Entries Tagged "NIST"

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NIST’s Post-Quantum Cryptography Standards

Quantum computing is a completely new paradigm for computers. A quantum computer uses quantum properties such as superposition, which allows a qubit (a quantum bit) to be neither 0 nor 1, but something much more complicated. In theory, such a computer can solve problems too complex for conventional computers.

Current quantum computers are still toy prototypes, and the engineering advances required to build a functionally useful quantum computer are somewhere between a few years away and impossible. Even so, we already know that that such a computer could potentially factor large numbers and compute discrete logs, and break the RSA and Diffie-Hellman public-key algorithms in all of the useful key sizes.

Cryptographers hate being rushed into things, which is why NIST began a competition to create a post-quantum cryptographic standard in 2016. The idea is to standardize on both a public-key encryption and digital signature algorithm that is resistant to quantum computing, well before anyone builds a useful quantum computer.

NIST is an old hand at this competitive process, having previously done this with symmetric algorithms (AES in 2001) and hash functions (SHA-3 in 2015). I participated in both of those competitions, and have likened them to demolition derbies. The idea is that participants put their algorithms into the ring, and then we all spend a few years beating on each other’s submissions. Then, with input from the cryptographic community, NIST crowns a winner. It’s a good process, mostly because NIST is both trusted and trustworthy.

In 2017, NIST received eighty-two post-quantum algorithm submissions from all over the world. Sixty-nine were considered complete enough to be Round 1 candidates. Twenty-six advanced to Round 2 in 2019, and seven (plus another eight alternates) were announced as Round 3 finalists in 2020. NIST was poised to make final algorithm selections in 2022, with a plan to have a draft standard available for public comment in 2023.

Cryptanalysis over the competition was brutal. Twenty-five of the Round 1 algorithms were attacked badly enough to remove them from the competition. Another eight were similarly attacked in Round 2. But here’s the real surprise: there were newly published cryptanalysis results against at least four of the Round 3 finalists just months ago—moments before NIST was to make its final decision.

One of the most popular algorithms, Rainbow, was found to be completely broken. Not that it could theoretically be broken with a quantum computer, but that it can be broken today—with an off-the-shelf laptop in just over two days. Three other finalists, Kyber, Saber, and Dilithium, were weakened with new techniques that will probably work against some of the other algorithms as well. (Fun fact: Those three algorithms were broken by the Center of Encryption and Information Security, part of the Israeli Defense Force. This represents the first time a national intelligence organization has published a cryptanalysis result in the open literature. And they had a lot of trouble publishing, as the authors wanted to remain anonymous.)

That was a close call, but it demonstrated that the process is working properly. Remember, this is a demolition derby. The goal is to surface these cryptanalytic results before standardization, which is exactly what happened. At this writing, NIST has chosen a single algorithm for general encryption and three digital-signature algorithms. It has not chosen a public-key encryption algorithm, and there are still four finalists. Check NIST’s webpage on the project for the latest information.

Ian Cassels, British mathematician and World War II cryptanalyst, once said that “cryptography is a mixture of mathematics and muddle, and without the muddle the mathematics can be used against you.” This mixture is particularly difficult to achieve with public-key algorithms, which rely on the mathematics for their security in a way that symmetric algorithms do not. We got lucky with RSA and related algorithms: their mathematics hinge on the problem of factoring, which turned out to be robustly difficult. Post-quantum algorithms rely on other mathematical disciplines and problems—code-based cryptography, hash-based cryptography, lattice-based cryptography, multivariate cryptography, and so on—whose mathematics are both more complicated and less well-understood. We’re seeing these breaks because those core mathematical problems aren’t nearly as well-studied as factoring is.

The moral is the need for cryptographic agility. It’s not enough to implement a single standard; it’s vital that our systems be able to easily swap in new algorithms when required. We’ve learned the hard way how algorithms can get so entrenched in systems that it can take many years to update them: in the transition from DES to AES, and the transition from MD4 and MD5 to SHA, SHA-1, and then SHA-3.

We need to do better. In the coming years we’ll be facing a double uncertainty. The first is quantum computing. When and if quantum computing becomes a practical reality, we will learn a lot about its strengths and limitations. It took a couple of decades to fully understand von Neumann computer architecture; expect the same learning curve with quantum computing. Our current understanding of quantum computing architecture will change, and that could easily result in new cryptanalytic techniques.

The second uncertainly is in the algorithms themselves. As the new cryptanalytic results demonstrate, we’re still learning a lot about how to turn hard mathematical problems into public-key cryptosystems. We have too much math and an inability to add more muddle, and that results in algorithms that are vulnerable to advances in mathematics. More cryptanalytic results are coming, and more algorithms are going to be broken.

