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I would like to know which area of Mathematics would be most beneficial to cryptography. Surely Algebraic Number Theory and maybe to a lesser extend, Elliptic Curves, are closely linked to Cryptography; but are there more fields that would apply neatly to Cryptography?
What topics would you recommend to a Maths graduate who is looking for a career in Cryptography?
(I wanted to tag this as a "soft-question" as they do in math.stackexchange)
This seems to me a situation of the tail wagging the dog. Personally I have always found something I want to do such as zero knowledge proofs, faster primality testing, shorter signatures and then learned the relevant maths - bilinear pairings, elementary number theory and elliptic curves respectively. Cryptography is now a big subject and you can't hope to know enough maths to be comfortable in all areas - for instance the maths needed for differential/linear cryptanalysis is completely separate from the maths for asymmetric cryptography.
If you really are a maths graduate, what would a career in cryptography look like? Who would be your supervisor? Which university? Similar constraints are relevant in a commercial setting too.
I would add Probabilities Theory and Linear Algebra as it turns to become the de facto source for intractable problems for the unreal yet fully homomorphic encryption schemes
