Entries Tagged "cryptography"

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Improving Shor’s Algorithm

We don’t have a useful quantum computer yet, but we do have quantum algorithms. Shor’s algorithm has the potential to factor large numbers faster than otherwise possible, which—if the run times are actually feasible—could break both the RSA and Diffie-Hellman public-key algorithms.

Now, computer scientist Oded Regev has a significant speed-up to Shor’s algorithm, at the cost of more storage.

Details are in this article. Here’s the result:

The improvement was profound. The number of elementary logical steps in the quantum part of Regev’s algorithm is proportional to n1.5 when factoring an n-bit number, rather than n2 as in Shor’s algorithm. The algorithm repeats that quantum part a few dozen times and combines the results to map out a high-dimensional lattice, from which it can deduce the period and factor the number. So the algorithm as a whole may not run faster, but speeding up the quantum part by reducing the number of required steps could make it easier to put it into practice.

Of course, the time it takes to run a quantum algorithm is just one of several considerations. Equally important is the number of qubits required, which is analogous to the memory required to store intermediate values during an ordinary classical computation. The number of qubits that Shor’s algorithm requires to factor an n-bit number is proportional to n, while Regev’s algorithm in its original form requires a number of qubits proportional to n1.5—a big difference for 2,048-bit numbers.

Again, this is all still theoretical. But now it’s theoretically faster.

Oded Regev’s paper.

This is me from 2018 on the potential for quantum cryptanalysis. I still believe now what I wrote then.

Posted on January 5, 2024 at 7:07 AM • View Comments

New SSH Vulnerability

This is interesting:

For the first time, researchers have demonstrated that a large portion of cryptographic keys used to protect data in computer-to-server SSH traffic are vulnerable to complete compromise when naturally occurring computational errors occur while the connection is being established.

[…]

The vulnerability occurs when there are errors during the signature generation that takes place when a client and server are establishing a connection. It affects only keys using the RSA cryptographic algorithm, which the researchers found in roughly a third of the SSH signatures they examined. That translates to roughly 1 billion signatures out of the 3.2 billion signatures examined. Of the roughly 1 billion RSA signatures, about one in a million exposed the private key of the host.

Research paper:

Passive SSH Key Compromise via Lattices

Abstract: We demonstrate that a passive network attacker can opportunistically obtain private RSA host keys from an SSH server that experiences a naturally arising fault during signature computation. In prior work, this was not believed to be possible for the SSH protocol because the signature included information like the shared Diffie-Hellman secret that would not be available to a passive network observer. We show that for the signature parameters commonly in use for SSH, there is an efficient lattice attack to recover the private key in case of a signature fault. We provide a security analysis of the SSH, IKEv1, and IKEv2 protocols in this scenario, and use our attack to discover hundreds of compromised keys in the wild from several independently vulnerable implementations.

Posted on November 15, 2023 at 12:51 PM • View Comments

Bounty to Recover NIST’s Elliptic Curve Seeds

This is a fun challenge:

The NIST elliptic curves that power much of modern cryptography were generated in the late ’90s by hashing seeds provided by the NSA. How were the seeds generated? Rumor has it that they are in turn hashes of English sentences, but the person who picked them, Dr. Jerry Solinas, passed away in early 2023 leaving behind a cryptographic mystery, some conspiracy theories, and an historical password cracking challenge.

So there’s a $12K prize to recover the hash seeds.

Some backstory:

Some of the backstory here (it’s the funniest fucking backstory ever): it’s lately been circulating—though I think this may have been somewhat common knowledge among practitioners, though definitely not to me—that the “random” seeds for the NIST P-curves, generated in the 1990s by Jerry Solinas at NSA, were simply SHA1 hashes of some variation of the string “Give Jerry a raise”.

At the time, the “pass a string through SHA1” thing was meant to increase confidence in the curve seeds; the idea was that SHA1 would destroy any possible structure in the seed, so NSA couldn’t have selected a deliberately weak seed. Of course, NIST/NSA then set about destroying its reputation in the 2000’s, and this explanation wasn’t nearly enough to quell conspiracy theories.

