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.