Diplomarbeit Johannes Weiß
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README.md

Diplomarbeit / Master's Thesis

This is the GitHub repository for my Diplomarbeit / Master's Thesis.

Abstract

Today, strong cryptography plays a very important role. Cryptography is of crucial importance mainly, but not limited, to important transactions via the Internet and other communication networks because the information should reach its destination reliably, confidentially and with integrity. The telematics research solves the reliability problem, but cryptography is used to ensure confidentiality and integrity. Since the overall problem is very complex, an increasing effort to use cryptographic primitives and protocols is discoverable. The benefit of this component based architecture is the possibility to prove the security of the components individually. Of course, the proofs must take into account the composability of the components which enables to build complex and secure systems from smaller building blocks.

This thesis concerns itself with cryptographic primitives for Secure Multi-Party Computations (MPC). MPC are joint computations of a set of parties which reveal the result of the computation to any party and nothing else. Every party should only learn information that can be calculated from its own input and the result. This thesis mainly deals with Oblivious Polynomial Evaluation (OPE), a subset of general MPC. OPE allows two parties to jointly evaluate a polynomial where the first party chooses the polynomial and learns nothing. The second party chooses the node and only learns the evaluated result of the polynomial at the chosen node. In addition to the evaluation of polynomials which is an obvious use case of OPE, OPE has many interesting applications, such as the share generation for Shamir's Secret Sharing. The methodology of this thesis also applies to the larger class of Secure Function Evaluation (SFE) which enables to securely evaluate arbitrary functions.

This thesis examines various approaches, leading to the novel result of a cryptographic protocol realizing OPE in linear time. The security of the methodology is proved in the Universal Composability (UC) framework which places very strict demands on the security of cryptographic protocols.

Alongside the theoretical debate, this thesis also features an efficient, secure and working implementation which manifests the properties of the protocol mentioned above.