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We propose and define a recursive Merkle structure with q-mercurialcommitments, in order to create a concise B-Merkle tree. This Merkle B-Treebuilds on previous work of q-ary Merkle trees which use concise, constant size,q-mercurial commitments for intranode proofs. Although these q-ary trees reducethe branching factor and height, they still have their heights based on the keylength, and are forced to fixed heights. Instead of basing nodes on q-aryprefix trees, the B Merkle Tree incorporates concise intranode commitmentswithin a self-balancing tree. The tree is based on the ordering of elements,which requires extra information to determine element placement, but it enablessignificantly smaller proof sizes. This allows for much lower tree heights(directed by the order of elements, not the size of the key), and thereforecreates smaller and more efficient proofs and operations. Additionally, the BMerkle Tree is defined with subset queries that feature similar communicationcosts to non-membership proofs. Our scheme has the potential to benefitoutsourced database models, like blockchain, which use authenticated datastructures and database indices to ensure immutability and integrity of data.We present potential applications in key-value stores, relational databases,and, in part, Merkle forests.

Dynamic Merkle B-tree with Efficient Proofs