf/Grkg/vaqr
Lrnu, vg'f n avpr flfgrz...
Re:fhnlsfdlkm&5nlkd%Bvbcvbc (Score:2, Funny)
Re:fhnlsfdlkm&5nlkd%Bvbcvbc (Score:2)
Re:fhnlsfdlkm&5nlkd%Bvbcvbc (Score:2)
u=t
Re:fhnlsfdlkm&5nlkd%Bvbcvbc (Score:2)
sml789234ls89*(&dammit(*@#(y8sdfljkg89
Secure SMTP? (Score:3, Interesting)
Re:Secure SMTP? (Score:2)
You can reject IP addresses that don't reverse and all sorts of hocus pocus with an MTA like Postfix.
So what you are asking is possible.
Re:Secure SMTP? (Score:3, Interesting)
So, I guess my question (to stay on subject) is
Re:Secure SMTP? (Score:2, Informative)
redundancy is key (Score:5, Insightful)
Therefore, "Please try not to ask questions that can be answered with a few minutes' worth of online research." should be rewritten as, "Please try not to ask or moderate up questions that can be answered with a few minutes' worth of online research. "
Social engineering (Score:5, Interesting)
I think.... (Score:2, Insightful)
Honestly, as long as a system can be accessed by someone. It can be accessed by someone that shouldn't.
Re:Social engineering (Score:2)
example:
In stead of letting the user determine the password, have the person scan there finger print at hire, then associate the finger print with permissions on a server, authenticate against the MAC address, and device ID.
This way there is no password to give out, and the user will thing somthing is wrong when 'security' calls and asked for something that isn't used.
Now to get into the system, you have to know the allowed MAC addres
Re:Social engineering (Score:2, Insightful)
reducing the ability for outsiders to influence access isn't solving much?
The problem is not people figuring out people's passwords. I'd just like to pose: What happens when a buffer overflow is discovered in the biometric information acceptance daemon?
stop using bad programming practices and allow for dynamic length buffers, or at the very least use che
Re:Social engineering (Score:2, Informative)
Theory vs. Practice (Score:4, Interesting)
what should manufacturers do? (Score:4, Interesting)
Ok it's well known that (Score:4, Interesting)
My first question is, how confident are you, as a crypto person, that you're not inadvertently peddling snake oil, that is, crypto the NSA has already cracked?
Second, the NSA allegedly has secret patents it uses to suppress new crypto. Do you think this is a significant inhibiter on research or am I worried for nothing?
NSA may not be that far ahead. (Score:5, Insightful)
In the '70s, '80s, and on up into the '90s, the NSA was certainly ahead of the civilian cryptanalytic community. DES, for instance, had its S-boxes strengthened against differential cryptanalysis in the '70s--about a decade and a half before the civilian cryptanalytic community discovered differential cryptanalysis.
But recently, there've been tantalizing signs the NSA is not as far ahead as people once thought. The civilian cryptanalytic community has grown tremendously in just the last ten years, and the quality of scholarship is the best we've seen since Turing and Shannon established the field. The civilian cryptanalytic community is now breaking NSA designs.
For instance: the NSA submitted a pretty cool cipher mode (Dual Counter Mode) for use with AES. People were looking forward to the opportunity to beat on an NSA design--and lo and behold, Dual Counter Mode was broken within a matter of weeks. The cryptoparanoids out there will say the NSA intentionally put out a weak mode in order to fool their enemies into underestimating their talents, but--really. Occam's Razor applies to the NSA as much as it applies to anyone else. The simpler explanation is that the NSA got egg on their face, just like everyone else has had. If you're going to be active in the crypto community, you're going to get your fair share of brain-os. Bruce Schneier presented MacGuffin at one conference only to have his brainchild be broken before the conference ended. If something like that can happen to Bruce, why should the NSA be immune?
The really fascinating NSA braino is, undoubtedly, SKIPJACK, the cipher which was going to be the heart of the Clipper Chip. It had a very solid design and 32 rounds. 32 rounds is a lot of rounds--the idea the NSA would make a 32-round cipher struck a lot of people as evidence that the NSA was being extremely conservative.
