Systems and Methods for Cryptography

A computer-implemented system comprising at least one processor and instructions executable by the at least one processor to cause the at least one processor to perform a maintainable Merkle-based vector commitment by performing operations comprising:

• a) computing a succinct batch proof of a subset of k leaves in a Merkle tree of n leaves using a recursive SNARK, wherein the recursive SNARK is run directly on Merkle paths belonging to elements in the batch to perform the computation of the subset hash inside the computation of the Merkle verification, by performing at least:
• i. verifying that the elements belong to the Merkle tree,
• ii. computing a batch hash for the elements in the batch using canonical hashing, and
• iii. making the batch hash part of a public statement;
• b) maintaining a data structure that stores previously computed recursive proofs;
• and
• c) updating the succinct batch proof, upon change of an element of the Merkle tree, in logarithmic time.

One or more non-transitory computer-readable storage media encoded with instructions executable by one or more processors to create an application for performing a maintainable Merkle-based vector commitment, the application comprising:

• a) a software module computing a succinct batch proof of a subset of k leaves in a Merkle tree of n leaves using a recursive SNARK, wherein the recursive SNARK is run directly on Merkle paths belonging to elements in the batch to perform the computation of the subset hash inside the computation of the Merkle verification, by operations comprising:
• i. verifying that the elements belong to the Merkle tree,
• ii. computing a batch hash for the elements in the batch using canonical hashing, and
• iii. making the batch hash part of a public statement;
• b) a software module maintaining a data structure that stores previously computed recursive proofs;
• and
• c) a software module updating the succinct batch proof, upon change of an element of the Merkle tree, in logarithmic time.

A computer-implemented method for providing parallelizable and updatable batch proofs in a decentralized network, the method comprising:

• a) accessing a first block added to a blockchain;
• b) computing a proof of the first block by computing a succinct batch proof of a subset of k leaves in a Merkle tree of n leaves using a recursive SNARK, wherein the subset of k leaves correspond to a subset of attestors of the decentralized network;
• and
• c) upon proofing the first block, issuing a token for the proof.