Entries Tagged "encryption"

Page 27 of 56

TEMPEST Attack

There’s a new paper on a low-cost TEMPEST attack against PC cryptography:

We demonstrate the extraction of secret decryption keys from laptop computers, by nonintrusively measuring electromagnetic emanations for a few seconds from a distance of 50 cm. The attack can be executed using cheap and readily-available equipment: a consumer-grade radio receiver or a Software Defined Radio USB dongle. The setup is compact and can operate untethered; it can be easily concealed, e.g., inside pita bread. Common laptops, and popular implementations of RSA and ElGamal encryptions, are vulnerable to this attack, including those that implement the decryption using modern exponentiation algorithms such as sliding-window, or even its side-channel resistant variant, fixed-window (m-ary) exponentiation.

We successfully extracted keys from laptops of various models running GnuPG (popular open source encryption software, implementing the OpenPGP standard), within a few seconds. The attack sends a few carefully-crafted ciphertexts, and when these are decrypted by the target computer, they trigger the occurrence of specially-structured values inside the decryption software. These special values cause observable fluctuations in the electromagnetic field surrounding the laptop, in a way that depends on the pattern of key bits (specifically, the key-bits window in the exponentiation routine). The secret key can be deduced from these fluctuations, through signal processing and cryptanalysis.

From Wired:

Researchers at Tel Aviv University and Israel’s Technion research institute have developed a new palm-sized device that can wirelessly steal data from a nearby laptop based on the radio waves leaked by its processor’s power use. Their spy bug, built for less than $300, is designed to allow anyone to “listen” to the accidental radio emanations of a computer’s electronics from 19 inches away and derive the user’s secret decryption keys, enabling the attacker to read their encrypted communications. And that device, described in a paper they’re presenting at the Workshop on Cryptographic Hardware and Embedded Systems in September, is both cheaper and more compact than similar attacks from the past—so small, in fact, that the Israeli researchers demonstrated it can fit inside a piece of pita bread.

Another article. NSA article from 1972 on TEMPEST. Hacker News thread. Reddit thread.

Posted on June 29, 2015 at 1:38 PMView Comments

What is the DoD's Position on Backdoors in Security Systems?

In May, Admiral James A. Winnefeld, Jr., vice-chairman of the Joint Chiefs of Staff, gave an address at the Joint Service Academies Cyber Security Summit at West Point. After he spoke for twenty minutes on the importance of Internet security and a good national defense, I was able to ask him a question (32:42 mark) about security versus surveillance:

Bruce Schneier: I’d like to hear you talk about this need to get beyond signatures and the more robust cyber defense and ask the industry to provide these technologies to make the infrastructure more secure. My question is, the only definition of “us” that makes sense is the world, is everybody. Any technologies that we’ve developed and built will be used by everyone—nation-state and non-nation-state. So anything we do to increase our resilience, infrastructure, and security will naturally make Admiral Rogers’s both intelligence and attack jobs much harder. Are you okay with that?

Admiral James A. Winnefeld: Yes. I think Mike’s okay with that, also. That’s a really, really good question. We call that IGL. Anyone know what IGL stands for? Intel gain-loss. And there’s this constant tension between the operational community and the intelligence community when a military action could cause the loss of a critical intelligence node. We live this every day. In fact, in ancient times, when we were collecting actual signals in the air, we would be on the operational side, “I want to take down that emitter so it’ll make it safer for my airplanes to penetrate the airspace,” and they’re saying, “No, you’ve got to keep that emitter up, because I’m getting all kinds of intelligence from it.” So this is a familiar problem. But I think we all win if our networks are more secure. And I think I would rather live on the side of secure networks and a harder problem for Mike on the intelligence side than very vulnerable networks and an easy problem for Mike. And part of that—it’s not only the right thing do, but part of that goes to the fact that we are more vulnerable than any other country in the world, on our dependence on cyber. I’m also very confident that Mike has some very clever people working for him. He might actually still be able to get some work done. But it’s an excellent question. It really is.

It’s a good answer, and one firmly on the side of not introducing security vulnerabilities, backdoors, key-escrow systems, or anything that weakens Internet systems. It speaks to what I have seen as a split in the Second Crypto War, between the NSA and the FBI on building secure systems versus building systems with surveillance capabilities.

I have written about this before:

But here’s the problem: technological capabilities cannot distinguish based on morality, nationality, or legality; if the US government is able to use a backdoor in a communications system to spy on its enemies, the Chinese government can use the same backdoor to spy on its dissidents.

