Tag Archives: cryptanalysis

No, RSA Is Not Broken

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2021/03/no-rsa-is-not-broken.html

I have been seeing this paper by cryptographer Peter Schnorr making the rounds: “Fast Factoring Integers by SVP Algorithms.” It describes a new factoring method, and its abstract ends with the provocative sentence: “This destroys the RSA cryptosystem.”

It does not. At best, it’s an improvement in factoring — and I’m not sure it’s even that. The paper is a preprint: it hasn’t been peer reviewed. Be careful taking its claims at face value.

Some discussion here.

I’ll append more analysis links to this post when I find them.

Military Cryptanalytics, Part III

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2021/01/military-cryptanalytics-part-iii.html

The NSA has just declassified and released a redacted version of Military Cryptanalytics, Part III, by Lambros D. Callimahos, October 1977.

Parts I and II, by Lambros D. Callimahos and William F. Friedman, were released decades ago — I believe repeatedly, in increasingly unredacted form — and published by the late Wayne Griswold Barker’s Agean Park Press. I own them in hardcover.

Like Parts I and II, Part III is primarily concerned with pre-computer ciphers. At this point, the document only has historical interest. If there is any lesson for today, it’s that modern cryptanalysis is possible primarily because people make mistakes

The monograph took a while to become public. The cover page says that the initial FOIA request was made in July 2012: eight and a half years ago.

And there’s more books to come. Page 1 starts off:

This text constitutes the third of six basic texts on the science of cryptanalytics. The first two texts together have covered most of the necessary fundamentals of cryptanalytics; this and the remaining three texts will be devoted to more specialized and more advanced aspects of the science.

Presumably, volumes IV, V, and VI are still hidden inside the classified libraries of the NSA.

And from page ii:

Chapters IV-XI are revisions of seven of my monographs in the NSA Technical Literature Series, viz: Monograph No. 19, “The Cryptanalysis of Ciphertext and Plaintext Autokey Systems”; Monograph No. 20, “The Analysis of Systems Employing Long or Continuous Keys”; Monograph No. 21, “The Analysis of Cylindrical Cipher Devices and Strip Cipher Systems”; Monograph No. 22, “The Analysis of Systems Employing Geared Disk Cryptomechanisms”; Monograph No.23, “Fundamentals of Key Analysis”; Monograph No. 15, “An Introduction to Teleprinter Key Analysis”; and Monograph No. 18, “Ars Conjectandi: The Fundamentals of Cryptodiagnosis.”

This points to a whole series of still-classified monographs whose titles we do not even know.

EDITED TO ADD: I have been informed by a reliable source that Parts 4 through 6 were never completed. There may be fragments and notes, but no finished works.

Cellebrite Can Break Signal

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2020/12/cellebrite-can-break-signal.html

Cellebrite announced that it can break Signal. (Note that the company has heavily edited its blog post, but the original — with lots of technical details — was saved by the Wayback Machine.)

News article. Slashdot post.

The whole story is puzzling. Cellebrite’s details will make it easier for the Signal developers to patch the vulnerability. So either Cellebrite believes it is so good that it can break whatever Signal does, or the original blog post was a mistake.

EDITED TO ADD (12/22): Signal’s Moxie Marlinspike takes serious issue with Cellebrite’s announcement. I have urged him to write it up, and will link to it when he does.

EDITED TO ADD (12/23): I need to apologize for this post. I finally got the chance to read all of this more carefully, and it seems that all Cellebrite is doing is reading the texts off of a phone they can already access. To this has nothing to do with Signal at all. So: never mind. False alarm. Apologies, again.

Zodiac Killer Cipher Solved

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2020/12/zodiac-killer-cipher-solved.html

The SF Chronicle is reporting (more details here), and the FBI is confirming, that a Melbourne mathematician and team has decrypted the 1969 message sent by the Zodiac Killer to the newspaper.

There’s no paper yet, but there are a bunch of details in the news articles.