Eli Biham took a look at the SKIPJACK design and, pretty much on a mental lark, decided to play around with some numbers. Before SKIPJACK had been published a month, Biham had invented an entirely new differential cryptanalysis scheme--"impossible differential cryptanalysis"--and had used it to break 31 of SKIPJACK's 32 rounds.
Remember: SKIPJACK was the NSA's effort at making a safe, strong cipher. They swore before Congressional intelligence subcommittees that SKIPJACK didn't have back doors, and they allowed a small number of outside experts (incl. Dorothy Denning, who's a crypto luminary) to review major portions of the classified cipher.
So either you've got to believe the NSA lied to Congress, deliberately deceived Denning, and that Denning wasn't smart enough to know she was being deceived... or you can believe the civilian cryptanalytic community is getting good enough to challenge the NSA on the NSA's own terms.
Anyway. Come to your own beliefs as to how far ahead the NSA is of the civilian cryptanalytic community. I think the answer is "not very", but reasonable people will certainly disagree on these things.
Re:NSA may not be that far ahead. (Score:5, Insightful)
Good post, but I disagree on a couple of minor points.
Bruce Schneier presented MacGuffin at one conference only to have his brainchild be broken before the conference ended. If something like that can happen to Bruce, why should the NSA be immune?
This doesn't really follow. Schneier's a smart guy, and he's among the better cryptographers in the world, but his screwup doesn't necessarily mean that the NSA would also.
However, the fact that *every* cryptographer who's been around for a while has had his or her share of public failures does.
Eli Biham took a look at the SKIPJACK design and, pretty much on a mental lark, decided to play around with some numbers. Before SKIPJACK had been published a month, Biham had invented an entirely new differential cryptanalysis scheme--"impossible differential cryptanalysis"--and had used it to break 31 of SKIPJACK's 32 rounds.
Umm, not quite. First, Biham and Shamir invented differential cryptanalysis in 1990; they didn't invent it to attack SKIPJACK (although their paper on SKIPJACK did introduce a new variant, IIRC). Second, there are two possible "lessons" to take away regarding the capabilities of the NSA. One is what you said, that the NSA had built in a lower safety margin than they thought they had, but the other is that they knew what they were doing and deliberately chose 32 rounds because they knew 31 could be broken and they're pretty confident in their analysis.
Breaking a 31-round reduction of SKIPJACK does absolutely no good if you need to decrypt messages encrypted with 32-round SKIPJACK.
Remember: SKIPJACK was the NSA's effort at making a safe, strong cipher. They swore before Congressional intelligence subcommittees that SKIPJACK didn't have back doors
Umm, SKIPJACK *doesn't* have any back doors or weaknesses that we know of. The LEAF (Law Enforcement Access Field) they proposed for Clipper (with SKIPJACK as the cipher) was soundly thrashed by Matt Blaze, but that was the opposite. The NSA intended to design in a back door whereby law enforcement officials could decrypte messages, but Blaze found a way to close that door.
The weakness in the LEAF, however, was almost certainly a significant "braino" by the NSA. Even if for some reason they wanted to be able to defeat the LEAF, they apparently underestimated the ability of academic cryptanalysts. It's more likely, however, that they just plain screwed up, just like they did with the dual counter mode.
who is the worst to deal with? (Score:5, Interesting)
- The software developers
- The software distributors
- The end users
My first guess would be the end users, but I am curious as to which group gives you the most problems.
Certification and SSL (Score:3, Interesting)
Given that an SSL connection is cryptographically secure, and that any security is only as strong as its weakest link...
How secure do you really think an SSL connection is when both parties are having to trust certificates signed by third parties? I don't know how Verisign store their root keys, nor do I know how they verify the identity of someone before issuing a certificate. So can I really trust that a certificate signed by them is valid and can you see any way of removing the trust element?
Z.
Re:Certification and SSL (Score:2)
I, for one, don't trust internationnal organizations. (Who elected them ? governments, money, NSA?)
Formulaic test for primality (Score:2, Interesting)
Re:Formulaic test for primality (Score:2)
Re:Formulaic test for primality (Score:2)
If you choose this question, editors, please make the correction?
thanks
How can I help? (Score:5, Interesting)
From the formal side of things, I am new to information security. I have been doing applied security work for about three years. I would really like the challenge of writing a thesis, but so far I haven't come up with anything.
