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In this thesis we give an in-depth introduction to the General Number FieldSieve, as it was used by Buhler, Lenstra, and Pomerance, before looking at oneof the modern developments of this algorithm: A randomized version withprovable complexity. This version was posited in 2017 by Lee and Venkatesan andwill be preceded by ample material from both algebraic and analytic numbertheory, Galois theory, and probability theory.

Number Field Sieve with Provable Complexity