Multiplier for Public-Key Cryptosystem Based on Cellular Automata - Computer Network Security - page 439

(a) Generalized modular multiplier (GM) (b) AOP modular multiplier (AM)

Fig. 1. Modular multiplier

Table 1. Comparison for modular multipliers

Item Function Number

of cells

Latency Hardware

Complexity

Critical
Path

Circuit

Chaudhury in
[3]

AB+C m m 2 m AND

2 m XOR
4m REG

AND+XOR

Kim in [5] AB m +1 2 m +1 ( m +1) AND

m XOR
2( m +1) REG

AND
+XOR(log 2 m )

AB+C m m

GM 2 m AND

2 m XOR
3 m REG

AND
+2 XOR

AM AB+C m +1 +1 m +1 AND

m +1 XOR
2( m +1) REG

AND+XOR

References

1. Reed, I. S. and Truong, T. K.: The use of finite fields to compute convolutions. IEEE Trans.
on Information Theory , IT-21 (Mar. 1975) 208-213
2. Neumann, V.: The theory of self-reproducing automata , Univ. of Illinois Press, Urbana
& London (1966)

3. Choudhury, P. Pal. and Barua, R.: Cellular Automata Based VLSI Architecture for Comput-
ing Multiplication and Inverses in GF(2 m ). IEEE 7 th International Conference on VLSI De-
sign , Jan. (1994)
4. Itoh, T. and Tsujii, S.: Structure of parallel multipliers for a class of finite fields GF(2 m ).
Info. Comp ., vol. 83 (1989) 21-40
5. Kim, H. S.: Bit-Serial AOP Arithmetic Architecture for Modular Exponentiation , Ph. D.
Thesis, Kyungpook National Univ. (2002)