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The Mathematics of Secrets

@mathofsecrets

Hi, I'm Josh Holden. I teach math, write books, and encrypt secret messages.

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Latest posts by The Mathematics of Secrets @mathofsecrets

Youโ€™re very welcome!

09.03.2026 14:14 ๐Ÿ‘ 1 ๐Ÿ” 0 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0

Fooled you, Daylight Savings Time! The hour you took from me last night was actually the hour I took when I fled Eastern Time the night before!

08.03.2026 16:50 ๐Ÿ‘ 0 ๐Ÿ” 0 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0

From @tenorfrank.bsky.social

08.03.2026 15:13 ๐Ÿ‘ 1 ๐Ÿ” 0 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0
Farris Exhibitions

Have you seen this: webpages.scu.edu/ftp/ffarris/...

08.03.2026 15:11 ๐Ÿ‘ 1 ๐Ÿ” 0 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0
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Yubikeys using ML-DSA including ML-DSA-87 are coming!

08.03.2026 07:17 ๐Ÿ‘ 13 ๐Ÿ” 2 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 3
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#fractal #fractalart #fractalwork #fractalartwork #artwork #math #mathematics #maths

24.02.2026 13:54 ๐Ÿ‘ 1 ๐Ÿ” 1 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
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Here's why Scotch tape screeches when it's peeled Micro-cracks travel along the peeling tape at supersonic speeds, producing shock waves and sound pulses.
24.02.2026 14:02 ๐Ÿ‘ 66 ๐Ÿ” 10 ๐Ÿ’ฌ 3 ๐Ÿ“Œ 3
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Not sure what phase of my life Iโ€™m in, but hereโ€™s that modelling balloon icosidodecahedron nobody asked for!

In theory it could be made out of a single modelling balloon, although in reality they donโ€™t make balloons long enough :(

22.02.2026 17:25 ๐Ÿ‘ 41 ๐Ÿ” 5 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 2

Shape nerds ASSEMBLE!

(In an icosahedral symmetry formation)

22.02.2026 20:32 ๐Ÿ‘ 23 ๐Ÿ” 3 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
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Connecting the Dots: An Investigative Study on Linking Private User Data Across Messaging Apps - NDSS Symposium View More Papers

Think your burner number keeps you anonymous? Kang et al. reveal a severe privacy threat, a cross-platform linking attack targeting messaging apps. Using contact discovery and SSO, it deanonymizes users and pinpoints their physical locations.

22.02.2026 20:45 ๐Ÿ‘ 3 ๐Ÿ” 4 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0

Today I was looking at an article on Multi-Party Threshold #Cryptography and wondered why "threshold" has only one h. Turns out the etymology is not "thresh-hold" at all, but "thresh-wold", possibly from the Middle English word "wold" meaning "forest". Mind blown.

07.02.2026 20:53 ๐Ÿ‘ 5 ๐Ÿ” 2 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0

For my next book, Iโ€™m reading some mid-20th century papers on color vision. These guys will go on for pages about the kind of filters they use, and then their discussion of the test subjects will be โ€œwe took the measurements on Mr. Perley G. Nutting, Jr., who sat still for a really long time.โ€

04.01.2026 05:38 ๐Ÿ‘ 1 ๐Ÿ” 0 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0

Love that paper!

02.01.2026 16:53 ๐Ÿ‘ 1 ๐Ÿ” 0 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
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At 26, during the Reign of Terror in France, Jean-Baptiste Joseph Fourier narrowly avoided the guillotine. A decade later, he made a discovery that changed mathematics forever.
www.quantamagazine.org/what-is-the-...

10.12.2025 21:04 ๐Ÿ‘ 42 ๐Ÿ” 13 ๐Ÿ’ฌ 2 ๐Ÿ“Œ 1
Figure 6. The quotientope lattice for n = 4: all quotientopes ordered by inclusion (which corresponds to refinement of the lattice congruences). We only consider lattice congruences whose fan
is essential. We have highlighted the cube (green), Lodayโ€™s associahedron [Lod04] (blue), another
one of Hohlwegโ€“Langeโ€™s associahedra [HL07] (purple), the diagonal rectangulation polytope [LR12]
(orange), and the permutahedron (red). Adapted from [PS19, Fig. 9].