Here’s an interview with one of the researchers:

Cryptologist David Oranchak, who has been trying to crack the notorious “340 cipher” (it contains 340 characters) for more than a decade, made a crucial breakthrough earlier this year when applied mathematician Sam Blake came up with about 650,000 different possible ways in which the code could be read. From there, using code-breaking software designed by Jarl Van Eycke, the team’s third member, they came up with a small number of valuable clues that helped them piece together a message in the cipher

Denmark, Sweden, Germany, the Netherlands and France SIGINT Alliance

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2020/05/denmark_sweden_.html

This paper describes a SIGINT and code-breaking alliance between Denmark, Sweden, Germany, the Netherlands and France called Maximator:

Abstract: This article is first to report on the secret European five-partner sigint alliance Maximator that started in the late 1970s. It discloses the name Maximator and provides documentary evidence. The five members of this European alliance are Denmark, Sweden, Germany, the Netherlands, and France. The cooperation involves both signals analysis and crypto analysis. The Maximator alliance has remained secret for almost fifty years, in contrast to its Anglo-Saxon Five-Eyes counterpart. The existence of this European sigint alliance gives a novel perspective on western sigint collaborations in the late twentieth century. The article explains and illustrates, with relatively much attention for the cryptographic details, how the five Maximator participants strengthened their effectiveness via the information about rigged cryptographic devices that its German partner provided, via the joint U.S.-German ownership and control of the Swiss producer Crypto AG of cryptographic devices.

Another Story of Bad 1970s Encryption

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2020/04/another_story_o.html

This one is from the Netherlands. It seems to be clever cryptanalysis rather than a backdoor.

The Dutch intelligence service has been able to read encrypted communications from dozens of countries since the late 1970s thanks to a microchip, according to research by de Volkskrant on Thursday. The Netherlands could eavesdrop on confidential communication from countries such as Iran, Egypt and Saudi Arabia.

Philips, together with Siemens, built an encryption machine in the late 1970s. The device, the Aroflex, was used for secret communication between NATO allies. In addition, the companies also wanted to market the T1000CA, a commercial variant of the Aroflex with less strong cryptography.

The Volkskrant investigation shows that the Ministry of Foreign Affairs and the Marine Intelligence Service (MARID) cracked the cryptography of this device before it was launched. Philips helped the ministry and the intelligence service.

Normally it would take at least a month and a half to crack the T1000CA encryption. “Too long to get useful information from intercepted communication,” the newspaper writes. But MARID employees, together with Philips, succeeded in accelerating this 2.500 times by developing a special microchip.

The T1000CA was then sold to numerous non-NATO countries, including the Middle East and Asia. These countries could then be overheard by the Dutch intelligence services for years.

The 1970s was a decade of really bad commercial cryptography. DES, in 1975, was an improvement with its 56-bit key. I’m sure there are lots of these stories.

Here’s more about the Aroflex. And here’s what I think is the original Dutch story.

RSA-240 Factored

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2019/12/rsa-240_factore.html

This just in:

We are pleased to announce the factorization of RSA-240, from RSA’s challenge list, and the computation of a discrete logarithm of the same size (795 bits):

RSA-240 = 12462036678171878406583504460810659043482037465167880575481878888328 966680118821085503603957027250874750986476843845862105486553797025393057189121 768431828636284694840530161441643046806687569941524699318570418303051254959437 1372159029236099 = 509435952285839914555051023580843714132648382024111473186660296521821206469746 700620316443478873837606252372049619334517 * 244624208838318150567813139024002896653802092578931401452041221336558477095178 155258218897735030590669041302045908071447


The previous records were RSA-768 (768 bits) in December 2009 [2], and a 768-bit prime discrete logarithm in June 2016 [3].

It is the first time that two records for integer factorization and discrete logarithm are broken together, moreover with the same hardware and software.

Both computations were performed with the Number Field Sieve algorithm, using the open-source CADO-NFS software [4].

The sum of the computation time for both records is roughly 4000 core-years, using Intel Xeon Gold 6130 CPUs as a reference (2.1GHz). A rough breakdown of the time spent in the main computation steps is as follows.

