The aim of this thesis is to identify the characteristics of lattice-based cryptosystems.
The use of encryption and signature schemes can be insecure considering attacks by a quantum computer and inefficient in the computation time. An alternative cryptography is proposed, which is based on worst-case lattice problems. The security and the hardness of the underlying computational problems will be analyzed by providing collaboration between the linear-algebra, complexity-theory and the public-key cryptography.
Contents
1 Introduction
1.1 Outline
2 Mathematical Background
2.1 Lattices and Lattice Reduction Problems
2.1.1 Definitions and Properties
2.1.2 Lattice Problems
2.1.3 Lattice-Reduction
2.2 Asymmetric Cryptosystems and Digital Signatures
2.2.1 Asymmetric Cryptography
2.2.2 Digital Signatures
3 Lattice-based Cryptosystems
3.1 GGH-Cryptosystem
3.1.1 Construction
3.1.2 Attacks
3.2 Comparison to other cryptosystems
4 Conclusion and Future Work
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