## 3 A New Dual-Rail-Based Power-Balancing Countermeasure without Look-Up Tables
### Constant ADD Operation
However, our method exhibits advantages in the multi-bit KS adder. [PERSON]'s KS adder cannot handle the carry bit of a lower word, and it was used only in a least significant word. To process \(n\) words, [PERSON]'s multi-bit adder required a total of \((n+1)\) KS adders, where the number of [PERSON]'s KS adders is \(1\) and the number of [PERSON]'s KS adders is \(n\). On the other hand, our method required a total of \(n\) KS adders, where the number of [PERSON]'s KS adders is \(1\) and the number of our KS adders is \((n-1)\). Furthermore, [PERSON]'s multi-bit adder requires conversion of the input and output between normal and decimal representations. ### SIMON/SPECK Block Cipher

The SIMON and SPECK families were developed for content security on constrained devices by a group of researchers at the US National Security Agency's Research Directorate [26]. The SIMON block cipher consists of only AND, ROTATION, and XOR operations. The SPECK block cipher consists of an ARX (ADD, ROTATION, and XOR) structure. We implemented SIMON and SPECK using the constant AND and ADD, and we compared the performance with the ARM simulator. Table 8 presents the ARM simulation results. The 32-bit coding is implemented using 32-bit long type registers, and the 8-bit coding is implemented using 8-bit char type registers. Because the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Operator** & **Ours** & **Coron’s** & **Won’s** \\ \hline ine [ConstAND] & & & \\ XOR & 2 & N/A & N/A \\ AND & 2 & N/A & N/A \\ OR & 2 & N/A & N/A \\ ine [KS algorithm] & & & \\ XOR & \(l+6\) & \(l+2\) & \(l+3\) \\ AND & \(2l+1\) & \(2l+1\) & \(2l+1\) \\ SHIFT & \(4l\) & \(4l\) & \(4l\) \\ ine [PB KS algorithm] & & & \\ XOR & \(5l+6\) & \(5l+3\) & \(5l+4\) \\ ConstAND(\# of operator) & \(2l\) (\(12l\)) & \(2l\) (\(12l\)) & \(2l\) (\(12l\)) \\ SHIFT & \(4l\) & \(4l\) & \(4l\) \\ ine [Multi-bit adder] & & & \\ Coron’s KS adder & 1 & N/A & 1 \\ Ours KS adder & \(n-1\) & N/A & - \\ Won’s KS adder & - & N/A & \(n\) \\ e.t.c. & - & N/A & Line 3, 4, 9, 11 \\ ine [PB Multi-bit adder] & & & \\ XOR & \(5 nl+6n-3\) & N/A & \(5 nl+4n+5l+3\) \\ ConstAND(\# of operator) & \(2 nl\) (\(12 nl\)) & N/A & \(2 nl+2l\) (\(12 nl+12l\)) \\ SHIFT & \(4 nl\) & N/A & \(4l\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the total number of operations. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Ours** & **Coron’s** & **Won’s** \\ \hline KS alg. \((k=8)\) & 76 & 68 & 72 \\ PB KS alg. \((k=8)\) & 277 & 270 & 274 \\ Multi-bit adder \((k=8,n=4)\) & 340 & N/A & 485 \\ PB Multi-bit adder \((k=8,n=4)\) & 1,133 & N/A & 1,603 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of the total number of operations 2. SPECK block cipher required 32-bit additions, these additions also used 32-bit additions even with the 8-bit coding. The nonlinear functions of the SIMON block cipher include AND operators. We implemented the protected SIMON cipher with [PERSON]'s method-1 and our ConstAND. As a result, it was found that our method demonstrated a performance improvement of 33% compared to [PERSON]'s method-1. This difference in performance was because [PERSON]'s method-1 handles a codeword in small LUT units, whereas our method processes the entire codeword. The nonlinear functions of the SPECK cipher include ADD operators. We implemented this cipher with four 32-bit codewords based on 1-to-4 encoding. As a result, our method demonstrated a performance improvement of 37% compared to [PERSON]'s method. The biggest reason for the difference in performance is that our method includes 4 times the number of KS adders, whereas [PERSON]'s method includes 5 times the number of KS adders for protected addition. ## 6 Conclusions

In this paper, we proposed power-balancing methods without LUTs. We designed new constant AND and ADD operations based on 1-to-4 encoding. We also evaluated the side-channel security on a real board and assessed the performance based on the number of operators and simulation results.