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I’m skeptical about—and not qualified to review—this new result in factorization with a quantum computer, but if it’s true it’s a theoretical improvement in the speed of factoring large numbers with a quantum computer.
A couple of months ago, a new paper demonstrated some new attacks against the Fiat-Shamir transformation. Quanta published a good article that explains the results.
This is a pretty exciting paper from a theoretical perspective, but I don’t see it leading to any practical real-world cryptanalysis. The fact that there are some weird circumstances that result in Fiat-Shamir insecurities isn’t new—many dozens of papers have been published about it since 1986. What this new result does is extend this known problem to slightly less weird (but still highly contrived) situations. But it’s a completely different matter to extend these sorts of attacks to “natural” situations.
What this result does, though, is make it impossible to provide general proofs of security for Fiat-Shamir. It is the most interesting result in this research area, and demonstrates that we are still far away from fully understanding what is the exact security guarantee provided by the Fiat-Shamir transform.
In the early 1960s, National Security Agency cryptanalyst and cryptanalysis instructor Lambros D. Callimahos coined the term “Stethoscope” to describe a diagnostic computer program used to unravel the internal structure of pre-computer ciphertexts. The term appears in the newly declassified September 1965 document Cryptanalytic Diagnosis with the Aid of a Computer, which compiled 147 listings from this tool for Callimahos’s course, CA-400: NSA Intensive Study Program in General Cryptanalysis.
The listings in the report are printouts from the Stethoscope program, run on the NSA’s Bogart computer, showing statistical and structural data extracted from encrypted messages, but the encrypted messages themselves are not included. They were used in NSA training programs to teach analysts how to interpret ciphertext behavior without seeing the original message.
The listings include elements such as frequency tables, index of coincidence, periodicity tests, bigram/trigram analysis, and columnar and transposition clues. The idea is to give the analyst some clues as to what language is being encoded, what type of cipher system is used, and potential ways to reconstruct plaintext within it.
Bogart was a special-purpose electronic computer tailored specifically for cryptanalytic tasks, such as statistical analysis of cipher texts, pattern recognition, and diagnostic testing, but not decryption per se.
Listings like these were revolutionary. Before computers, cryptanalysts did this type of work manually, painstakingly counting letters and testing hypotheses. Stethoscope automated the grunt work, allowing analysts to focus on interpretation, and cryptanalytical strategy.
These listings were part of the Intensive Study Program in General Cryptanalysis at NSA. Students were trained to interpret listings without seeing the original ciphertext, a method that sharpened their analytical intuitive skills.
Also mentioned in the report is Rob Roy, another NSA diagnostic tool focused on different cryptanalytic tasks, but also producing frequency counts, coincidence indices, and periodicity tests. NSA had a tradition of giving codebreaking tools colorful names—for example, DUENNA, SUPERSCRITCHER, MADAME X, HARVEST, and COPPERHEAD.
In response to a FOIA request, the NSA released “Fifty Years of Mathematical Cryptanalysis (1937-1987),” by Glenn F. Stahly, with a lot of redactions.
Weirdly, this is the second time the NSA has declassified the document. John Young got a copy in 2019. This one has a few less redactions. And nothing that was provided in 2019 was redacted here.
If you find anything interesting in the document, please tell us about it in the comments.
New paper: “GPU Assisted Brute Force Cryptanalysis of GPRS, GSM, RFID, and TETRA: Brute Force Cryptanalysis of KASUMI, SPECK, and TEA3.”
Abstract: Key lengths in symmetric cryptography are determined with respect to the brute force attacks with current technology. While nowadays at least 128-bit keys are recommended, there are many standards and real-world applications that use shorter keys. In order to estimate the actual threat imposed by using those short keys, precise estimates for attacks are crucial.
In this work we provide optimized implementations of several widely used algorithms on GPUs, leading to interesting insights on the cost of brute force attacks on several real-word applications.
In particular, we optimize KASUMI (used in GPRS/GSM),SPECK (used in RFID communication), andTEA3 (used in TETRA). Our best optimizations allow us to try 235.72, 236.72, and 234.71 keys per second on a single RTX 4090 GPU. Those results improve upon previous results significantly, e.g. our KASUMI implementation is more than 15 times faster than the optimizations given in the CRYPTO’24 paper [ACC+24] improving the main results of that paper by the same factor.
With these optimizations, in order to break GPRS/GSM, RFID, and TETRA communications in a year, one needs around 11.22 billion, and 1.36 million RTX 4090GPUs, respectively.