Figure 6. The quotientope lattice for n = 4: all quotientopes ordered by inclusion (which corresponds to refinement of the lattice congruences). We only consider lattice congruences whose fan is essential. We have highlighted the cube (green), Lodayโ€™s associahedron [Lod04] (blue), another one of Hohlwegโ€“Langeโ€™s associahedra [HL07] (purple), the diagonal rectangulation polytope [LR12] (orange), and the permutahedron (red). Adapted from [PS19, Fig. 9].

This diagram should win some kind of prize for mathematical illustration. From arxiv.org/abs/2305.08471. ๐Ÿงฎ

05.12.2025 22:27 ๐Ÿ‘ 38 ๐Ÿ” 4 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0
The Complete Secrets of Kryptos: Jim Sanborn's Private Archive | RR Sold for $962,500 | Jim Sanborn's original Kryptos archive that reveals the secrets of K4 and the much anticipated K5, plus an afternoon with Sanborn as he p

Looks like the Kryptos kerfuffle didn't hurt the auction much! #cryptography www.rrauction.com/auctions/lot...

26.11.2025 22:48 ๐Ÿ‘ 1 ๐Ÿ” 0 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
LeaKissner (@leak@hachyderm.io) Cryptography is a tool for turning a whole swathe of problems into key management problems. Key management problems are way harder than (virtually all) cryptographers think.

So, the IACR held an election, but one of the three trustees lost their private key, which prevented them from verifying the results of the election. Forcing them to start over.

The cryptography association was foiled by key management.

hachyderm.io/@leak/110784...

20.11.2025 22:35 ๐Ÿ‘ 34 ๐Ÿ” 5 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
picture of text. For this election and in accordance with the bylaws of the ACR, the three members of the ACR 2025 Election Committee acted as independent trustees, each holding a portion of the cryptographic key material required to jointly decrypt the results. This aspect of Helios' design ensures that no two trustees could collude to determine the outcome of an election or the contents of individual votes on their own: all trustees must provide their decryption shares.
Unfortunately, one of the three trustees has irretrievably lost their private key, an honest but unfortunate human mistake, and therefore cannot compute their decryption share. As a result, Helios is unable to complete the decryption process, and it is technically impossible for us to obtain or verify the final outcome of this election.

picture of text. For this election and in accordance with the bylaws of the ACR, the three members of the ACR 2025 Election Committee acted as independent trustees, each holding a portion of the cryptographic key material required to jointly decrypt the results. This aspect of Helios' design ensures that no two trustees could collude to determine the outcome of an election or the contents of individual votes on their own: all trustees must provide their decryption shares. Unfortunately, one of the three trustees has irretrievably lost their private key, an honest but unfortunate human mistake, and therefore cannot compute their decryption share. As a result, Helios is unable to complete the decryption process, and it is technically impossible for us to obtain or verify the final outcome of this election.

This IACR election news is so relatable

21.11.2025 08:51 ๐Ÿ‘ 11 ๐Ÿ” 1 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0

Did you know?
Keccak is everywhere, quietly protecting real systems, such as:
โ€ข Connected devices checking data integrity
โ€ข Firmware updates verifying authenticity
โ€ข Embedded products securing messages
โ€ข PQC standards like ML-KEM, ML-DSA, and SLH-DSA
โฌ‡

21.11.2025 13:32 ๐Ÿ‘ 2 ๐Ÿ” 1 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0
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โ€œKey Managementโ€ is the cryptographic communityโ€™s version of โ€œโ€ฆitโ€™s always DNSโ€ International Association for Cryptologic Research runs secure vote and then loses the keys so nobody knows what the result is. As one commenter put it: โ€œSo a single member can collude to resโ€ฆ

โ€œKey Managementโ€ is the cryptographic communityโ€™s version of โ€œโ€ฆitโ€™s always DNSโ€
https://alecmuffett.com/article/126061
#cryptography #iacr

21.11.2025 14:05 ๐Ÿ‘ 8 ๐Ÿ” 3 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0
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Post-Quantum Cryptography in .NET - .NET Blog What we've added for PQC, and how we got there.