Here are my requirements: I want the topic to be challenging, I want it to be within the grasp of a Master's level understanding of information security, and I want it to be valuable to the community.
Are there any areas or topics that need to be addressed but have not? Is there something the community needs but has not yet received? If background info helps, I really enjoy picking apart IP traffic, and have some interest in fractals from a mathematic perspective.
Also, I'd like to say thanks for the links on your site. I now have tons more reading material.
So.... (Score:4, Interesting)
Re:So.... (Score:5, Interesting)
Furthermore, since we require more and more passwords for things such as networks, email, online banking, ebay, and on and on, what do you think is the best method for joe average to keep track of all of these, aside from a) using the same password for all of them and b) using a "trusted" framework (passport, palladium). Can there ever be a solution to such a problem?
Not a question, but a comment for slashdot (Score:4, Insightful)
Why not make stories have a ten or fifteen minute delay to allow people to actually READ the articles. Have a little timer that says how long until the story goes live for comments. This might take care of some of those who never read the articles.
Just a thought....
Re:Not a question, but a comment for slashdot (Score:2)
Why not make stories have a ten or fifteen minute delay to allow people to actually READ the articles. Have a little timer that says how long until the story goes live for comments. This might take care of some of those who never read the articles.
Ju
Worst implementation? (Score:5, Interesting)
Re:Worst implementation? (Score:5, Interesting)
I was recruited from a major telco to work for a competing telco in 1999, ostensibly to work as part of their tiger team. When I showed up for work, there was nobody else on the team. "Don't worry," I was told, "we're hiring more. Just try and get some good design work done on securing our billing back-end, because right now it's wide-open."
Wait, your billing back-end is wide open?
"Yes."
And it's deployed?
"Yes."
Oh, fuck.
So I went to work on the back-end (which, at the time, was handling about $1 billion a year), with a great feeling of doom hanging over my head. When you're getting paid $38K and have no backup and you're told that "if we lose money from insecurity, it's all your fault, regardless of the fact we deployed it without any security to speak of"... well. You can figure it out.
A month later I had a binder full of attacks against the network, and another binder full of design ideas for how to secure it. By "binder", I mean 2-inch binders stuffed to the gills with paper. I was shortly thereafter called into my manager's office. An HR representative was present, so I knew the news was bad.
"Rob," my manager said, "we're concerned that you've made no progress on your task..."
What? I asked. I pulled out the Binders o' Doom from my satchel (we didn't have any secure storage in the development group, so I didn't ever let those binders out of my sight) and set them on her desk.
"Oh," she said as she leafed through the binders. The look on her face was roughly that of an indigenous South Pacific islander who was seeing an indoor toilet for the first time. "Um. Rob. Didn't anyone tell you?"
Tell me what?
"We already have a design we want you to use. You just have to implement it. No, no, you're not anywhere near senior enough to come up with a design for the security of the billing system..."
I breathed a sigh of relief. Sanity at last! And then she handed me a very thin folder.
I opened it up and it was, I shit you not, RFC1991. Classic PGP.
I laughed, handed the binder back, and told her she grabbed the wrong folder. Then she got very angry with me and asked me what, precisely, was wrong with using Classic PGP to secure the back-end?
I gave her the litany:
Finally I asked "so who's the genius who came up with this one?"
Whoops. Turns out said genius was sitting across the desk from me.
By the end of the day I was busy writing Classic PGP in C++, under Management orders. The Sword of Damocles was falling and I was right under it. I protested, loudly and vociferously, until finally I got canned for "not being a team player and not performing according to expectation".
I was climbing in my car to leave the company for the last time when I realized... hey, I still have the Binders o' Doom in my satchel.
I got out of my car and walked back towards the building. An HR representative stopped me at the door and told me that if I walked in, it'd be considered trespass. I explained that I just wanted to drop off something for w
Re:Worst implementation? (Score:3, Interesting)
Its like when I heard an android describing the security requirements for an electronic financial derivatives exchange:
"Its not like we're dealing with money"
No, just a government bond worth about $100000.
