Flaw in the Enigma Code - Numberphile

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

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.

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

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