This paper proves the unconditional security of quantum key distribution (QKD) protocols, specifically the Bennett and Brassard protocol from 1984. The proof considers a practical variation of the protocol where the channel is noisy and photons may be lost. The security is guaranteed against any possible attack, including those with unlimited computational power. The paper reviews basic principles of quantum key distribution and introduces a security criterion based on the Shannon entropy of the key conditional on Eve's view. It defines a privacy criterion where the key must be uniformly distributed, and provides a formal definition of f-private protocols. The paper also discusses the use of a fictive test lemma to analyze the security of the protocol and provides a privacy amplification technique to extract a smaller key from a nonprivate string. The paper concludes with a detailed analysis of the quantum model used to represent attacks against QKD protocols, including the use of POVM formalism and the separation of classical and quantum components in the protocol. The paper emphasizes the importance of understanding the connection between classical and quantum parts of the protocol to ensure the security of the key distribution.This paper proves the unconditional security of quantum key distribution (QKD) protocols, specifically the Bennett and Brassard protocol from 1984. The proof considers a practical variation of the protocol where the channel is noisy and photons may be lost. The security is guaranteed against any possible attack, including those with unlimited computational power. The paper reviews basic principles of quantum key distribution and introduces a security criterion based on the Shannon entropy of the key conditional on Eve's view. It defines a privacy criterion where the key must be uniformly distributed, and provides a formal definition of f-private protocols. The paper also discusses the use of a fictive test lemma to analyze the security of the protocol and provides a privacy amplification technique to extract a smaller key from a nonprivate string. The paper concludes with a detailed analysis of the quantum model used to represent attacks against QKD protocols, including the use of POVM formalism and the separation of classical and quantum components in the protocol. The paper emphasizes the importance of understanding the connection between classical and quantum parts of the protocol to ensure the security of the key distribution.