The present invention contemplates a method or cryptographic
system for communicating securely over an insecure
communication channel of the type which communicates a message from a
transmitter to a
receiver. The method includes the step of providing a finite filed serial-serial multiplication / reduction structure wherein an initial
delay and
clock-cycle are inherently independent of
word length and wherein input operands are serially entered one digit at a time and the output result is computed serially one digit at a time, wherein the digit size can be one bit or more. As disclosed, the multiplication structure is scalable and a
serial transfer reduces the
bus width needed to transfer data back and forth between memory and a multiplication / reduction step. A finite field multiplication structure in which an
operand multiplication and a finite field reduction are formulated as a serial-serial computation is also disclosed. Further, a digit serial-serial finite field multiplication / reduction method and structure as an integral operation in a cryptographic
system is disclosed. In such methods and structures, the inherent
word length independence of the initial
delay is achieved by defining both
operand multiplication and field reduction as serial-serial computation. In such computations, all of the numbers needed for the computation are fed serially one digit at a time. Therefore, the inter-connection between the
memory module and the multiplier module need only to support the transfer of data one digit at a time.