With the widespread application of blockchain technology, authenticated storage, as its core component, plays an important role in ensuring data integrity and consistency. In traditional blockchain systems, authenticated storage verifies transactions and maintains the integrity of ledger status through a series of cryptographic algorithms. However, the emergence of quantum computers has made the existing blockchain authenticated storage technology face the threat of being cracked, which makes blockchain face the risk of data leakage and integrity damage. The most advanced authenticated storage technology is mainly based on the bilinear Diffie-Hellman assumption, which may become vulnerable to quantum attacks. In order to improve the security and efficiency of authenticated storage, this paper introduces a stateless hash signature technology and proposes a quantum-resistant blockchain authenticated storage scheme EQAS. This scheme decouples data storage and data authentication, uses random forest chains to efficiently generate commitment proofs, and performs efficient authentication through a hypertree structure. Security analysis shows that EQAS can resist attacks from quantum algorithms. By comparing with other authenticated storage schemes, experimental results verify the efficiency of the EQAS scheme and show its excellent performance in processing blockchain authenticated storage tasks.