This book presents a complete and accurate study of algebraic circuits, digital circuits whose performance can be associated with any algebraic structure. The authors distinguish between basic algebraic circuits, such as Linear Feedback Shift Registers (LFSRs) and cellular automata and algebraic circuits, such as finite fields or Galois fields. The book includes a comprehensive review of representation systems, of arithmetic circuits implementing basic and more complex operations and of the residue number systems (RNS). It presents a study of basic algebraic circuits such as LFSRs and cellular automata as well as a study of circuits related to Galois fields, including two real cryptographic applications of Galois fields.1 output bits of the adder are stored in r2n-1 ...rn-1 (recall that r n-1 is the serial input of the shift register and, in each iteration there is a shift to the right ... As an example, the results generated in the four iterations by multiplying the 4-bit numbers ... This circuit can be transformed into another allowing that M could be multiplied by more than one bit of the multiplier in each iteration. ... Thus, using two 8-bit parallel adders, this multiplication can be implemented, as shown in the same Fig.
|Author||:||Antonio Lloris Ruiz, Encarnación Castillo Morales, Luis Parrilla Roure, Antonio García Ríos|
|Publisher||:||Springer Science & Business Media - 2014-04-05|