the modular exponentiation function used in public key encryption and decryption systems is implemented in a standalone engine having at its core modular multiplication circuits which operate in two phases which share overlapping hardware structures . the partitioning of large arrays in the hardware structure , for multiplication and addition , into smaller structures results in a multiplier design comprising a series of nearly identical processing elements linked together in a chained fashion . as a result of the two - phase operation and the chaining together of partitioned processing elements , the overall structure is operable in a pipelined fashion to improve throughput and speed . the chained processing elements are constructed so as to provide a partitionable chain with separate parts for processing factors of the modulus . in this mode , the system is particularly useful for exploiting characteristics of the chinese remainder theorem to perform rapid exponentiation operations . a checksum mechanism is also provided to insure accurate operation without impacting speed and without significantly increasing complexity . while the present disclosure is directed to a complex system which includes a number of features , the present application is particularly directed a system and method for performing modular checksum operations .