Even worse, modern computer technology is inherently democratizing. Today’s NSA secrets become tomorrow’s PhD theses and the next day’s hacker tools. As long as we’re all using the same computers, phones, social networking platforms, and computer networks, a vulnerability that allows us to spy also allows us to be spied upon.

We can’t choose a world where the US gets to spy but China doesn’t, or even a world where governments get to spy and criminals don’t. We need to choose, as a matter of policy, communications systems that are secure for all users, or ones that are vulnerable to all attackers. It’s security or surveillance.

NSA Director Admiral Mike Rogers was in the audience (he spoke earlier), and I saw him nodding at Winnefeld’s answer. Two weeks later, at CyCon in Tallinn, Rogers gave the opening keynote, and he seemed to be saying the opposite.

“Can we create some mechanism where within this legal framework there’s a means to access information that directly relates to the security of our respective nations, even as at the same time we are mindful we have got to protect the rights of our individual citizens?”

[…]

Rogers said a framework to allow law enforcement agencies to gain access to communications is in place within the phone system in the United States and other areas, so “why can’t we create a similar kind of framework within the internet and the digital age?”

He added: “I certainly have great respect for those that would argue that they most important thing is to ensure the privacy of our citizens and we shouldn’t allow any means for the government to access information. I would argue that’s not in the nation’s best long term interest, that we’ve got to create some structure that should enable us to do that mindful that it has to be done in a legal way and mindful that it shouldn’t be something arbitrary.”

Does Winnefeld know that Rogers is contradicting him? Can someone ask JCS about this?

Posted on June 24, 2015 at 7:42 AMView Comments

Why We Encrypt

Encryption protects our data. It protects our data when it’s sitting on our computers and in data centers, and it protects it when it’s being transmitted around the Internet. It protects our conversations, whether video, voice, or text. It protects our privacy. It protects our anonymity. And sometimes, it protects our lives.

This protection is important for everyone. It’s easy to see how encryption protects journalists, human rights defenders, and political activists in authoritarian countries. But encryption protects the rest of us as well. It protects our data from criminals. It protects it from competitors, neighbors, and family members. It protects it from malicious attackers, and it protects it from accidents.

Encryption works best if it’s ubiquitous and automatic. The two forms of encryption you use most often—https URLs on your browser, and the handset-to-tower link for your cell phone calls—work so well because you don’t even know they’re there.

Encryption should be enabled for everything by default, not a feature you turn on only if you’re doing something you consider worth protecting.

This is important. If we only use encryption when we’re working with important data, then encryption signals that data’s importance. If only dissidents use encryption in a country, that country’s authorities have an easy way of identifying them. But if everyone uses it all of the time, encryption ceases to be a signal. No one can distinguish simple chatting from deeply private conversation. The government can’t tell the dissidents from the rest of the population. Every time you use encryption, you’re protecting someone who needs to use it to stay alive.

It’s important to remember that encryption doesn’t magically convey security. There are many ways to get encryption wrong, and we regularly see them in the headlines. Encryption doesn’t protect your computer or phone from being hacked, and it can’t protect metadata, such as e-mail addresses that need to be unencrypted so your mail can be delivered.

But encryption is the most important privacy-preserving technology we have, and one that is uniquely suited to protect against bulk surveillance—the kind done by governments looking to control their populations and criminals looking for vulnerable victims. By forcing both to target their attacks against individuals, we protect society.

Today, we are seeing government pushback against encryption. Many countries, from States like China and Russia to more democratic governments like the United States and the United Kingdom, are either talking about or implementing policies that limit strong encryption. This is dangerous, because it’s technically impossible, and the attempt will cause incredible damage to the security of the Internet.

There are two morals to all of this. One, we should push companies to offer encryption to everyone, by default. And two, we should resist demands from governments to weaken encryption. Any weakening, even in the name of legitimate law enforcement, puts us all at risk. Even though criminals benefit from strong encryption, we’re all much more secure when we all have strong encryption.

This originally appeared in Securing Safe Spaces Online.

EDITED TO ADD: Last month, I blogged about a UN report on the value of encryption technologies to human freedom worldwide. This essay is the foreword to a companion document:

To support the findings contained in the Special Rapporteur’s report, Privacy International, the Harvard Law School’s International Human Rights Law Clinic and ARTICLE 19 have published an accompanying booklet, Securing Safe Spaces Online: Encryption, online anonymity and human rights which explores the impact of measures to restrict online encryption and anonymity in four particular countries ­—the United Kingdom, Morocco, Pakistan and South Korea.