For KASUMI, the time-memory trade-off attacks of [ACC+24] can be performed with142 RTX 4090 GPUs instead of 2400 RTX 3090 GPUs or, when the same amount of GPUs are used, their table creation time can be reduced to 20.6 days from 348 days,crucial improvements for real world cryptanalytic tasks.
Attacks always get better; they never get worse. None of these is practical yet, and they might never be. But there are certainly more optimizations to come.
EDITED TO ADD (4/14): One of the paper’s authors responds.
Interesting research: “How to Securely Implement Cryptography in Deep Neural Networks.”
Abstract: The wide adoption of deep neural networks (DNNs) raises the question of how can we equip them with a desired cryptographic functionality (e.g, to decrypt an encrypted input, to verify that this input is authorized, or to hide a secure watermark in the output). The problem is that cryptographic primitives are typically designed to run on digital computers that use Boolean gates to map sequences of bits to sequences of bits, whereas DNNs are a special type of analog computer that uses linear mappings and ReLUs to map vectors of real numbers to vectors of real numbers. This discrepancy between the discrete and continuous computational models raises the question of what is the best way to implement standard cryptographic primitives as DNNs, and whether DNN implementations of secure cryptosystems remain secure in the new setting, in which an attacker can ask the DNN to process a message whose “bits” are arbitrary real numbers.
In this paper we lay the foundations of this new theory, defining the meaning of correctness and security for implementations of cryptographic primitives as ReLU-based DNNs. We then show that the natural implementations of block ciphers as DNNs can be broken in linear time by using such nonstandard inputs. We tested our attack in the case of full round AES-128, and had success rate in finding randomly chosen keys. Finally, we develop a new method for implementing any desired cryptographic functionality as a standard ReLU-based DNN in a provably secure and correct way. Our protective technique has very low overhead (a constant number of additional layers and a linear number of additional neurons), and is completely practical.
Really interesting research into the structure of prime numbers. Not immediately related to the cryptanalysis of prime-number-based public-key algorithms, but every little bit matters.
Matthew Green wrote a really good blog post on what Telegram’s encryption is and is not.
EDITED TO ADD (8/28): Another good explainer from Kaspersky.
Really interesting article on the ancient-manuscript scholars who are applying their techniques to the Voynich Manuscript.
No one has been able to understand the writing yet, but there are some new understandings:
Davis presented her findings at the medieval-studies conference and published them in 2020 in the journal Manuscript Studies. She had hardly solved the Voynich, but she’d opened it to new kinds of investigation. If five scribes had come together to write it, the manuscript was probably the work of a community, rather than of a single deranged mind or con artist. Why the community used its own language, or code, remains a mystery. Whether it was a cloister of alchemists, or mad monks, or a group like the medieval Béguines—a secluded order of Christian women—required more study. But the marks of frequent use signaled that the manuscript served some routine, perhaps daily function.
Davis’s work brought like-minded scholars out of hiding. In just the past few years, a Yale linguist named Claire Bowern had begun performing sophisticated analyses of the text, building on the efforts of earlier scholars and on methods Bowern had used with undocumented Indigenous languages in Australia. At the University of Malta, computer scientists were figuring out how to analyze the Voynich with tools for natural-language processing. Researchers found that the manuscript’s roughly 38,000 words—and 9,000-word vocabulary—had many of the statistical hallmarks of actual language. The Voynich’s most common word, whatever it meant, appeared roughly twice as often as the second-most-common word and three times as often as the third-commonest, and so on—a touchstone of natural language known as Zipf’s law. The mix of word lengths and the ratio of unique words to total words were similarly language-like. Certain words, moreover, seemed to follow one another in predictable order, a possible sign of grammar.
Finally, each of the text’s sections—as defined by the drawings of plants, stars, bathing women, and so on—had different sets of overrepresented words, just as one would expect in a real book whose chapters focused on different subjects.
Spelling was the chief aberration. The Voynich alphabet—if that’s what it was—appeared to have a conventional 20-odd letters. But compared with known languages, too many of those letters repeated in the same order, both within words and across neighboring words, like a children’s rhyme. In some places, the spellings of adjacent words so converged that a single word repeated two or three times in a row. A rough English equivalent might be something akin to “She sells sea shells by the sea shore.” Another possibility, Bowern told me, was something like pig Latin, or the Yiddishism—known as “shm-reduplication”—that begets phrases such as fancy shmancy and rules shmules.
A group of cryptographers have analyzed the eiDAS 2.0 regulation (electronic identification and trust services) that defines the new EU Digital Identity Wallet.
Sidebar photo of Bruce Schneier by Joe MacInnis.