But when Jerry Solinas went back to reconstruct the seeds, so NIST could demonstrate that the seeds really were benign, he found that he’d forgotten the string he used!

If you’re a true conspiracist, you’re certain nobody is going to find a string that generates any of these seeds. On the flip side, if anyone does find them, that’ll be a pretty devastating blow to the theory that the NIST P-curves were maliciously generated—even for people totally unfamiliar with basic curve math.

Note that this is not the constants used in the Dual_EC_PRNG random-number generator that the NSA backdoored. This is something different.

Posted on October 12, 2023 at 7:09 AM • View Comments

New Revelations from the Snowden Documents

Jake Appelbaum’s PhD thesis contains several new revelations from the classified NSA documents provided to journalists by Edward Snowden. Nothing major, but a few more tidbits.

Kind of amazing that that all happened ten years ago. At this point, those documents are more historical than anything else.

And it’s unclear who has those archives anymore. According to Appelbaum, The Intercept destroyed their copy.

I recently published an essay about my experiences ten years ago.

Posted on September 21, 2023 at 7:03 AM • View Comments

You Can’t Rush Post-Quantum-Computing Cryptography Standards

I just read an article complaining that NIST is taking too long in finalizing its post-quantum-computing cryptography standards.

This process has been going on since 2016, and since that time there has been a huge increase in quantum technology and an equally large increase in quantum understanding and interest. Yet seven years later, we have only four algorithms, although last week NIST announced that a number of other candidates are under consideration, a process that is expected to take “several years.

The delay in developing quantum-resistant algorithms is especially troubling given the time it will take to get those products to market. It generally takes four to six years with a new standard for a vendor to develop an ASIC to implement the standard, and it then takes time for the vendor to get the product validated, which seems to be taking a troubling amount of time.

Yes, the process will take several years, and you really don’t want to rush it. I wrote this last year:

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.

[…]

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.

As to the long time it takes to get new encryption products to market, work on shortening it:

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.

Whatever NIST comes up with, expect that it will get broken sooner than we all want. It’s the nature of these trap-door functions we’re using for public-key cryptography.

Posted on August 8, 2023 at 7:13 AM • View Comments

Backdoor in TETRA Police Radios

Seems that there is a deliberate backdoor in the twenty-year-old TErrestrial Trunked RAdio (TETRA) standard used by police forces around the world.

The European Telecommunications Standards Institute (ETSI), an organization that standardizes technologies across the industry, first created TETRA in 1995. Since then, TETRA has been used in products, including radios, sold by Motorola, Airbus, and more. Crucially, TETRA is not open-source. Instead, it relies on what the researchers describe in their presentation slides as “secret, proprietary cryptography,” meaning it is typically difficult for outside experts to verify how secure the standard really is.

The researchers said they worked around this limitation by purchasing a TETRA-powered radio from eBay. In order to then access the cryptographic component of the radio itself, Wetzels said the team found a vulnerability in an interface of the radio.

[…]

Most interestingly is the researchers’ findings of what they describe as the backdoor in TEA1. Ordinarily, radios using TEA1 used a key of 80-bits. But Wetzels said the team found a “secret reduction step” which dramatically lowers the amount of entropy the initial key offered. An attacker who followed this step would then be able to decrypt intercepted traffic with consumer-level hardware and a cheap software defined radio dongle.

Looks like the encryption algorithm was intentionally weakened by intelligence agencies to facilitate easy eavesdropping.

Specifically on the researchers’ claims of a backdoor in TEA1, Boyer added “At this time, we would like to point out that the research findings do not relate to any backdoors. The TETRA security standards have been specified together with national security agencies and are designed for and subject to export control regulations which determine the strength of the encryption.”

And I would like to point out that that’s the very definition of a backdoor.

Why aren’t we done with secret, proprietary cryptography? It’s just not a good idea.

Details of the security analysis. Another news article.