EDITED TO ADD (7/8): this essay has been translated into Russian.

EDITED TO ADD (4/29/2019): this essay has been translated into Spanish.

EDITED TO ADD (11/13/2019): this essay has been translated into Bosnian.

EDITED TO ADD (10/28/2020): this essay has been translated into French and Hungarian.

EDITED TO ADD: this essay has been translated into German.

Posted on June 23, 2015 at 6:02 AMView Comments

The Secrecy of the Snowden Documents

Last weekend, the Sunday Times published a front-page story (full text here), citing anonymous British sources claiming that both China and Russia have copies of the Snowden documents. It’s a terrible article, filled with factual inaccuracies and unsubstantiated claims about both Snowden’s actions and the damage caused by his disclosure, and others have thoroughly refuted the story. I want to focus on the actual question: Do countries like China and Russia have copies of the Snowden documents?

I believe the answer is certainly yes, but that it’s almost certainly not Snowden’s fault.

Snowden has claimed that he gave nothing to China while he was in Hong Kong, and brought nothing to Russia. He has said that he encrypted the documents in such a way that even he no longer has access to them, and that he did this before the US government stranded him in Russia. I have no doubt he did as he said, because A) it’s the smart thing to do, and B) it’s easy. All he would have had to do was encrypt the file with a long random key, break the encrypted text up into a few parts and mail them to trusted friends around the world, then forget the key. He probably added some security embellishments, but—regardless—the first sentence of the Times story simply makes no sense: “Russia and China have cracked the top-secret cache of files…”

But while cryptography is strong, computer security is weak. The vulnerability is not Snowden; it’s everyone who has access to the files.

First, the journalists working with the documents. I’ve handled some of the Snowden documents myself, and even though I’m a paranoid cryptographer, I know how difficult it is to maintain perfect security. It’s been open season on the computers of the journalists Snowden shared documents with since this story broke in July 2013. And while they have been taking extraordinary pains to secure those computers, it’s almost certainly not enough to keep out the world’s intelligence services.

There is a lot of evidence for this belief. We know from other top-secret NSA documents that as far back as 2008, the agency’s Tailored Access Operations group has extraordinary capabilities to hack into and “exfiltrate” data from specific computers, even if those computers are highly secured and not connected to the Internet.

These NSA capabilities are not unique, and it’s reasonable to assume both that other countries had similar capabilities in 2008 and that everyone has improved their attack techniques in the seven years since then. Last week, we learned that Israel had successfully hacked a wide variety of networks, including that of a major computer antivirus company. We also learned that China successfully hacked US government personnel databases. And earlier this year, Russia successfully hacked the White House’s network. These sorts of stories are now routine.

Which brings me to the second potential source of these documents to foreign intelligence agencies: the US and UK governments themselves. I believe that both China and Russia had access to all the files that Snowden took well before Snowden took them because they’ve penetrated the NSA networks where those files reside. After all, the NSA has been a prime target for decades.

Those government hacking examples above were against unclassified networks, but the nation-state techniques we’re seeing work against classified and unconnected networks as well. In general, it’s far easier to attack a network than it is to defend the same network. This isn’t a statement about willpower or budget; it’s how computer and network security work today. A former NSA deputy director recently said that if we were to score cyber the way we score soccer, the tally would be 462­456 twenty minutes into the game. In other words, it’s all offense and no defense.

In this kind of environment, we simply have to assume that even our classified networks have been penetrated. Remember that Snowden was able to wander through the NSA’s networks with impunity, and that the agency had so few controls in place that the only way they can guess what has been taken is to extrapolate based on what has been published. Does anyone believe that Snowden was the first to take advantage of that lax security? I don’t.

This is why I find allegations that Snowden was working for the Russians or the Chinese simply laughable. What makes you think those countries waited for Snowden? And why do you think someone working for the Russians or the Chinese would go public with their haul?

I am reminded of a comment made to me in confidence by a US intelligence official. I asked him what he was most worried about, and he replied: “I know how deep we are in our enemies’ networks without them having any idea that we’re there. I’m worried that our networks are penetrated just as deeply.”

Seems like a reasonable worry to me.

