Abstract: The present disclosure relates to methods of mining a block of a distributed ledger. The methods include: receiving a block to be mined, the block including a header hash and a plurality of transactions; creating a first signature based on a first function, where inputs to the first function include the header hash and the plurality of transactions; and creating a second signature based on a second function, where an input to the second function is the first signature. In one example, the second function is a multiplicative inverse function and the method further includes creating the second signature that is a multiplicative inverse value of the first signature with respect to a first irreducible polynomial. The method additionally includes creating a chain of signatures, where each of the signatures is a multiplicative inverse value of a previous output with respect to a respective irreducible polynomial.

Abstract: The present disclosure relates to methods of mining a block of a distributed ledger. The methods include: receiving a block to be mined, the block including a header hash and a plurality of transactions; creating a first signature based on a first function, where inputs to the first function include the header hash and the plurality of transactions; and creating a second signature based on a second function, where an input to the second function is the first signature. In one example, the second function is a multiplicative inverse function and the method further includes creating the second signature that is a multiplicative inverse value of the first signature with respect to a first irreducible polynomial. The method additionally includes creating a chain of signatures, where each of the signatures is a multiplicative inverse value of a previous output with respect to a respective irreducible polynomial.

Abstract: The present disclosure relates to a digital data management system implemented, at least in part, on a server, where the server includes: one or more processors; non-transitory computer-readable media storing instructions executable by the one or more processors to perform operations including: receives a request to sell a digital asset; generating one or more sale offer terms associated with the request to sell the digital asset; receiving an offer to purchase the digital asset from a prospective buyer; verifying that the offer to purchase the digital asset conforms to the one or more sale offer terms; facilitating the purchase of the digital asset at least in part by executing a smart contract on a distributed ledger, the smart contract including at least one self-executing term; and storing information associated with the sale of the digital asset in the distributed ledger.