Table 2 Comparison of computational complexity (\(s = \frac{n}{2}\)).
From: Optimized quantum folding Barrett reduction for quantum modular multipliers
Algorithm | Multiplication \(\{times[bits]\}\) | Addition/Subtraction \(\{times[bits]\}\) |
|---|---|---|
General Barrett Reduction | \(1 [(2s+1)\times (2s+1)]\) | \(1 [(2s+1)-(2s+1)]\) |
\(1 [(2s+1)\times 2s]\) | \(1 [(2s+2)-(2s+2)]\) | |
| Â | \(1 [(2s+2)+(2s+2)]\) | |
Folding Barrett Reduction | \(1 [s\times 2s]\) | \(1 [3s+3s]\) |
\(1 [(s+1)\times (s+1)]\) | \(1 [(2s+1)-(2s+1)]\) | |
\(1 [(s+2)\times 2s]\) | \(3 [(2s+2)-(2s+2)]\) | |
| Â | \(1 [(2s+2)+(2s+2)]\) | |
Optimized Folding Barrett Reduction | \(1 [s\times 2s]\) | \(1 [3s+3s]\) |
\(1 [(s+3)\times (s+4)]\) | \(1 [(2s+1)-(2s+1)]\) | |
\(1 [(s+2)\times 2s]\) | \(3 [(2s+2)-(2s+2)]\) | |
| Â | \(1 [(2s+2)+(2s+2)]\) |