The open question is which countries have sophisticated enough cyberespionage operations to mount a successful attack against one of the journalists or against the intelligence agencies themselves. And while I have my own mental list, the truth is that I don’t know. But certainly Russia and China are on the list, and it’s just as certain they didn’t have to wait for Snowden to get access to the files. While it might be politically convenient to blame Snowden because, as the Sunday Times reported an anonymous source saying, “we have now seen our agents and assets being targeted,” the NSA and GCHQ should first take a look into their mirrors.

This essay originally appeared on Wired.com.

EDITED TO ADD: I wrote about this essay on Lawfare:

A Twitter user commented: “Surely if agencies accessed computers of people Snowden shared with then is still his fault?”

Yes, that’s right. Snowden took the documents out of the well-protected NSA network and shared with people who don’t have those levels of computer security. Given what we’ve seen of the NSA’s hacking capabilities, I think the odds are zero that other nations were unable to hack at least one of those journalists’ computers. And yes, Snowden has to own that.

The point I make in the article is that those nations didn’t have to wait for Snowden. More specifically, GCHQ claims that “we have now seen our agents and assets being targeted.” One, agents and assets are not discussed in the Snowden documents. Two, it’s two years after Snowden handed those documents to reporters. Whatever is happening, it’s unlikely to be related to Snowden.

EDITED TO ADD: Slashdot thread. Hacker News thread.

EDITED TO ADD (7/13): Two threads on Reddit.

EDITED TO ADD (7/14): Another refutation.

Posted on June 22, 2015 at 6:13 AMView Comments

Encrypting Windows Hard Drives

Encrypting your Windows hard drives is trivially easy; choosing which program to use is annoyingly difficult. I still use Windows—yes, I know, don’t even start—and have intimate experience with this issue.

Historically, I used PGP Disk. I used it because I knew and trusted the designers. I even used it after Symantec bought the company. But big companies are always suspect, because there are a lot of ways for governments to manipulate them.

Then, I used TrueCrypt. I used it because it was open source. But the anonymous developers weirdly abdicated in 2014 when Microsoft released Windows 8. I stuck with the program for a while, saying:

For Windows, the options are basically BitLocker, Symantec’s PGP Disk, and TrueCrypt. I choose TrueCrypt as the least bad of all the options.

But soon after that, despite the public audit of TrueCrypt, I bailed for BitLocker.

BitLocker is Microsoft’s native file encryption program. Yes, it’s from a big company. But it was designed by my colleague and friend Niels Ferguson, whom I trust. (Here’s Niels’s statement from 2006 on back doors.) It was a snap decision; much had changed since 2006. (Here I am in March speculating about an NSA back door in BitLocker.) Specifically, Microsoft made a bunch of changes in BitLocker for Windows 8, including removing something Niels designed called the “Elephant Diffuser.”

The Intercept’s Micah Lee recently recommended BitLocker and got a lot of pushback from the security community. Last week, he published more research and explanation about the trade-offs. It’s worth reading. Microsoft told him they removed the Elephant Diffuser for performance reasons. And I agree with his ultimate conclusion:

Based on what I know about BitLocker, I think it’s perfectly fine for average Windows users to rely on, which is especially convenient considering it comes with many PCs. If it ever turns out that Microsoft is willing to include a backdoor in a major feature of Windows, then we have much bigger problems than the choice of disk encryption software anyway.

Whatever you choose, if trusting a proprietary operating system not to be malicious doesn’t fit your threat model, maybe it’s time to switch to Linux.

Micah also nicely explains how TrueCrypt is becoming antiquated, and not keeping up with Microsoft’s file system changes.

Lately, I am liking an obscure program called BestCrypt, by a Finnish company called Jetico. Micah quotes me:

Considering Schneier has been outspoken for decades about the importance of open source cryptography, I asked if he recommends that other people use BestCrypt, even though it’s proprietary. “I do recommend BestCrypt,” Schneier told me, “because I have met people at the company and I have a good feeling about them. Of course I don’t know for sure; this business is all about trust. But right now, given what I know, I trust them.”

I know it’s not a great argument. But, again, I’m trying to find the least bad option. And in the end, you either have to write your own software or trust someone else to write it for you.

But, yes, this should be an easier decision.