Another one at a bank, there is a story about the international payments system. It is split into two parts, the payment transmission system and the ledger. Great idea. Then why save money by having one guy to support both wit
what progress... (Score:3, Interesting)
I have read a lot about it and it seems to be the direction public-key crypto is going nowadays. Have you done any serious work in this field? and if so, when do you think the public will start to see it implemented full force?
SSL VPNs? (Score:3, Interesting)
Are SSL VPNs up to par? What are their strengths and weaknesses? Was SSL designed for such applications?
Re:SSL VPNs? (Score:3, Insightful)
I'm unaware of any weaknesses this has versus a real
Re:WHY DONT YOU (etc.) (Score:3, Insightful)
However, I was not referring to the same kinds of VPNs the AC mentions. I understand why TCP over TCP is a bad idea [sites.inka.de].
I was thinking of these kinds of products:
Internet broken? (Score:5, Interesting)
What is worth protecting? (Score:4, Insightful)
Along these lines, of your own personal communications and data storage, what do you encrypt and what do you leave unencrypted?
Unsecurity (Score:2, Interesting)
How will the SSL team improve security in the new version of the SSL protocol?
Palladium (Score:5, Interesting)
Quantum Computing and Cryptography (Score:5, Interesting)
Re:Quantum Computing and Cryptography (Score:2)
Dive Right In (Score:5, Interesting)
DRM systems? (Score:5, Interesting)
What is your opinion about where DRM systems should go? How can we protect fair use and still get movies released in HD?
Crypto in the scope of the real world. (Score:5, Interesting)
What contingency plans are you aware of? What sort of research is being done to avoid this single point of failure problem in future solutions? Are we just hoping for quantum encryption to save us? Of course, the real solution is to not depend solely on crypto for security, as crypto it self will never be perfect (implementation problems, etc). Security organizations, who haven't already, need to update their risk assessments to include risks to crypto solutions. It's still interesting to look at crypto in a more narrow scope than the real world :)
From a Student's Perspective (Score:5, Interesting)
What is the best way to go about finding a career in cryptography/cryptology?
How did you start in the field?
Is there a "job market" per se, or is it more of a position that one falls into?
Re:From a Student's Perspective (Score:3, Funny)
This had been explained quite clearly in many, many movies.
First, you crack some secret government super hard code, snoop around.
Secret Agency use there 'really good software', written and operated by some overweight obnoxius individule, to track you to your address.
they then send someone to kill you, you narrowly escape, befriend some mysterious former agent.
after he saves you from more assassination attempt, he finally dies saving your life. after which the agency feels bad and brings
64 Bit Computing (Score:5, Interesting)
Alternative to uid/pw logins to establish identity (Score:5, Interesting)
Now, if I was on a handful of systems, this would make sense. However, I've found that many websites I come to are increasingly requiring registration, including creating a userid and password to log in to their systems. The personalization of my interface with their system is nice, but makes following the rules about passwords unmanageable -- I can't keep track of several dozen strong passwords from memory.
As an alternative to that, for website uses such as I've mentioned, it seems to me that making use of a public-key encryption system, something along the lines of what I understand SSL to do, would seem to make more sense. My system could exchange encrypted data with the web server using our known public keys, enabling us each to know that we are, in fact, who we claim to be. Even if I was required to use my pass-phrase that goes with that public key each time I logged in, it would be easier for me to remember that one pass-phrase (which could be even more secure than a 6-8 character password) than is currently available.
Obviously there would be change-over costs involved with this, but is there some big reason that this kind of a system would be less secure than the current system, particularly if we take into account the problem of weak and repeatedly used passwords?
Passwords (Score:4, Interesting)
My wife has several files and pieces of paper with all of her passwords written down. She has to keep these on 3 or 4 computers, in her wallet, in her hotmail account, etc.
How problematic is this? Can this ever be solved? How?
Re:Passwords (Score:2)
Why should the public care? (Score:3, Insightful)
Your use and abuse of Cryptography (Score:5, Interesting)
The reason I'm asking is because there are a lot of great techies out there, but it's rather the geeks that seem to do most of the advocacy and who seem to be able best to stick to their guns and force their peers to use GPG, etc.
