Numberphile
4 HN recommenders · recommended in 4 months, 2013–2025
10:58 · 5.4M views · Jan 14, 2013
Numberphile's Dr James Grime explains the flaw in the Enigma machine, namely that a letter could never be encrypted to itself, and how that helped the Allies break the code. It touches on the Bombe and Alan Turing.
HN points to it as a short, clear explanation of why Enigma was breakable and how search-space elimination works.
4 comments from Hacker News
In this case, a more relevant example from World War II might be the exploitation of flaws in the Enigma machine, namely: 1) the re-use of common phrases in weather reports, and 2) the fact that a letter could not be encoded as itself in the ciphertext, providing a mechanism of contradiction that drastically sped up elimination of possible settings [LINK] Numberphile gives a nice, succinct explanation this video
none of it is "brute force", GNFS is a process that rapidly excludes numbers from the search space that cannot be the answer, in principle similar to the way they broke enigma. numberphile has a great video on that one this video Also, taking the OP as a "worse case", afaik: 512bit = $8 so 1024 = 8^2 = $64 2048 = 8^2^2 = $4,096 4096 = 8^2^2 = $16,777,216 noting $8 for 512 seems very expensive to me.
There's the entertaining bit in the film The Imitation Game (the breaking of Enigma code by Alan Turing) where they realised that a weakness was the daily weather report always containing the words "weatherreport" and "heil bloody hitler" (with obvious addition!) [LINK] or longer version: [LINK] Also a more proper explanation: this video
Some people might like this from Numberphile which describes the flaw in the enigma machine that British code breakers used to eventually break the code. this video