This paper presents a simplified proof of the security of the BB84 quantum key distribution protocol. The authors first describe an entanglement purification protocol based on Calderbank-Shor-Steane (CSS) codes, which can be proven secure using methods from Lo and Chau's proof. They then show that the security of this protocol implies the security of BB84. The security of BB84 relies on the fact that quantum states cannot be simultaneously measured in two conjugate bases, making it impossible for an eavesdropper to obtain information without being detected. The BB84 protocol involves Alice and Bob agreeing on a secret key, with Alice sending each bit of the key in one of two conjugate bases. The security of BB84 has been proven against certain attacks, but not against all possible quantum attacks. The authors provide a simpler proof by relating the security of BB84 to entanglement purification protocols and quantum error correcting codes. The paper explains CSS codes and their use in entanglement purification. These codes are subspaces of the Hilbert space that protect against errors in a small number of qubits. The security of BB84 is demonstrated by showing that the error correction for phases is decoupled from that for bit values. This allows for the correction of both bit and phase errors, ensuring that the encoded state remains protected. The authors also describe a modified Lo-Chau protocol and a CSS code-based protocol, both of which are shown to be equivalent to BB84. The security of these protocols relies on the fact that for a sufficiently low error rate, a CSS code transmits the information encoded by it with very high fidelity, making it impossible for an eavesdropper to obtain significant information. The paper concludes by noting that while the proofs provided are secure against certain types of attacks, they require perfect single-photon sources. A more recent proof by Ben-Or shows that any source sufficiently close to a single-photon source is still secure. However, most experimental quantum key distribution systems use weak coherent sources, and no currently known proof covers this case. The authors thank several colleagues for their contributions to the security proofs.This paper presents a simplified proof of the security of the BB84 quantum key distribution protocol. The authors first describe an entanglement purification protocol based on Calderbank-Shor-Steane (CSS) codes, which can be proven secure using methods from Lo and Chau's proof. They then show that the security of this protocol implies the security of BB84. The security of BB84 relies on the fact that quantum states cannot be simultaneously measured in two conjugate bases, making it impossible for an eavesdropper to obtain information without being detected. The BB84 protocol involves Alice and Bob agreeing on a secret key, with Alice sending each bit of the key in one of two conjugate bases. The security of BB84 has been proven against certain attacks, but not against all possible quantum attacks. The authors provide a simpler proof by relating the security of BB84 to entanglement purification protocols and quantum error correcting codes. The paper explains CSS codes and their use in entanglement purification. These codes are subspaces of the Hilbert space that protect against errors in a small number of qubits. The security of BB84 is demonstrated by showing that the error correction for phases is decoupled from that for bit values. This allows for the correction of both bit and phase errors, ensuring that the encoded state remains protected. The authors also describe a modified Lo-Chau protocol and a CSS code-based protocol, both of which are shown to be equivalent to BB84. The security of these protocols relies on the fact that for a sufficiently low error rate, a CSS code transmits the information encoded by it with very high fidelity, making it impossible for an eavesdropper to obtain significant information. The paper concludes by noting that while the proofs provided are secure against certain types of attacks, they require perfect single-photon sources. A more recent proof by Ben-Or shows that any source sufficiently close to a single-photon source is still secure. However, most experimental quantum key distribution systems use weak coherent sources, and no currently known proof covers this case. The authors thank several colleagues for their contributions to the security proofs.