Posted on July 26, 2023 at 7:05 AM • View Comments

Power LED Side-Channel Attack

This is a clever new side-channel attack:

The first attack uses an Internet-connected surveillance camera to take a high-speed video of the power LED on a smart card reader­—or of an attached peripheral device—­during cryptographic operations. This technique allowed the researchers to pull a 256-bit ECDSA key off the same government-approved smart card used in Minerva. The other allowed the researchers to recover the private SIKE key of a Samsung Galaxy S8 phone by training the camera of an iPhone 13 on the power LED of a USB speaker connected to the handset, in a similar way to how Hertzbleed pulled SIKE keys off Intel and AMD CPUs.

There are lots of limitations:

When the camera is 60 feet away, the room lights must be turned off, but they can be turned on if the surveillance camera is at a distance of about 6 feet. (An attacker can also use an iPhone to record the smart card reader power LED.) The video must be captured for 65 minutes, during which the reader must constantly perform the operation.

[…]

The attack assumes there is an existing side channel that leaks power consumption, timing, or other physical manifestations of the device as it performs a cryptographic operation.

So don’t expect this attack to be recovering keys in the real world anytime soon. But, still, really nice work.

More details from the researchers.

Posted on June 19, 2023 at 6:52 AM • View Comments

AI-Generated Steganography

New research suggests that AIs can produce perfectly secure steganographic images:

Abstract: Steganography is the practice of encoding secret information into innocuous content in such a manner that an adversarial third party would not realize that there is hidden meaning. While this problem has classically been studied in security literature, recent advances in generative models have led to a shared interest among security and machine learning researchers in developing scalable steganography techniques. In this work, we show that a steganography procedure is perfectly secure under Cachin (1998)’s information theoretic-model of steganography if and only if it is induced by a coupling. Furthermore, we show that, among perfectly secure procedures, a procedure is maximally efficient if and only if it is induced by a minimum entropy coupling. These insights yield what are, to the best of our knowledge, the first steganography algorithms to achieve perfect security guarantees with non-trivial efficiency; additionally, these algorithms are highly scalable. To provide empirical validation, we compare a minimum entropy coupling-based approach to three modern baselines—arithmetic coding, Meteor, and adaptive dynamic grouping—using GPT-2, WaveRNN, and Image Transformer as communication channels. We find that the minimum entropy coupling-based approach achieves superior encoding efficiency, despite its stronger security constraints. In aggregate, these results suggest that it may be natural to view information-theoretic steganography through the lens of minimum entropy coupling.

News article.

EDITED TO ADD (6/13): Comments.

Posted on June 12, 2023 at 7:18 AM • View Comments

Side-Channel Attack against CRYSTALS-Kyber

CRYSTALS-Kyber is one of the public-key algorithms currently recommended by NIST as part of its post-quantum cryptography standardization process.

Researchers have just published a side-channel attack—using power consumption—against an implementation of the algorithm that was supposed to be resistant against that sort of attack.

The algorithm is not “broken” or “cracked”—despite headlines to the contrary—this is just a side-channel attack. What makes this work really interesting is that the researchers used a machine-learning model to train the system to exploit the side channel.

Posted on February 28, 2023 at 7:19 AM • View Comments

Mary Queen of Scots Letters Decrypted

This is a neat piece of historical research.

The team of computer scientist George Lasry, pianist Norbert Biermann and astrophysicist Satoshi Tomokiyo—all keen cryptographers—initially thought the batch of encoded documents related to Italy, because that was how they were filed at the Bibliothèque Nationale de France.

However, they quickly realised the letters were in French. Many verb and adjectival forms being feminine, regular mention of captivity, and recurring names—such as Walsingham—all put them on the trail of Mary. Sir Francis Walsingham was Queen Elizabeth’s spymaster.

The code was a simple replacement system in which symbols stand either for letters, or for common words and names. But it would still have taken centuries to crunch all the possibilities, so the team used an algorithm that homed in on likely solutions.

Academic paper.

EDITED TO ADD (2/13): More news.

Posted on February 9, 2023 at 7:15 AM • View Comments

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Sidebar photo of Bruce Schneier by Joe MacInnis.