Also, I used the word "abuse" also. Do you think you've ever gone over the top with crypting everything, or have you ever used your knowledge to gain access to information that you should not have seen (however trivial), or have you ever been paid to crack something encrypted, won prizes, that sort of thing?
Which algorithm / program... (Score:2, Insightful)
RMN
~~~
Re:Which algorithm / program... (Score:2)
The beauty is that he can securely access his files from anywhere he as an internet connection.
Pure genius
Re:Which algorithm / program... (Score:2)
Doesn't everybody store secret information on the Gibson, relying on ThePlague to keep the information safe?
Interface with Government agencies (Score:5, Interesting)
Password... (Score:2, Funny)
TLS/SSL as a sockopt? (Score:2, Interesting)
Granted, openssl's interface may be trivially more complex, but just the thought of managing yet another set of certificates makes me cringe.
Is Cryptology a House of Cards? (Score:5, Insightful)
You're actually +1 Funny! (Score:2)
However, all of these primitives are not proven secure. How do you feel about cryptology being built on such a fragile foundation, essentially making it a house of cards?
Are you aware how amusing it is that you posted this question over a connection based on IP primitives?
Your use of cryptography in everyday tasks ... (Score:4, Interesting)
thanks.
Re:Your use of cryptography in everyday tasks ... (Score:2)
Transparency to the user is a great thing, until they break something. (Eg. XP encrypted folders)
If the public won't learn something new, what do you do to make the tools more attractive to them?
Is the Technology ahead of us? (Score:5, Interesting)
Over the last couple of decades, cryptography has gone from being the domain of major governments, big business, and the odd hobbyist and researcher to being a massive public industry that anyone can (and does) participate in, with new algorithms published and new applications announced almost every week. Meanwhile, we learn of vulnerabilities in various implementations of cryptosystems much more frequently than we hear of people discovering fundamental flaws in the cryptosystems themselves.
Given these facts, do you think we need to change focus, turning to validating and "approving" implementations of cryptosystems (such as your own SSL 3.0) or should the emphasis of the "crypto community" continue to be innovation in fundamentals of cryptographic systems and new applications for them? How important is it to have someone verify that a cryptosystem is implemented well?
Thanks, and I'll take my answer off the air
Books, scientific journals etc (Score:4, Interesting)
Can you recommend some good hardcore books, or journals to follow for what's going on currently in the crypto scientific community?
Cryptography for Dual Computing Paradigms (Score:2, Interesting)
I know I'm making a lot of assumptions here, but my guesses on what will happen to cryptrographic algorithms with the advent of an atomic computing paradigm mostly center around how useless current cryptography methods (designed for the turing machine) will become.
Do you envision it being possible to design a cryptographic algorithm that is "one-way" and remains that way in both the turing machine computing paradigm and the quantum computing paradigm, and if so, how long do you think developing those alg
The Human Factor (Score:3, Interesting)
Roles of quantum cryptography (Score:2, Interesting)
Which side would you take? (Score:3, Interesting)
The Importance of Cryptography (Score:5, Interesting)
So, my question is this:
Has cryptography to include the human factor itself into the calculation or is it still only about mathematics? Can you imagine a strong encryption system with a special focus on people with low awareness?
How does the Via C3 "Nehemiah" RNG work? (Score:2, Interesting)
So... how does it work? I know Intel's chipsets count cycles of a high-speed (~300 MHz) clock between cycles of a low-speed VCO controlled by resistor noise.
Did they repeat Intel's mistake implementing hardware whitening, or is it feasable to implement on-like quality checks by testing to see if the deviation from randomness is as expected?
What's the software interface?
Experts and/or The Masses (Score:3, Interesting)
On the other hand no where is the Open Source Modle more touted as the panacea of computing then in cryptography. Many eyes it is said will catch backdoors and reveil poor implimentations before they become security issues.
My question then: When developing and implementing encryption, How would you weigh the need for experties with the trust and scrutiny availible from Open Source development?
