With the widespread application of blockchain technology, authenticated storage, as a core component, plays a crucial role in ensuring data integrity and consistency. In traditional blockchain systems, authenticated storage is maintained through a series of cryptographic algorithms, which verify transactions and preserve the integrity of ledger states. However, the advent of quantum computers has introduced a significant threat to existing blockchain authentication storage technologies, raising the risk of data breaches and compromised integrity. The most advanced authenticated storage schemes primarily rely on the bilinear Diffie-Hellman assumption, which is susceptible to quantum attacks. To enhance the security and efficiency of authenticated storage, this paper introduces a stateless hash signature mechanism and proposes the quantum-resistant blockchain authenticated storage scheme EQAS. The proposed scheme decouples data storage from data authentication, utilizes random forest chains to efficiently generate commitment proofs, and employs a hyper tree structure to perform efficient authentication. Security analyses show that EQAS is resistant to quantum algorithm attacks. Comparative experiments with other authenticated storage schemes demonstrate the superior efficiency and performance of EQAS in handling blockchain authentication storage tasks.