[Cryptography] reality +- mathematical guarantees

Sampo Syreeni decoy at iki.fi
Tue Jun 9 00:30:52 EDT 2015


On 2015-06-08, John Denker wrote:

> In the real world, there are no "hard" guarantees, not for any form of 
> error correction ... nor for anything else. Specifically:  There are 
> lots of ways in which a channel can fail that will not reliably be 
> detected using CRC32.

True, but the error floor by S/N is flatter. That's why they did all of 
that linear and modulo coding work in the first place, instead of just 
randomizing the fuck out of it, per Shannon's original proof.

> Sure, one can create /mathematical models/ for which such-and-such 
> method provides a hard guarantee ... but more generally we would do 
> well to remember the dictum:
>
>    "Insofar as the propositions of mathematics refer to reality, they
>    are not certain; and insofar they are certain, they do not refer to
>    reality"
>
>                        -- Albert Einstein
>                          "Geometrie und Erfahrung" (1921)

      "This is the conclusion of the theorem."

                          -- Claude E. Shannon
                            "Coding Theorems for a Discrete Source With
                             a Fidelity Criterion" (1959)
-- 
Sampo Syreeni, aka decoy - decoy at iki.fi, http://decoy.iki.fi/front
+358-40-3255353, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2


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