[Cryptography] Terakey, An Encryption Method Whose Security Can Be Analyzed from First Principles

[Phillip Hallam-Baker]

On Thu, Jul 16, 2020 at 1:22 PM Jerry Leichter <leichter at lrw.com> wrote:

>
> Thanks. An architect proposing a skyscraper with a structural design based
> on an unproven mathematical theory, would ridiculed. But a large part of
> the world economy is secured based on mathematical conjectures and no one
> seems to mind.
>
> This is a really bad analogy.  A skyscraper isn't built on the basis of
> mathematical theories.  It's based mainly on physical measurements of
> various properties of materials, combined using mathematical
> approximations.  The measurements and approximations are all validated
> empirically.  Mathematical proof plays a surprising small role.
>
> Case in point:  A story relayed to me by someone who started out as an
> architect/structural engineer and had this case presented as a warning in a
> class at MIT, taught by a faculty member who was actually involved.
>
> A number of years back, an unusual skyscraper was constructed in
> Manhattan.  Typically, the weight of a building is carried primarily (at
> ground level) along its corners.  But the architect of this building wanted
> a large open area under the building itself and wanted to avoid big, heavy
> supports at the corners.  So he came up with the idea of rotating the
> weight-bearing supports by 45 degrees:  The weight was carried by supports
> along the centers of each side.  Of course, this was fed into all the
> standard structural analysis programs and it passed the tests, including
> for stability in the face of "worst case" wind loads.
>
> A class learning how to do this kind of analysis was given the assignment
> of using the standard tools to repeat the wind analysis for the building
> and show that it was, indeed, safe.  One student in the class came to the
> professor and said that her analysis showed that the building would
> actually collapse under the design wind loads, and she couldn't figure out
> why she was getting "the wrong answer."  The professor looked closely at
> what she was doing, found that it was correct ... and finally understood
> what was going on.  It turns out that one can mathematically prove that the
> worse case for wind loading is when the wind is normal to one of the sides
> of the building.  So the standard analysis is just run for the four normal
> directions; if those are good, the building is fine.
>
> The student, for some reason, decided to also run the analysis for other
> wind directions - and found the hole in the proof.  The proof is valid *for
> buildings supported at the corners.*  It isn't valid for an unusual
> building supported at the midpoints of the sides.  In fact, the worst case
> for such a building is at some angle to one of the corners (probably
> depending on the ratio of the orthogonal sides).  A good hurricane coming
> from just the wrong direction would cause the building to collapse.
>
> So much for structural design based on proven mathematical theory.
>
> (In case you're wondering what happened to the building:  The professor
> involved was very well connected and quickly gained the attention of the
> architects and structural engineers involved in the building's design. They
> agreed, once they saw the analysis, that something needed to be done.  The
> building - fully occupied by then - was retrofitted with various braces and
> other devices to make it safe; as far as I know, it's in active use to this
> day.  The work was all done quietly; the actual reasons were not publicly
> explained.  Today, this story has become part of the education of
> architects and structural engineers, a caution alongside such classics as
> the collapse of the Tacoma Narrows bridge, aka "Gallopin' Gertie.")
>
>
> Gee, sounds like an old idea to use a high-resolution photo of the moon.
> The way that was set up, the underlying random-looking database - in this
> case, the brightness values of the picture - didn't even have to be private.
>
>
> Sorry, I don’t understand the connection to what I am proposing. A photo
> of the Moon or pretty much anything else is highly non-random, except
> perhaps for low order bits which might encode digitization noise, and even
> a 10,000 by 10,000 pixel image would be much smaller than secret keys I am
> suggesting. Am I missing something? If there was an earlier proposal
> similar to mine, I’d like to include a reference.
>
> It was quite some time ago, and I can't locate the reference.  As I
> recall, it was related to a book code, using a sequence generator of some
> sort to choose bits (yes, low-order bits which are very random) from what
> was at the time an unusual example of a publicly available immense
> database:  A very high resolution picture of the Moon produced by NASA.
> Again, I don't remember the details and as a result can't speak to the
> actual system or its properties.
>
>                                                         -- Jerry
>

That is almost but not quite what happened.

There was a TV special on the building. The architects had covered the wind
load issue correctly, the student was correct but so were the architects.
But it was when replying to the student and their prof that the architect
revisited a different issue which was the decision to bolt the cross
members in place rather than weld.

They re-ran the numbers on that and discovered that they had the serious
issue. And so they ended up having to send in crews every night to weld all
the cross braces in place.


There is a good book on this sort of stuff 'why buildings fall down'.
https://www.amazon.com/Why-Buildings-Fall-Down-Structures/dp/039331152X/ref=sr_1_1?dchild=1&keywords=why+buildings+fall+down&qid=1594941701&sr=8-1

I will see if I can locate my copy.
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