The BlockChain (BC) is considered as one of the most exciting developments in information and communication technology in the past decade and is widely known as a crypto intensive phenomenon. Achieving an efficient solution (e.g., decentralization, immutability, security, and transparency) using BC requires a considerable range of factors, such as: scalability, security, and privacy, which have a profound role in determining an overall solution’s performance. Meanwhile, digital auctioning is one of the cornerstones of the modern Internet economy. Many of the existing auctions are open-bid auction systems where all bids are made open to either party. E-auctions rely on human resources, and often require the services of a third-party intermediary, which leads to a high cost in terms of money and time, and there is no guarantee that the third party is trustworthy. Moreover, BC’s efficiency is a big challenge for large databases, particularly when the bidding system encompasses multiple options with geographically dispersed users. To address these issues, this paper proposes a BC-based framework for an open-bid auction system, for which privacy and security constraints are considered with different cryptographic primitives. The novelty of this framework derives from an enhanced approach for integrating BC structures by replacing the original chain structure with a tree structure. Throughout the online world, user privacy is a primary concern, because the electronic environment enables the collection of personal data. Hence this paper proposes a suitable cryptographic protocol for an open-bid auction atop BC. Here, the primary aim is to achieve security and privacy with greater efficiency, which largely depends on the effectiveness of the encryption algorithms used by BC. Essentially this paper considers Elliptic Curve Cryptography (ECC) and a dynamic cryptographic accumulator encryption algorithm to enhance security between auctioneer and bidder. The proposed e-bidding scheme and the findings from this study should foster further growth of BC strategies.