@MISC{Mol06latticesand, author = {Petros Mol}, title = { Lattices and their Applications to RSA Cryptosystem}, year = {2006} }

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Abstract

The purpose of this diploma thesis is the study both of the mathematical background on lattice theory and of the corresponding applications to the RSA Cryptosystem. In bibliography, there are two quite di erent mathematical structures that are usually called lattices. The rst one has to do with partially ordered sets while the other has to do with regular arrangements of points in space. In this thesis we exclusively consider the second case. Historically, lattices were investigated since the late 18th century by mathematicians such as Lagrange and Gauss. In the 19th century, important results due to Minkowski motivated the use of lattice theory in the theory and geometry of numbers. The evolution of computer science in the 20th century led to lattice applications in various theoretical areas such as factorization of integer polynomials, integer programming and Public-Key Cryptography. In the latter area, lattice theory has played a crucial role in the de nition of new cryptosystems, in the study of cryptographic primitives and in cryptanalysis. The main goal