Cryptographic hashing circuitry such as mining circuitry used to mine digital currency may be formed on an integrated circuit. The hashing circuitry may include sequential rounds of register and logic circuitry that perform operations of a cryptographic protocol. A final hash output from the hashing circuitry may be checked using a difficulty comparison circuit to determine whether the hash output satisfies predetermined difficulty criteria. The difficulty comparison circuit may be configured as a hardwired comparison circuit having logic gates for checking only a subset of bits in the hash output. The comparison circuit may be adapted to change the number of bits that is checked based on a target number of bits for comparison set by the Bitcoin protocol. Candidate solutions found using the hardwired comparison circuit may then be fed to a host controller that checks the entire hash output to determine whether the candidate solution is valid.