Posted on June 15, 2015 at 6:31 AMView Comments

Eighth Movie-Plot Threat Contest Winner

On April 1, I announced the Eighth Movie-Plot Threat Contest:

I want a movie-plot threat that shows the evils of encryption. (For those who don’t know, a movie-plot threat is a scary-threat story that would make a great movie, but is much too specific to build security policies around. Contest history here.) We’ve long heard about the evils of the Four Horsemen of the Internet Apocalypse—terrorists, drug dealers, kidnappers, and child pornographers. (Or maybe they’re terrorists, pedophiles, drug dealers, and money launderers; I can never remember.) Try to be more original than that. And nothing too science fictional; today’s technology or presumed technology only.

On May 14, I announced the five semifinalists. The votes are in, and the winner is TonyK:

November 6 2020, the morning of the presidential election. This will be the first election where votes can be cast from smart phones and laptops. A record turnout is expected.

There is much excitement as live results are being displayed all over the place. Twitter, television, apps and websites are all displaying the vote counts. It is a close race between the leading candidates until about 9 am when a third candidate starts to rapidly close the gap. He was an unknown independent that had suspected ties to multiple terrorist organizations. There was outrage when he got on to the ballot, but it had quickly died down when he put forth no campaign effort.

By 11 am the independent was predicted to win, and the software called it for him at 3:22 pm.

At 4 the CEO of the software maker was being interviewed on CNN. There were accusations of everything from bribery to bugs to hackers being responsible for the results. Demands were made for audits and recounts. Some were even asking for the data to be made publicly available. The CEO calmly explained that there could be no audit or recount. The system was encrypted end to end and all the votes were cryptographically anonymized.

The interviewer was stunned and sat there in silence. When he eventually spoke, he said “We just elected a terrorist as the President of the United States.”

For the record, Nick P was a close runner-up.

Congratulations, TonyK. Contact me by e-mail, and I’ll send you your fabulous prizes.

Previous contests.

EDITED TO ADD (6/14): Slashdot thread.

Posted on June 13, 2015 at 12:11 PMView Comments

UN Report on the Value of Encryption to Freedom Worldwide

The United Nation’s Office of the High Commissioner released a report on the value of encryption and anonymity to the world:

Summary: In the present report, submitted in accordance with Human Rights Council resolution 25/2, the Special Rapporteur addresses the use of encryption and anonymity in digital communications. Drawing from research on international and national norms and jurisprudence, and the input of States and civil society, the report concludes that encryption and anonymity enable individuals to exercise their rights to freedom of opinion and expression in the digital age and, as such, deserve strong protection.

Here’s the bottom line:

60. States should not restrict encryption and anonymity, which facilitate and often enable the rights to freedom of opinion and expression. Blanket prohibitions fail to be necessary and proportionate. States should avoid all measures that weaken the security that individuals may enjoy online, such as backdoors, weak encryption standards and key escrows. In addition, States should refrain from making the identification of users a condition for access to digital communications and online services and requiring SIM card registration for mobile users. Corporate actors should likewise consider their own policies that restrict encryption and anonymity (including through the use of pseudonyms). Court-ordered decryption, subject to domestic and international law, may only be permissible when it results from transparent and publicly accessible laws applied solely on a targeted, case-by-case basis to individuals (i.e., not to a mass of people) and subject to judicial warrant and the protection of due process rights of individuals.

One news report called this “wishy-washy when it came to government-mandated backdoors to undermine encryption,” but I don’t see that. Government mandated backdoors, key escrow, and weak encryption are all bad. Corporations should offer their users strong encryption and anonymity. Any systems that still leave corporations with the keys and/or the data—and there are going to be lots of them—should only give them up to the government in the face of an individual and lawful court order.

I think the principles are reasonable.

Posted on May 29, 2015 at 7:49 AMView Comments

The Logjam (and Another) Vulnerability against Diffie-Hellman Key Exchange

Logjam is a new attack against the Diffie-Hellman key-exchange protocol used in TLS. Basically:

The Logjam attack allows a man-in-the-middle attacker to downgrade vulnerable TLS connections to 512-bit export-grade cryptography. This allows the attacker to read and modify any data passed over the connection. The attack is reminiscent of the FREAK attack, but is due to a flaw in the TLS protocol rather than an implementation vulnerability, and attacks a Diffie-Hellman key exchange rather than an RSA key exchange. The attack affects any server that supports DHE_EXPORT ciphers, and affects all modern web browsers. 8.4% of the Top 1 Million domains were initially vulnerable.

Here’s the academic paper.

