
Chasing diagrams in cryptography (2016) - mpiedrav
https://arxiv.org/abs/1401.6488
======
mrkgnao
The first line of the abstract reminds me of some recent work allowing plain
Haskell functions to be sent to the Z3 theorem prover/SMT program:

[http://newartisans.com/2017/04/haskell-
and-z3/](http://newartisans.com/2017/04/haskell-and-z3/)

It leverages some cool work of Conal Elliott that develops (formulas in)
cartesian closed categories into something like an "intermediate
representation" for functional language compilation.

[http://conal.net/blog/posts/haskell-to-hardware-via-
cccs](http://conal.net/blog/posts/haskell-to-hardware-via-cccs)
[http://conal.net/blog/posts/overloading-
lambda](http://conal.net/blog/posts/overloading-lambda)

[http://conal.net/papers/compiling-to-
categories/](http://conal.net/papers/compiling-to-categories/) (the "LaTeX
goals" ICFP 2017 paper)

\--

Also, something I always like to link when this kind of thing comes up: the
salamander lemma!

[https://sbseminar.wordpress.com/2007/11/13/anton-
geraschenko...](https://sbseminar.wordpress.com/2007/11/13/anton-geraschenko-
the-salamander-lemma/)

[https://mathoverflow.net/questions/6749/a-proof-of-the-
salam...](https://mathoverflow.net/questions/6749/a-proof-of-the-salamander-
lemma-without-mitchells-embedding-theorem)

------
jordigh
Huh, diagram chasing attributed to Lambek? Kind of surprising, but plausible.
I would have thought Steenrod would have gotten the credit.

Also, kind of melancholic, this paper is for Lambek's 90th birthday, but it
has a publication date two years after his death. I was lucky to attend one of
Lambek's lectures and take a course he designed. He was a great expositor, and
I'll miss him.

~~~
homalg
I don't think this attribution makes sense without some further qualification.
There is diagram chasing ten years earlier in Cartan-Eilenberg's Homological
Algebra (1955) -- they prove the five lemma early on -- and Mac Lane mentions
the term in his Homology (1963). I wouldn't be surprised if it appears in
Eilenberg-Steenrod, or, as you say, Steenrod's earlier work or the Cartan
Seminar notes (which I don't have near me right now).

------
sleepingeights
I am a bit lost. How is cryptography about secrecy of the text through some
operation, like a function, while at the same time being a system that defines
itself?

Cryptography has nothing to do with secrecy at all. It has to do with
maintaining the integrity of the communication (or specifically, the message)
given highly active and adversarial entities.

Anyone who thinks they can have security through secrecy (i.e. 'cryptography')
is a fool, imo.

~~~
irishsultan
> It has to do with maintaining the integrity of the communication

This requires secrecy, or else any adversary can do exactly what you did and
fake a message.

Note that it doesn't require secrecy of the method, but it does require
secrecy of at least some of the input (a key). Therefore whatever method you
use should preserve the secrecy of that input to be suitable for cryptography.