RSA-240 sieving: 800 physical core-years
RSA-240 matrix: 100 physical core-years
DLP-240 sieving: 2400 physical core-years
DLP-240 matrix: 700 physical core-years

The computation times above are well below the time that was spent with the previous 768-bit records. To measure how much of this can be attributed to Moore’s law, we ran our software on machines that are identical to those cited in the 768-bit DLP computation [3], and reach the conclusion that sieving for our new record size on these old machines would have taken 25% less time than the reported sieving time of the 768-bit DLP computation.

EDITED TO ADD (12/4): News article. Dan Goodin points out that the speed improvements were more due to improvements in the algorithms than from Moore’s Law.

The NSA Warns of TLS Inspection

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2019/11/the_nsa_warns_o.html

The NSA has released a security advisory warning of the dangers of TLS inspection:

Transport Layer Security Inspection (TLSI), also known as TLS break and inspect, is a security process that allows enterprises to decrypt traffic, inspect the decrypted content for threats, and then re-encrypt the traffic before it enters or leaves the network. Introducing this capability into an enterprise enhances visibility within boundary security products, but introduces new risks. These risks, while not inconsequential, do have mitigations.


The primary risk involved with TLSI’s embedded CA is the potential abuse of the CA to issue unauthorized certificates trusted by the TLS clients. Abuse of a trusted CA can allow an adversary to sign malicious code to bypass host IDS/IPSs or to deploy malicious services that impersonate legitimate enterprise services to the hosts.


A further risk of introducing TLSI is that an adversary can focus their exploitation efforts on a single device where potential traffic of interest is decrypted, rather than try to exploit each location where the data is stored.Setting a policy to enforce that traffic is decrypted and inspected only as authorized, and ensuring that decrypted traffic is contained in an out-of-band, isolated segment of the network prevents unauthorized access to the decrypted traffic.


To minimize the risks described above, breaking and inspecting TLS traffic should only be conducted once within the enterprise network. Redundant TLSI, wherein a client-server traffic flow is decrypted, inspected, and re-encrypted by one forward proxy and is then forwarded to a second forward proxy for more of the same,should not be performed.Inspecting multiple times can greatly complicate diagnosing network issues with TLS traffic. Also, multi-inspection further obscures certificates when trying to ascertain whether a server should be trusted. In this case, the “outermost” proxy makes the decisions on what server certificates or CAs should be trusted and is the only location where certificate pinning can be performed.Finally, a single TLSI implementation is sufficient for detecting encrypted traffic threats; additional TLSI will have access to the same traffic. If the first TLSI implementation detected a threat, killed the session, and dropped the traffic, then additional TLSI implementations would be rendered useless since they would not even receive the dropped traffic for further inspection. Redundant TLSI increases the risk surface, provides additional opportunities for adversaries to gain unauthorized access to decrypted traffic, and offers no additional benefits.

Nothing surprising or novel. No operational information about who might be implementing these attacks. No classified information revealed.

News article.

Factoring 2048-bit Numbers Using 20 Million Qubits

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2019/10/factoring_2048-.html

This theoretical paper shows how to factor 2048-bit RSA moduli with a 20-million qubit quantum computer in eight hours. It’s interesting work, but I don’t want overstate the risk.

We know from Shor’s Algorithm that both factoring and discrete logs are easy to solve on a large, working quantum computer. Both of those are currently beyond our technological abilities. We barely have quantum computers with 50 to 100 qubits. Extending this requires advances not only in the number of qubits we can work with, but in making the system stable enough to read any answers. You’ll hear this called “error rate” or “coherence” — this paper talks about “noise.”

Advances are hard. At this point, we don’t know if they’re “send a man to the moon” hard or “faster-than-light travel” hard. If I were guessing, I would say they’re the former, but still harder than we can accomplish with our current understanding of physics and technology.

I write about all this generally, and in detail, here. (Short summary: Our work on quantum-resistant algorithms is outpacing our work on quantum computers, so we’ll be fine in the short run. But future theoretical work on quantum computing could easily change what “quantum resistant” means, so it’s possible that public-key cryptography will simply not be possible in the long run. That’s not terrible, though; we have a lot of good scalable secret-key systems that do much the same things.)

