Category: cryptanalysis

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 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.

Interesting summary of various ways to derive the public key from digitally signed files.

Normally, with a signature scheme, you have the public key and want to know whether a given signature is valid. But what if we instead have a message and a signature, assume the signature is valid, and want to know which public key signed it? A rather delightful property if you want to attack anonymity in some proposed “everybody just uses cryptographic signatures for everything” scheme.

A new paper presents a polynomial-time quantum algorithm for solving certain hard lattice problems. This could be a big deal for post-quantum cryptographic algorithms, since many of them base their security on hard lattice problems.

A few things to note. One, this paper has not yet been peer reviewed. As this comment points out: “We had already some cases where efficient quantum algorithms for lattice problems were discovered, but they turned out not being correct or only worked for simple special cases.” I expect we’ll learn more about this particular algorithm with time. And, like many of these algorithms, there will be improvements down the road.

Two, this is a quantum algorithm, which means that it has not been tested. There is a wide gulf between quantum algorithms in theory and in practice. And until we can actually code and test these algorithms, we should be suspicious of their speed and complexity claims.

And three, I am not surprised at all. We don’t have nearly enough analysis of lattice-based cryptosystems to be confident in their security.

EDITED TO ADD (4/20): The paper had a significant error, and has basically been retracted. From the new abstract:

Note: Update on April 18: Step 9 of the algorithm contains a bug, which I don’t know how to fix. See Section 3.5.9 (Page 37) for details. I sincerely thank Hongxun Wu and (independently) Thomas Vidick for finding the bug today. Now the claim of showing a polynomial time quantum algorithm for solving LWE with polynomial modulus-noise ratios does not hold. I leave the rest of the paper as it is (added a clarification of an operation in Step 8) as a hope that ideas like Complex Gaussian and windowed QFT may find other applications in quantum computation, or tackle LWE in other ways.