One of the problems with patching the vulnerability is that it breaks things:

On the plus side, the vulnerability has largely been patched thanks to consultation with tech companies like Google, and updates are available now or coming soon for Chrome, Firefox and other browsers. The bad news is that the fix rendered many sites unreachable, including the main website at the University of Michigan, which is home to many of the researchers that found the security hole.

This is a common problem with version downgrade attacks; patching them makes you incompatible with anyone who hasn’t patched. And it’s the vulnerability the media is focusing on.

Much more interesting is the other vulnerability that the researchers found:

Millions of HTTPS, SSH, and VPN servers all use the same prime numbers for Diffie-Hellman key exchange. Practitioners believed this was safe as long as new key exchange messages were generated for every connection. However, the first step in the number field sieve—the most efficient algorithm for breaking a Diffie-Hellman connection—is dependent only on this prime. After this first step, an attacker can quickly break individual connections.

The researchers believe the NSA has been using this attack:

We carried out this computation against the most common 512-bit prime used for TLS and demonstrate that the Logjam attack can be used to downgrade connections to 80% of TLS servers supporting DHE_EXPORT. We further estimate that an academic team can break a 768-bit prime and that a nation-state can break a 1024-bit prime. Breaking the single, most common 1024-bit prime used by web servers would allow passive eavesdropping on connections to 18% of the Top 1 Million HTTPS domains. A second prime would allow passive decryption of connections to 66% of VPN servers and 26% of SSH servers. A close reading of published NSA leaks shows that the agency’s attacks on VPNs are consistent with having achieved such a break.

Remember James Bamford’s 2012 comment about the NSA’s cryptanalytic capabilities:

According to another top official also involved with the program, the NSA made an enormous breakthrough several years ago in its ability to cryptanalyze, or break, unfathomably complex encryption systems employed by not only governments around the world but also many average computer users in the US. The upshot, according to this official: “Everybody’s a target; everybody with communication is a target.”

[…]

The breakthrough was enormous, says the former official, and soon afterward the agency pulled the shade down tight on the project, even within the intelligence community and Congress. “Only the chairman and vice chairman and the two staff directors of each intelligence committee were told about it,” he says. The reason? “They were thinking that this computing breakthrough was going to give them the ability to crack current public encryption.”

And remember Director of National Intelligence James Clapper’s introduction to the 2013 “Black Budget“:

Also, we are investing in groundbreaking cryptanalytic capabilities to defeat adversarial cryptography and exploit internet traffic.

It’s a reasonable guess that this is what both Bamford’s source and Clapper are talking about. It’s an attack that requires a lot of precomputation—just the sort of thing a national intelligence agency would go for.

But that requirement also speaks to its limitations. The NSA isn’t going to put this capability at collection points like Room 641A at AT&T’s San Francisco office: the precomputation table is too big, and the sensitivity of the capability is too high. More likely, an analyst identifies a target through some other means, and then looks for data by that target in databases like XKEYSCORE. Then he sends whatever ciphertext he finds to the Cryptanalysis and Exploitation Services (CES) group, which decrypts it if it can using this and other techniques.

Ross Anderson wrote about this earlier this month, almost certainly quoting Snowden:

As for crypto capabilities, a lot of stuff is decrypted automatically on ingest (e.g. using a “stolen cert”, presumably a private key obtained through hacking). Else the analyst sends the ciphertext to CES and they either decrypt it or say they can’t.

The analysts are instructed not to think about how this all works. This quote also applied to NSA employees:

Strict guidelines were laid down at the GCHQ complex in Cheltenham, Gloucestershire, on how to discuss projects relating to decryption. Analysts were instructed: “Do not ask about or speculate on sources or methods underpinning Bullrun.”

I remember the same instructions in documents I saw about the NSA’s CES.

Again, the NSA has put surveillance ahead of security. It never bothered to tell us that many of the “secure” encryption systems we were using were not secure. And we don’t know what other national intelligence agencies independently discovered and used this attack.

The good news is now that we know reusing prime numbers is a bad idea, we can stop doing it.

EDITED TO ADD: The DH precomputation easily lends itself to custom ASIC design, and is something that pipelines easily. Using BitCoin mining hardware as a rough comparison, this means a couple orders of magnitude speedup.

EDITED TO ADD (5/23): Good analysis of the cryptography.

EDITED TO ADD (5/24): Good explanation by Matthew Green.

Posted on May 21, 2015 at 6:30 AMView Comments

1 25 26 27 28 29 56

Sidebar photo of Bruce Schneier by Joe MacInnis.