SSL and Forward Security (Score:5, Interesting)
First of all, thank you for agreeing to be interviewed here. It's greatly appreciated.
I'm curious if you wouldn't mind elaborating a bit on the catastrophic failure of the SSL security architecture given the compromise of an RSA private key. An attacker can literally sniff all traffic for a year, break in once to steal the key, then continue to passively decrypt not only all of last year's traffic but all of next year's too. And if he'd like to partake in more active attacks -- session hijacking, malicious data insertion, etc. -- that's fine too.
In short, why? After so much work was done to come up with a secure per-session master secret, what caused the asymmetric component to be left so vulnerable? Yes, PGP's just as vulnerable to this failure mode, but PGP doesn't have the advantage of a live socket to the other host.
More importantly, what can be done for those nervous about this shortcoming in an otherwise laudable architecture? I looked at the DSA modes, but nothing seems to accelerate them (which kills its viability for the sites who would need it most). Ephemeral RSA seemed interesting, but according to Rescola's documentation it only supports a maximum of 512 bits for the per-session asymmetric key -- insufficient. If Verisign would sign a newly generated key each day, that'd work -- but then, you'd probably need to sign over part of your company to afford the service. Would it even be possible for them to sign one long term key, tied to a single fully qualified domain name, that could then sign any number of ephemeral or near-ephemeral short term keys within the timeframe allotted in the long term cert?
Thanks again for any insight on the matter you may be able to provide!
Yours Truly,
Dan Kaminsky
DoxPara Research
http://www.doxpara.com
Threat from professional brute force methods (Score:2)
James Bamford's books on the NSA tell us that government security agencies have a long and documented history of obtaining back doors (political engineering?) or outright cracking codes. I remember a very public government effort several years ago to lobby for backdoors ("clipper chip" and others), an effort that seems to ha
trust in open p2p communities (Score:5, Interesting)
what can we do to maintain an open environment and establish trust between peers?
Factoring (Score:2, Interesting)
USPTO (Score:5, Interesting)
Grid Computing and Crypto (Score:4, Interesting)
Security/Cryptography vs Development (Score:3, Interesting)
How do you think? (Score:5, Interesting)
I normally hate the cliche of "thinking outside of the box", but here it is fully appropriate.
Human adoption? (Score:3, Insightful)
Re:Legit Question (Score:2)
Re:Combining cryptographic hashes (Score:2)
Don't know how weak MD5 is, but Applied Cryptography disses it.
NOT an interview question ... (Score:3, Funny)
Re:NOT an interview question ... (Score:2, Funny)
Re:RISC, Quantums and Security (Score:2)
Re:The Government (Score:2)
Unbreakable encryption is not achievable.
The goal is to make the cost of breaking the encryption more than the value of the information.
Governments have a great deal of money to throw at a problem. But they're not going to throw that much money at cracking your PGP-encrypted email unless they think they're going to find something worth while. They couldn't care less about your personal life (excepting the case where you somehow have become, through your own fault or not, a
Please use Google. (Score:5, Insightful)
In order to flip a bit requires a thermodynamic minimum of 4.4 * 10**-26 joules of energy. (Ignore the time/power theoretical tradeoff and energyless reversible computing, please: those are still purely theoretical, and we have no computers which can do it. For that matter, we have no computers which can approach the thermodynamic minimum, but let's give the NSA some credit.)
That means it requires a minimum of 1.1 * 10**-23 joules of power to store a 256-bit AES key. Let's assume you have some kind of truly bizarre key cracker that can do an energyless rekey and key trial: all you have to do is have 1.1 * 10**-23 joules of power for each key you want to test. That's the thermodynamic minimum energy you need just to store the key.
To break a 256-bit key by brute force requires, on average, 2**255 operations. Multiply 1.1 * 10**-23 joules of power by 2**255, and you get 6.5 * 10**53 joules of power.
Let me repeat this.
It requires
65000000000000000000000000000000000000000000000
By comparison, the Sun's annual power output is in the realm of 1.2 * 10**34 joules.
Or
120000000000000000000000000000000000
Are you beginning to see why it's such a silly question to ask whether or not modern ciphers can be brute-forced with Crays?
Please. Use Google before asking questions.