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.