We can’t stop the development of quantum computing. Maybe the engineering challenges will turn out to be impossible, but it’s not the way to bet. In the face of all that uncertainty, agility is the only way to maintain security.

This essay originally appeared in IEEE Security & Privacy.

EDITED TO ADD: One of the four public-key encryption algorithms selected for further research, SIKE, was just broken.

Posted on August 8, 2022 at 6:20 AMView Comments

SIKE Broken

SIKE is one of the new algorithms that NIST recently added to the post-quantum cryptography competition.

It was just broken, really badly.

We present an efficient key recovery attack on the Supersingular Isogeny Diffie­-Hellman protocol (SIDH), based on a “glue-and-split” theorem due to Kani. Our attack exploits the existence of a small non-scalar endomorphism on the starting curve, and it also relies on the auxiliary torsion point information that Alice and Bob share during the protocol. Our Magma implementation breaks the instantiation SIKEp434, which aims at security level 1 of the Post-Quantum Cryptography standardization process currently ran by NIST, in about one hour on a single core.

News article.

Posted on August 4, 2022 at 6:56 AMView Comments

NIST Announces First Four Quantum-Resistant Cryptographic Algorithms

NIST’s post-quantum computing cryptography standard process is entering its final phases. It announced the first four algorithms:

For general encryption, used when we access secure websites, NIST has selected the CRYSTALS-Kyber algorithm. Among its advantages are comparatively small encryption keys that two parties can exchange easily, as well as its speed of operation.

For digital signatures, often used when we need to verify identities during a digital transaction or to sign a document remotely, NIST has selected the three algorithms CRYSTALS-Dilithium, FALCON and SPHINCS+ (read as “Sphincs plus”). Reviewers noted the high efficiency of the first two, and NIST recommends CRYSTALS-Dilithium as the primary algorithm, with FALCON for applications that need smaller signatures than Dilithium can provide. The third, SPHINCS+, is somewhat larger and slower than the other two, but it is valuable as a backup for one chief reason: It is based on a different math approach than all three of NIST’s other selections.

NIST has not chosen a public-key encryption standard. The remaining candidates are BIKE, Classic McEliece, HQC, and SIKE.

I have a lot to say on this process, and have written an essay for IEEE Security & Privacy about it. It will be published in a month or so.

Posted on July 6, 2022 at 11:49 AMView Comments

On the Subversion of NIST by the NSA

Nadiya Kostyuk and Susan Landau wrote an interesting paper: “Dueling Over DUAL_EC_DRBG: The Consequences of Corrupting a Cryptographic Standardization Process”:

Abstract: In recent decades, the U.S. National Institute of Standards and Technology (NIST), which develops cryptographic standards for non-national security agencies of the U.S. government, has emerged as the de facto international source for cryptographic standards. But in 2013, Edward Snowden disclosed that the National Security Agency had subverted the integrity of a NIST cryptographic standard­the Dual_EC_DRBG­enabling easy decryption of supposedly secured communications. This discovery reinforced the desire of some public and private entities to develop their own cryptographic standards instead of relying on a U.S. government process. Yet, a decade later, no credible alternative to NIST has emerged. NIST remains the only viable candidate for effectively developing internationally trusted cryptography standards.

Cryptographic algorithms are essential to security yet are hard to understand and evaluate. These technologies provide crucial security for communications protocols. Yet the protocols transit international borders; they are used by countries that do not necessarily trust each other. In particular, these nations do not necessarily trust the developer of the cryptographic standard.

Seeking to understand how NIST, a U.S. government agency, was able to remain a purveyor of cryptographic algorithms despite the Dual_EC_DRBG problem, we examine the Dual_EC_DRBG situation, NIST’s response, and why a non-regulatory, non-national security U.S. agency remains a successful international supplier of strong cryptographic solutions.

Posted on June 23, 2022 at 6:05 AMView Comments

The NSA Says that There are No Known Flaws in NIST’s Quantum-Resistant Algorithms

Rob Joyce, the director of cybersecurity at the NSA, said so in an interview:

The NSA already has classified quantum-resistant algorithms of its own that it developed over many years, said Joyce. But it didn’t enter any of its own in the contest. The agency’s mathematicians, however, worked with NIST to support the process, trying to crack the algorithms in order to test their merit.

“Those candidate algorithms that NIST is running the competitions on all appear strong, secure, and what we need for quantum resistance,” Joyce said. “We’ve worked against all of them to make sure they are solid.”

The purpose of the open, public international scrutiny of the separate NIST algorithms is “to build trust and confidence,” he said.

I believe him. This is what the NSA did with NIST’s candidate algorithms for AES and then for SHA-3. NIST’s Post-Quantum Cryptography Standardization Process looks good.

