Radix-4 and Radix-8 Booth Encoded Multi-Modulus Multipliers

Novel multi-modulus designs capable of performing the desired modulo operation for more than one modulus in Residue Number System (RNS) are explored in this paper to lower the hardware overhead of residue multiplication. Two multi-modulus multipliers that reuse the hardware resources amongst the modulo 2
ⁿ
-1, modulo 2
ⁿ
and modulo 2
ⁿ
+1 multipliers by virtue of their analogous number theoretic properties are proposed. The former employs the radix- 2
²
Booth encoding algorithm and the latter employs the radix- 2
³
Booth encoding algorithm. In the proposed radix- 2
²
and radix- 2
³
Booth encoded multi-modulus multipliers, the modulo-reduced products for the moduli 2
ⁿ
-1, 2
ⁿ
and 2
ⁿ
+1 are computed successively. With the basis of the radix- 2
²
Booth encoded modulo 2
ⁿ
+1 and radix- 2
³
Booth encoded modulo 2
ⁿ
-1 and modulo 2
ⁿ
+1 multiplier architectures, new Booth encoded modulo 2
ⁿ
multipliers are proposed to maximally share the hardware resources in the multi-modulus architectures. Our experimental results on {2
ⁿ
-1,2
ⁿ
,2
ⁿ
+1} based RNS multiplication show that the proposed radix- 2
²
and radix- 2
³
Booth encoded multi-modulus multipliers save nearly 60% of area over the corresponding single-modulus multipliers. The proposed radix- 2
²
and radix- 2
³
Booth encoded multi-modulus multipliers increase the delay of the corresponding single-modulus multipliers by 18% and 13%, respectively in the worst case. Compared to the single-modulus multipliers, the proposed multi-modulus multipliers incur a minor power dissipation penalty of 5%.