Lecture Notes on Lattices, Bases, and the Reduction Problem: Expository Notes

Excerpt from Lecture Notes on Lattices, Bases, and the Reduction Expository Notes

The subject of geometry of numbers was developed by Minkowski around the turn of the century. This has been a classical tool in subjects such as integral quadratic forms, diophantine approximations. However, it occupied its renewed role as a powerful tool in Computer Science, after h.w. Lenstra used it to give a polynomial time algorithm for the Integer Programming (feasibility) Problem for fixed number of variables. Since then it has been used to give efficient algorithms in as diverse areas as simultaneous diophan tine approximations, cryptography, solvability by radicals, low density subset sum problem, computing with algebraic numbers, factorization of polynomi als over finite fields.

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