This dissertation presents a comprehensive analysis of the security of quantum key distribution (QKD), a method for securely exchanging cryptographic keys over quantum channels. The research introduces new concepts in quantum information theory, including smooth min- and max-entropies, which generalize the von Neumann entropy and provide a framework for quantifying uncertainty in quantum systems. These tools are essential for analyzing the security of QKD protocols, particularly in scenarios where the independence assumptions of traditional information-theoretic methods do not hold. The dissertation develops a quantum version of de Finetti's representation theorem, which allows the analysis of symmetric quantum states. This theorem is crucial for understanding the behavior of quantum systems with high symmetry and is used to show that collective attacks—where an adversary applies the same operation to each particle—suffice for the security analysis of QKD. This result implies that the security of QKD protocols can be analyzed using these simplified attack models, which are easier to handle than more general attacks. The security of QKD is proven using these tools, showing that the protocols are secure against arbitrary attacks under a universal security definition. This definition ensures that the generated keys can be safely used in any application, such as one-time pad encryption, which is not guaranteed by many standard security definitions. The dissertation also provides explicit bounds on the efficiency of QKD protocols, including improved versions of existing protocols like the six-state protocol and the BB84 protocol. The research addresses practical implementations of QKD, considering imperfections in real-world systems, such as noisy channels and faulty detectors. It shows that the security results apply to these practical scenarios, ensuring that the keys generated can be used reliably. The dissertation also discusses the security of privacy amplification against quantum adversaries, demonstrating that the smooth min-entropy provides a robust measure for quantifying the secrecy of keys. Overall, the dissertation contributes to the understanding of quantum information theory and cryptography, providing a solid foundation for the security analysis of QKD protocols and their practical applications.This dissertation presents a comprehensive analysis of the security of quantum key distribution (QKD), a method for securely exchanging cryptographic keys over quantum channels. The research introduces new concepts in quantum information theory, including smooth min- and max-entropies, which generalize the von Neumann entropy and provide a framework for quantifying uncertainty in quantum systems. These tools are essential for analyzing the security of QKD protocols, particularly in scenarios where the independence assumptions of traditional information-theoretic methods do not hold. The dissertation develops a quantum version of de Finetti's representation theorem, which allows the analysis of symmetric quantum states. This theorem is crucial for understanding the behavior of quantum systems with high symmetry and is used to show that collective attacks—where an adversary applies the same operation to each particle—suffice for the security analysis of QKD. This result implies that the security of QKD protocols can be analyzed using these simplified attack models, which are easier to handle than more general attacks. The security of QKD is proven using these tools, showing that the protocols are secure against arbitrary attacks under a universal security definition. This definition ensures that the generated keys can be safely used in any application, such as one-time pad encryption, which is not guaranteed by many standard security definitions. The dissertation also provides explicit bounds on the efficiency of QKD protocols, including improved versions of existing protocols like the six-state protocol and the BB84 protocol. The research addresses practical implementations of QKD, considering imperfections in real-world systems, such as noisy channels and faulty detectors. It shows that the security results apply to these practical scenarios, ensuring that the keys generated can be used reliably. The dissertation also discusses the security of privacy amplification against quantum adversaries, demonstrating that the smooth min-entropy provides a robust measure for quantifying the secrecy of keys. Overall, the dissertation contributes to the understanding of quantum information theory and cryptography, providing a solid foundation for the security analysis of QKD protocols and their practical applications.