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 value output by the hashing circuitry may include hash values stored at previous rounds of the cryptographic hashing circuitry. The hashing circuitry may be formed with only two registers per round, thereby optimizing chip area consumption. The hashing circuitry may perform sequential rounds of cryptographic hashing based on an initial hash value and multiple message words. One or more message registers may store the message words. Control circuitry may selectively route the message words from the message register to the hashing circuitry using pointers. If desired, the message registers may be replaced by one or more arrays of memory elements read using row and column pointers.