I still worry about the long-term security of the submissions, though. In 2018, in an essay titled “Cryptography After the Aliens Land,” I wrote:

…there is always the possibility that those algorithms will fall to aliens with better quantum techniques. I am less worried about symmetric cryptography, where Grover’s algorithm is basically an upper limit on quantum improvements, than I am about public-key algorithms based on number theory, which feel more fragile. It’s possible that quantum computers will someday break all of them, even those that today are quantum resistant.

It took us a couple of decades to fully understand von Neumann computer architecture. I’m sure it will take years of working with a functional quantum computer to fully understand the limits of that architecture. And some things that we think of as computationally hard today will turn out not to be.

EDITED TO ADD (6/14): Since I wrote this, flaws were found in at least four candidates.

Posted on May 16, 2022 at 6:34 AMView Comments

Update on NIST's Post-Quantum Cryptography Program

NIST has posted an update on their post-quantum cryptography program:

After spending more than three years examining new approaches to encryption and data protection that could defeat an assault from a quantum computer, the National Institute of Standards and Technology (NIST) has winnowed the 69 submissions it initially received down to a final group of 15. NIST has now begun the third round of public review. This “selection round” will help the agency decide on the small subset of these algorithms that will form the core of the first post-quantum cryptography standard.

[…]

For this third round, the organizers have taken the novel step of dividing the remaining candidate algorithms into two groups they call tracks. The first track contains the seven algorithms that appear to have the most promise.

“We’re calling these seven the finalists,” Moody said. “For the most part, they’re general-purpose algorithms that we think could find wide application and be ready to go after the third round.”

The eight alternate algorithms in the second track are those that either might need more time to mature or are tailored to more specific applications. The review process will continue after the third round ends, and eventually some of these second-track candidates could become part of the standard. Because all of the candidates still in play are essentially survivors from the initial group of submissions from 2016, there will also be future consideration of more recently developed ideas, Moody said.

“The likely outcome is that at the end of this third round, we will standardize one or two algorithms for encryption and key establishment, and one or two others for digital signatures,” he said. “But by the time we are finished, the review process will have been going on for five or six years, and someone may have had a good idea in the interim. So we’ll find a way to look at newer approaches too.”

Details are here. This is all excellent work, and exemplifies NIST at its best. The quantum-resistant algorithms will be standardized far in advance of any practical quantum computer, which is how we all want this sort of thing to go.

Posted on July 24, 2020 at 6:36 AMView Comments

Calculating the Benefits of the Advanced Encryption Standard

NIST has completed a study—it was published last year, but I just saw it recently—calculating the costs and benefits of the Advanced Encryption Standard.

From the conclusion:

The result of performing that operation on the series of cumulated benefits extrapolated for the 169 survey respondents finds that present value of benefits from today’s perspective is approximately $8.9 billion. On the other hand, the present value of NIST’s costs from today’s perspective is $127 million. Thus, the NPV from today’s perspective is $8,772,000,000; the B/C ratio is therefore 70.2/1; and a measure (explained in detail in Section 6.1) of the IRR for the alternative investment perspective is 31%; all are indicators of a substantial economic impact.

Extending the approach of looking back from 2017 to the larger national economy required the selection of economic sectors best represented by the 169 survey respondents. The economic sectors represented by ten or more survey respondents include the following: agriculture; construction; manufacturing; retail trade; transportation and warehousing; information; real estate rental and leasing; professional, scientific, and technical services; management services; waste management; educational services; and arts and entertainment. Looking at the present value of benefits and costs from 2017’s perspective for these economic sectors finds that the present value of benefits rises to approximately $251 billion while the present value of NIST’s costs from today’s perspective remains the same at $127 million. Therefore, the NPV of the benefits of the AES program to the national economy from today’s perspective is $250,473,200,000; the B/C ratio is roughly 1976/1; and the appropriate, alternative (explained in Section 6.1) IRR and investing proceeds at the social rate of return is 53.6%.

The report contains lots of facts and figures relevant to crypto policy debates, including the chaotic nature of crypto markets in the mid-1990s, the number of approved devices and libraries of various kinds since then, other standards that invoke AES, and so on.

There’s a lot to argue with about the methodology and the assumptions. I don’t know if I buy that the benefits of AES to the economy are in the billions of dollars, mostly because we in the cryptographic community would have come up with alternative algorithms to triple-DES that would have been accepted and used. Still, I like seeing this kind of analysis about security infrastructure. Security is an enabling technology; it doesn’t do anything by itself, but instead allows all sorts of things to be done. And I certainly agree that the benefits of a standardized encryption algorithm that we all trust and use outweigh the cost by orders of magnitude.

And this isn’t the first time NIST has conducted economic impact studies. It released a study of the economic impact of DES in 2001.

Posted on October 22, 2019 at 5:56 AMView Comments

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Sidebar photo of Bruce Schneier by Joe MacInnis.