This dissertation, submitted to the Swiss Federal Institute of Technology Zurich for the degree of Doctor of Natural Sciences, focuses on the security of Quantum Key Distribution (QKD). The author, Renato Renner, introduces new concepts and results in quantum information theory, particularly in the context of QKD. Key contributions include: 1. **New Entropy Measures**: The introduction of smooth min- and max-entropies, which are generalizations of the von Neumann entropy, to quantify uncertainty in quantum systems. 2. **De Finetti Representation Theorem**: A finite version of the quantum de Finetti representation theorem for symmetric states, which helps in analyzing the security of QKD protocols. 3. **Universal Security Definition**: A universal security definition for secret keys that guarantees the keys can be used in any application, except with a negligible probability. 4. **Security of QKD**: A generic security proof for QKD protocols, showing that it is sufficient to consider collective attacks where the adversary applies the same operation to each particle sent over the quantum channel. 5. **Improved Bounds**: Explicit bounds on the secrecy and length of keys generated from finite invocations of the quantum channel, applicable to practical implementations with noisy channels. The dissertation also discusses the implications of these results, including the security of practical QKD implementations, the ability to use keys generated by QKD in applications like one-time pad encryption, and improved bounds on the efficiency of concrete QKD protocols. The work is supported by the Swiss National Science Foundation.This dissertation, submitted to the Swiss Federal Institute of Technology Zurich for the degree of Doctor of Natural Sciences, focuses on the security of Quantum Key Distribution (QKD). The author, Renato Renner, introduces new concepts and results in quantum information theory, particularly in the context of QKD. Key contributions include: 1. **New Entropy Measures**: The introduction of smooth min- and max-entropies, which are generalizations of the von Neumann entropy, to quantify uncertainty in quantum systems. 2. **De Finetti Representation Theorem**: A finite version of the quantum de Finetti representation theorem for symmetric states, which helps in analyzing the security of QKD protocols. 3. **Universal Security Definition**: A universal security definition for secret keys that guarantees the keys can be used in any application, except with a negligible probability. 4. **Security of QKD**: A generic security proof for QKD protocols, showing that it is sufficient to consider collective attacks where the adversary applies the same operation to each particle sent over the quantum channel. 5. **Improved Bounds**: Explicit bounds on the secrecy and length of keys generated from finite invocations of the quantum channel, applicable to practical implementations with noisy channels. The dissertation also discusses the implications of these results, including the security of practical QKD implementations, the ability to use keys generated by QKD in applications like one-time pad encryption, and improved bounds on the efficiency of concrete QKD protocols. The work is supported by the Swiss National Science Foundation.