Privacy is a key feature in the successful adoption of Central Bank Digital Currency (CBDC). However, ensuring privacy in this disruptive innovation, particularly in offline payments, presents several challenges. Due to the nature of offline transactions, where one or both parties may not be immediately linked to a central network, security must be guaranteed with the utmost reliability. This study focuses on the development of an innovative protocol for Central Bank Digital Currencies, ensuring privacy and security for offline payments. The foundation of this protocol makes use of blind signature technology, a method that keeps a message's content secret from the signer and upholds the privacy of transaction Data. The zk-SNARK (Zero-knowledge Succint Non-interactive Argument of Knowledge) protocol, which assures that transactions are both private and verifiable without necessitating interaction between the prover and verifier, provides a complement to this. By leveraging blind signature technology and the zk-SNARK protocol, we explore how to overcome privacy-related challenges in retail CBDC while ensuring resilience against quantum attacks.