More Cryptanalysis of Solitaire

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2019/10/more_cryptanaly.html

In 1999, I invented the Solitaire encryption algorithm, designed to manually encrypt data using a deck of cards. It was written into the plot of Neal Stephenson’s novel Cryptonomicon, and I even wrote an afterward to the book describing the cipher.

I don’t talk about it much, mostly because I made a dumb mistake that resulted in the algorithm not being reversible. Still, for the short message lengths you’re likely to use a manual cipher for, it’s still secure and will likely remain secure.

Here’s some new cryptanalysis:

Abstract: The Solitaire cipher was designed by Bruce Schneier as a plot point in the novel Cryptonomicon by Neal Stephenson. The cipher is intended to fit the archetype of a modern stream cipher whilst being implementable by hand using a standard deck of cards with two jokers. We find a model for repetitions in the keystream in the stream cipher Solitaire that accounts for the large majority of the repetition bias. Other phenomena merit further investigation. We have proposed modifications to the cipher that would reduce the repetition bias, but at the cost of increasing the complexity of the cipher (probably beyond the goal of allowing manual implementation). We have argued that the state update function is unlikely to lead to cycles significantly shorter than those of a random bijection.

Crown Sterling Claims to Factor RSA Keylengths First Factored Twenty Years Ago

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2019/09/crown_sterling_.html

Earlier this month, I made fun of a company called Crown Sterling, for…for…for being a company that deserves being made fun of.

This morning, the company announced that they “decrypted two 256-bit asymmetric public keys in approximately 50 seconds from a standard laptop computer.” Really. They did. This keylength is so small it has never been considered secure. It was too small to be part of the RSA Factoring Challenge when it was introduced in 1991. In 1977, when Ron Rivest, Adi Shamir, and Len Adelman first described RSA, they included a challenge with a 426-bit key. (It was factored in 1994.)

The press release goes on: “Crown Sterling also announced the consistent decryption of 512-bit asymmetric public key in as little as five hours also using standard computing.” They didn’t demonstrate it, but if they’re right they’ve matched a factoring record set in 1999. Five hours is significantly less than the 5.2 months it took in 1999, but slower than would be expected if Crown Sterling just used the 1999 techniques with modern CPUs and networks.

Is anyone taking this company seriously anymore? I honestly wouldn’t be surprised if this was a hoax press release. It’s not currently on the company’s website. (And, if it is a hoax, I apologize to Crown Sterling. I’ll post a retraction as soon as I hear from you.)

EDITED TO ADD: First, the press release is real. And second, I forgot to include the quote from CEO Robert Grant: “Today’s decryptions demonstrate the vulnerabilities associated with the current encryption paradigm. We have clearly demonstrated the problem which also extends to larger keys.”

People, this isn’t hard. Find an RSA Factoring Challenge number that hasn’t been factored yet and factor it. Once you do, the entire world will take you seriously. Until you do, no one will. And, bonus, you won’t have to reveal your super-secret world-destabilizing cryptanalytic techniques.

EDITED TO ADD (9/21): Others are laughing at this, too.

EDITED TO ADD (9/24): More commentary.

Cryptanalysis of SIMON-32/64

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2019/05/cryptanalysis_o_4.html

A weird paper was posted on the Cryptology ePrint Archive (working link is via the Wayback Machine), claiming an attack against the NSA-designed cipher SIMON. You can read some commentary about it here. Basically, the authors claimed an attack so devastating that they would only publish a zero-knowledge proof of their attack. Which they didn’t. Nor did they publish anything else of interest, near as I can tell.

The paper has since been deleted from the ePrint Archive, which feels like the correct decision on someone’s part.

Cryptanalyzing a Pair of Russian Encryption Algorithms

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2019/05/cryptanalyzing_.html

A pair of Russia-designed cryptographic algorithms — the Kuznyechik block cipher and the Streebog hash function — have the same flawed S-box that is almost certainly an intentional backdoor. It’s just not the kind of mistake you make by accident, not in 2014.

