A system generates a randomized hash value and/or verifies data against a randomized hash value. A hashing circuit can respond to data by randomly selecting a hashing algorithm parameter among a defined set of different hashing algorithm parameters, and by applying a hashing algorithm that uses the selected hashing algorithm parameter to hash the received data to generate a randomized hash value. Another hashing circuit randomly selects a hashing algorithm among a defined set of different hashing algorithms, and applies the selected hashing algorithm to hash the received data to generate a randomized hash value. Another hashing circuit applies a hashing algorithm to hash received data to generate an intermediate hash value that occupies a defined memory space, and randomly selects a partial segment of the hash value from a segment of the defined memory space to generate a randomized hash value.