Post-Quantum Cryptography in .NET

ift.tt/osS9nPf

#dotnet #pqc #cryptography #programming #csharp

19.11.2025 18:00 ๐Ÿ‘ 2 ๐Ÿ” 2 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
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This December, the Faculty of Engineering at #USyd is delighted to welcome Dr Moti Yung, who will speak at the Basser seminar series in our School. He will tell us about "Malicious Cryptography: beyond adhering to specifications in secure systems"

๐Ÿ•’ Tuesday, Dec 2
3:30โ€”4:30pm

19.11.2025 21:26 ๐Ÿ‘ 2 ๐Ÿ” 5 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 2
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Physicists Take the Imaginary Numbers Out of Quantum Mechanics | Quanta Magazine Quantum mechanics has at last been formulated exclusively with real numbers, bringing a mathematical puzzle at the heart of the theory into a new era of inquiry.

Hot take: I hate to say it, but this is silly. Mathematicians have known for at least a century that you can replace imaginary numbers with 2x2 matrices of real numbers. Would the result be useful? Sounds like the answer is no. #quantumcomputing www.quantamagazine.org/physicists-t...

08.11.2025 00:42 ๐Ÿ‘ 3 ๐Ÿ” 0 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
Part Four of The Kryptos Sculpture Two people found the solution. They used the power of research, not cryptanalysis, finding clues amongst the Sanborn papers at the Smithsonianโ€™s Archives of American Art. This comes as an awkward time, as Sanborn is auctioning off the solution. There were legal threatsโ€”I donโ€™t understand their basisโ€”and the solvers are not publishing their solution.
24.10.2025 11:01 ๐Ÿ‘ 1 ๐Ÿ” 1 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
Solution to CIAโ€™s Kryptos Sculpture Is Found in Smithsonian Vault Jim Sanborn planned to auction off the solution to Kryptos, the puzzle he sculpted for the intelligence agencyโ€™s headquarters. Two fans of the work then discovered the solution.

Well, that's a #cryptography oops. web.archive.org/web/20251016...

26.10.2025 00:15 ๐Ÿ‘ 2 ๐Ÿ” 2 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
The Mathematics of Secrets https://wordpress.rose-hulman.edu/holden/the-mathematics-of-secrets/

Doing some profile editing --- this should really be a pinned post, not my bio!

In his book The Mathematics of Secrets, Joshua Holden takes readers on a tour of the mathematics behind cryptographyโ€”the science of sending secret messages.

mathofsecrets.com

11.10.2025 20:44 ๐Ÿ‘ 0 ๐Ÿ” 1 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0
Eavesdropping on Phone Conversations Through Vibrations - Schneier on Security Researchers have managed to eavesdrop on cell phone voice conversations by using radar to detect vibrations. Itโ€™s more a proof of concept than anything else. The radar detector is only ten feet away, ...

Found this in my old tabs. Kind of a scary idea! #Cryptography can't do much about attacks like this. @schneier.com www.schneier.com/blog/archive...

11.10.2025 20:40 ๐Ÿ‘ 0 ๐Ÿ” 1 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
Proof

Proof

An incredible proof from โ€œWhen Least is Bestโ€ by Paul Nahin

12.03.2025 21:47 ๐Ÿ‘ 5 ๐Ÿ” 1 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
The Mathematical Radio: Inside the Magic of AM, FM, and Single-Sideband by Paul J. Nahin

The Mathematical Radio: Inside the Magic of AM, FM, and Single-Sideband by Paul J. Nahin

How a modern radio works, told through mathematics, history, and selected puzzles.

Paul J. Nahin's The Mathematical Radio is now available in #paperback. Learn more: press.princeton.edu/books/paperb...

#Math #Mathematics #History

18.09.2025 18:48 ๐Ÿ‘ 10 ๐Ÿ” 2 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 1

Everything involving generating functions seems like a great magic trick to me! :)

10.10.2025 00:55 ๐Ÿ‘ 2 ๐Ÿ” 0 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0