Does the word 'law' need to be capitalised? [duplicate]

To quote the relevant sections of the Chicago Manual of Style (CMoS):

8.28 Names of degrees, fellowships, and the like are lowercased when referred to generically.

8.84 Academic subjects are not capitalized unless they form part of a department name or an official course name or are themselves proper nouns (e.g., English, Latin).

So if you were to follow CMoS, you would write:

I hope to one day go on to complete a master's degree in computer science, with a focus in applied cryptography.

CMoS notes in 8.85 that "official names of courses of study are capitalized." So if you wanted to highlight that you "took Bruce Schneier's Applied Cryptography 420 course," capitalizing "applied cryptography" would be appropriate in that case.