# SIMECK-T: An Ultra-Lightweight Encryption Scheme for Resource-Constrained Devices
## 2 Methodology
### Implementation
For example, the full-round SIMECK cipher is 44 rounds, SIMON is 42 rounds, SPECK is 26 rounds, and the TEA family is 32 rounds. All have been carefully analyzed both in original form and with the substitution boxes inserted for SIMECK-R, SIMON-R, SPECK-R, TEA-R, XTEA-R, and XXTEA-R starting from round 1 until the full version. It is quite obvious that substitution boxes using the SPECK-R strategy [19] produce fewer failures in reduced-round versions of the ciphers. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**SIMECK** & **SIMON** & **SPECK** & **TEA** & **XTEA** & **XXTEA** & **Rounds** \\ \hline
187 & 186 & 188 & 187 & 163 & 169 & 1 \\ \hline
186 & 186 & 187 & 187 & 164 & 163 & 2 \\
175 & 165 & 187 & 164 & 158 & 161 & 3 \\ \hline
170 & 165 & 23 & 22 & 3 & 20 & 4 \\ \hline
170 & 161 & 92 & 1 & 2 & 4 & 5 \\
170 & 161 & 7 & 0 & 3 & 0 & 6 \\ \hline
168 & 159 & 0 & 1 & 1 & 1 & 7 \\ \hline
161 & 159 & 0 & 0 & 0 & 1 & 8 \\
163 & 6 & 1 & 0 & 0 & 0 & 9 \\
161 & 6 & 2 & 1 & 2 & 3 & 10 \\ \hline
162 & 0 & 0 & 0 & 1 & 0 & 11 \\
160 & 0 & 3 & 0 & 0 & 1 & 12 \\
61 & 0 & 1 & 2 & 0 & 0 & 13 \\
11 & 0 & 0 & 2 & 0 & 0 & 14 \\ \hline \end{tabular}
\end{table} 
Table 1: NIST Statistical Test Suite—number of failed randomness tests for full round ciphers (lower is better). \begin{table}
\begin{tabular}{c c c c c c c} \hline
**XXTEA-R** & **TEA-R** & **SIMECK-R** & **SIMON-R** & **SPECK-R** & **XTEA-R** & **Rounds** \\ \hline
167 & 172 & 0 & 160 & 161 & 163 & 1 \\ \hline
165 & 165 & 1 & 161 & 158 & 53 & 2 \\
10 & 12 & 1 & 159 & 107 & 0 & 3 \\ \hline
3 & 2 & 0 & 158 & 1 & 3 & 4 \\ \hline
1 & 0 & 0 & 2 & 2 & 0 & 5 \\ \hline \end{tabular}
\end{table} 
Table 2: NIST Statistical Test Suite—the number of failed randomness tests for reduced round ciphers (lower is better). The SPECK and SIMON ciphers are used with a 64-bit block size and a key length of 96 bits just as the original SPECK-R cipher [19]. SIMECK has a 64-bit block size and a key length of 128 bits, just like the TEA family of ciphers. It can be observed that the best cipher in terms of producing random output using as few rounds as possible is SIMECK-R, according to the data in Tables 2 and 4. This cipher is going to be used in order to compare it with SIMECK-T.

#### 4.1.3 Analysis with the Law of Iterated Logarithm

For resources-constrained devices, the SIMECK-R dynamic substitution boxes are an obvious bottleneck. Not only must the three tables be memorized and exchanged based on certain thresholds, but each table takes 1024 bits, which may not be affordable for medical implants and other healthcare devices, or even for mass production in smart agriculture systems. The proposed SIMECK-T cipher has none of these problems when at least 18 rounds are used (3 rounds of SIMECK each containing 5 rounds of TEA). Although standardized randomness tests are a norm for validating the output of ciphers [88], it has been shown, with an emphasis on the NIST statistical tests [24], that weak ciphers can also successfully pass them [89]. In order to further investigate the randomness of the SIMECK-T output, the law of the iterated logarithm (LIL) suggested by [PERSON] as a stronger validation was used [27; 28]. Figure 2 shows that the density function for the output of SIMECK-T closely follows the expected curve. The results have been generated using the Java tool developed by [PERSON] [89; 90]. A minimum of 1000 sequences is recommended for accurate testing and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**XXTEA- R** & **TEA- R** & **SIMECK- R** & **SIMON- R** & **SPECK- R** & **XTEA- R** & **Rounds** \\
**9** & **9** & 0 & 6 & 7 & 8 & 1 \\
2 & 2 & 0 & 3 & 3 & 0 & 3 \\
0 & 0 & 0 & 2 & 0 & 0 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: AIS.31 Statistical Test Suite—number of failed randomness tests for reduced round ciphers (lower is better).