TASK DEFINITION: You will be given a trivia clue, and the category it belongs to. You should answer with the best answer that belongs in the category and is described by the clue. For consistency, answers should be in all lower cased letters.
PROBLEM: Category: YELLOW THERE! 
Clue: A sushi favorite, hamachi is this type of fish

SOLUTION: the yellowtail

PROBLEM: Category: LETHAL WEAPONS 
Clue: In the largest man-made explosion in history, the USSR detonated a 50-megaton one of these in 1961

SOLUTION: a hydrogen bomb

PROBLEM: Category: UNBREAKABLE 
Clue: Gilbert Vernam, an engineer with this telecom company, came up with an "unbreakable" cipher, using a random code

SOLUTION:
at&t