Evidence for the Security of PKCS #1 Digital Signatures

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2018/09/evidence_for_th.html

This is interesting research: “On the Security of the PKCS#1 v1.5 Signature Scheme“:

Abstract: The RSA PKCS#1 v1.5 signature algorithm is the most widely used digital signature scheme in practice. Its two main strengths are its extreme simplicity, which makes it very easy to implement, and that verification of signatures is significantly faster than for DSA or ECDSA. Despite the huge practical importance of RSA PKCS#1 v1.5 signatures, providing formal evidence for their security based on plausible cryptographic hardness assumptions has turned out to be very difficult. Therefore the most recent version of PKCS#1 (RFC 8017) even recommends a replacement the more complex and less efficient scheme RSA-PSS, as it is provably secure and therefore considered more robust. The main obstacle is that RSA PKCS#1 v1.5 signatures use a deterministic padding scheme, which makes standard proof techniques not applicable.

We introduce a new technique that enables the first security proof for RSA-PKCS#1 v1.5 signatures. We prove full existential unforgeability against adaptive chosen-message attacks (EUF-CMA) under the standard RSA assumption. Furthermore, we give a tight proof under the Phi-Hiding assumption. These proofs are in the random oracle model and the parameters deviate slightly from the standard use, because we require a larger output length of the hash function. However, we also show how RSA-PKCS#1 v1.5 signatures can be instantiated in practice such that our security proofs apply.

In order to draw a more complete picture of the precise security of RSA PKCS#1 v1.5 signatures, we also give security proofs in the standard model, but with respect to weaker attacker models (key-only attacks) and based on known complexity assumptions. The main conclusion of our work is that from a provable security perspective RSA PKCS#1 v1.5 can be safely used, if the output length of the hash function is chosen appropriately.

I don’t think the protocol is “provably secure,” meaning that it cannot have any vulnerabilities. What this paper demonstrates is that there are no vulnerabilities under the model of the proof. And, more importantly, that PKCS #1 v1.5 is as secure as any of its successors like RSA-PSS and RSA Full-Domain.

New Findings About Prime Number Distribution Almost Certainly Irrelevant to Cryptography

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2018/09/new_findings_ab.html

Lots of people are e-mailing me about this new result on the distribution of prime numbers. While interesting, it has nothing to do with cryptography. Cryptographers aren’t interested in how to find prime numbers, or even in the distribution of prime numbers. Public-key cryptography algorithms like RSA get their security from the difficulty of factoring large composite numbers that are the product of two prime numbers. That’s completely different.

Defeating the iPhone Restricted Mode

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2018/07/defeating_the_i.html

Recently, Apple introduced restricted mode to protect iPhones from attacks by companies like Cellebrite and Greyshift, which allow attackers to recover information from a phone without the password or fingerprint. Elcomsoft just announced that it can easily bypass it.

There is an important lesson in this: security is hard. Apple Computer has one of the best security teams on the planet. This feature was not tossed out in a day; it was designed and implemented with a lot of thought and care. If this team could make a mistake like this, imagine how bad a security feature is when implemented by a team without this kind of expertise.

This is the reason actual cryptographers and security engineers are very skeptical when a random company announces that their product is “secure.” We know that they don’t have the requisite security expertise to design and implement security properly. We know they didn’t take the time and care. We know that their engineers think they understand security, and designed to a level that they couldn’t break.

Getting security right is hard for the best teams on the world. It’s impossible for average teams.

Critical PGP Vulnerability

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2018/05/critical_pgp_vu.html

EFF is reporting that a critical vulnerability has been discovered in PGP and S/MIME. No details have been published yet, but one of the researchers wrote:

We’ll publish critical vulnerabilities in PGP/GPG and S/MIME email encryption on 2018-05-15 07:00 UTC. They might reveal the plaintext of encrypted emails, including encrypted emails sent in the past. There are currently no reliable fixes for the vulnerability. If you use PGP/GPG or S/MIME for very sensitive communication, you should disable it in your email client for now.

This sounds like a protocol vulnerability, but we’ll learn more tomorrow.

News articles.