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Prime theory is of great interest to me! It is currently used in many cryptosystems to protect data (in making public keys, for example). There are always a few obscure researchers studying how to make prime factorization easier (or stronger I suppose). There are so many branches of math that we use in cryptography (matrices, primes, ellipses, modular ...


4

Abstract mathematics has played an important role in the development of cryptography. From Analytical number theory, tools like factorization and computing logarithms in a finite field. Enough is said and known about these techniques! Combinatorial problems, like knapsack and subset-sum has been used in cryptosystem. You can find a very nice connection ...


4

I would like to add my two cents (mostly related to asymmetric cryptography): Number theoretic primitives (RSA/DH/EC/Pairing based crypto) [Mainstream] Coding theory based crypto systems (McEliece) [research] Lattice based systems [research] Other models of information theory, e.g. wiretap model [research] Combinatorics (knapsack problems) [research]


4

"Algebraic Geometry Codes: Basic Notions" by Tsfasman, Vladut, and Nogin is a textbook that is available as a PDF. Discussion of Hermitian curves begins on page 167. I haven't read it and no very little about coding theory. It was the reference a friend provided in his dissertation, which included constructing universal hash functions from Hermitian curves. ...


3

Surprised nobody has mentioned this. Abstract algebra is a big player in the design of AES, specifically AES uses finite field arithmetic over a specific field. This article introduces the field in question. The field in question is also called a Galois Field, from Galois theory which neatly solves questions about higher order polynomials as well as linking ...


2

I am not sure on the implementation status of hyperelliptic curves. Two other significant uses of mathematical techniques: Bilinear pairings on appropriate elliptic curves - mainstream (Voltage) Ideal lattices - mainstream (NTRU) and in research (Gentry's fully homomorphic encryption) Another area of interest is based on coding theory: Learning ...



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