Question: Able Seaman Colin Grazier, GC was posthumously awarded what, for "bravery and steadfast devotion to duty", he displayed on 30 October 1942 in action in the eastern Mediterranean when capturing codebooks vital for the breaking of the German naval "Shark" Enigma cipher from the sinking, the Enigma machines were a series of electro-mechanical rotor cipher machines developed and used in the early- to mid-20th century to protect commercial, diplomatic and military communication?

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Banburismus: Banburismus was a cryptanalytic process developed by Alan Turing at Bletchley Park in England during the Second World War.  It was used by Bletchley Park's Hut 8 to help break German "Kriegsmarine" (naval) messages enciphered on Enigma machines.  The process used sequential conditional probability to infer information about the likely settings of the Enigma machine.  It gave rise to Turing's invention of the "ban" as a measure of the weight of evidence in favour of a hypothesis.  This concept was later applied in Turingery and all the other methods used for breaking the Lorenz cipher.

Colin Grazier: Able Seaman Colin Grazier, GC was posthumously awarded the George Cross for the "outstanding bravery and steadfast devotion to duty in the face of danger" which he displayed on 30 October 1942 in action in the eastern Mediterranean when capturing codebooks vital for the breaking of the German naval "Shark" Enigma cipher from the sinking  .

Typex: In the history of cryptography, Typex (alternatively, Type X or TypeX) machines were British cipher machines used from 1937.  It was an adaptation of the commercial German Enigma with a number of enhancements that greatly increased its security.  The cipher machine (and its many revisions) was used until the mid-1950s when other more modern military encryption systems came into use.

Grill (cryptology): The grill method (Polish: "metoda rusztu" ), in cryptology, was a method used chiefly early on, before the advent of the cyclometer, by the mathematician-cryptologists of the Polish Cipher Bureau ("Biuro Szyfrów") in decrypting German Enigma machine ciphers.  The Enigma rotor cipher machine changes plaintext characters into cipher text using a different permutation for each character, and so implements a polyalphabetic substitution cipher.

Heath Robinson (codebreaking machine): Heath Robinson was a machine used by British codebreakers at the Government Code and Cypher School (GC&CS) at Bletchley Park during World War II in Cryptanalysis of the Lorenz cipher.  This achieved the decryption of messages in the German teleprinter cipher produced by the Lorenz SZ40/42 in-line cipher machine.  Both the cipher and the machines were called "Tunny" by the codebreakers, who named different German teleprinter ciphers after fish.  It was mainly an electro-mechanical machine, containing no more than a couple of dozen valves (vacuum tubes), and was the predecessor to the electronic Colossus computer.  It was dubbed "Heath Robinson" by the Wrens who operated it, after cartoonist William Heath Robinson, who drew immensely complicated mechanical devices for simple tasks, similar to (and somewhat predating) Rube Goldberg in the USA.

Tony Fasson: Lieutenant Francis Anthony Blair Fasson, {'1': ", '2': ", '3': ", '4': "} (17 July 1913 – 30 October 1942), known as Tony Fasson, was a British Royal Navy officer.  He was posthumously awarded the George Cross "for outstanding bravery and steadfast devotion to duty in the face of danger" when on 30 October 1942 in action in the Mediterranean Sea he captured codebooks vital for the breaking of the German naval "Shark" Enigma cipher from the sinking  .

Enigma machine: The Enigma machines were a series of electro-mechanical rotor cipher machines developed and used in the early- to mid-20th century to protect commercial, diplomatic and military communication.  Enigma was invented by the German engineer Arthur Scherbius at the end of World War I.  Early models were used commercially from the early 1920s, and adopted by military and government services of several countries, most notably Nazi Germany before and during World War II.  Several different Enigma models were produced, but the German military models, having a plugboard, were the most complex.  Japanese and Italian models were also in use.

Polish Enigma double: A Polish Enigma "double" was a machine produced by the Polish Cipher Bureau that replicated the German Enigma rotor cipher machine.  The Enigma double was one result of Marian Rejewski's remarkable achievement of determining the wiring of the Enigma's rotors and reflectors.

Reflector (cipher machine): A reflector, in cryptology, is a component of some rotor cipher machines, such as the Enigma machine, that sends electrical impulses that have reached it from the machine's rotors, back in reverse order through those rotors.  The reflector simplified using the same machine setup for encryption and decryption, but it creates a weakness in the encryption: with a reflector the encrypted version of a given letter can never be that letter itself.  That limitation aided World War II code breakers in cracking Enigma encryption.  The comparable WW II U.S. cipher machine, SIGABA, did not include a reflector.

Ludomir Danilewicz: Beginning in 1933, after the Cipher Bureau's mathematician-cryptologist Marian Rejewski reconstructed the German military Enigma rotor cipher machine, AVA built Enigma "doubles" as well as all the electro-mechanical equipment subsequently designed at the Cipher Bureau to expedite routine breaking and reading of Enigma ciphers.

Supporting paragraphs: Colin Grazier Enigma machine
Answer: George Cross