# SIMECK-T: An Ultra-Lightweight Encryption Scheme for Resource-Constrained Devices
## 2 Methodology
### Implementation
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**SIMECK** & **SIMON** & **SPECK** & **TEA** & **XTEA** & **XXTEA** & **Rounds** \\
**9** & **9** & **9** & **9** & **9** & **9** & 1 \\
**9** & **9** & **9** & **9** & **9** & **9** & **2** \\
8 & 10 & 6 & 8 & 6 & 7 & 3 \\
9 & 10 & 3 & 9 & 0 & 1 & 4 \\
9 & 7 & 5 & 0 & 0 & 0 & 5 \\
8 & 7 & 1 & 0 & 0 & 0 & 6 \\
9 & 5 & 0 & 0 & 0 & 0 & 7 \\
9 & 5 & 0 & 0 & 0 & 0 & 8 \\
8 & 1 & 0 & 0 & 0 & 0 & 9 \\
7 & 1 & 0 & 0 & 0 & 0 & 10 \\
7 & 0 & 0 & 0 & 0 & 0 & 11 \\
6 & 0 & 0 & 0 & 0 & 0 & 12 \\
2 & 0 & 0 & 0 & 0 & 0 & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: AIS.31 Statistical Test Suite—number of failed randomness tests for full round ciphers (lower is better). 10000 have been used for the SIMECK-T cipher using a fixed number of SIMECK-3 and TEA-5 rounds. That is, the \(pmul\) and \(psum\) variables in Algorithm 1 have been forced to zero. The total variance (TV), the Hellinger distance (HD), and the root mean square deviation (RMSD) show values lower than the required limit for true random data, which means that SIMECK-T passes all tests. For random data obtained with the OneRNG true random number generator (TRNG) [91], TV is 0.05325 \(<\) 0.09161, HD is 0.04715 \(<\) 0.08054 and RMSD is 0.00306 \(<\) 0.00607 for 1000 sequences. Table 5 presents the minimal number of rounds that are necessary for each cipher, augmented or not, to pass the LIL test. SIMECK-R is once again the best cipher, showing that SIMECK is the best candidate for augmentation into a reduced round lightweight cipher. ### Cipher Strength Analysis

#### 4.2.1 Avalanche Effect

SIMECK-T fails 0 tests from the NIST Statistical Test Suite [71] and the AIS.31 test suite [72]. It also passes the randomness tests of other known test suites like Dieharder [92] and ENT [93]. Tables 6 and 7 show the avalanche effect and the time required to compute the round function using various numbers of rounds. It can be observed that, on average, half of the bits are flipped when only 1 input bit is modified. This shows that the two ciphers have good avalanche properties. Figure 2: Density function from the output of SIMECK-T. \begin{table}
\begin{tabular}{c c c c c c} \hline SIMECK & SIMON & SPECK & TEA & XTEA & XXTEA \\
16 & 11 & 4 & 6 & 4 & 5 \\ \hline \(1\) & 7 & 4 & 4 & 3 & 5 \\ SIMECK-R & SIMON-R & SPECK-R & TEA-R & XTEA-R & XXTEA-R \\ \hline \end{tabular}
\end{table} 
Table 5: Law of iterated logarithm—minimal number of rounds for passing. #### 4.2.2 Linear Cryptanalysis

Given a sufficiently large number of random samples, a secure cryptosystem will produce a bias closer to 0%. Table 8 shows the results obtained for large numbers of pairs (plaintext, ciphertext), with a percentage bias that converges to 0%. The largest pool of pairs randomly sampled is \(2^{32}\) using memory-mapped files for hash tables. The goal is to identify suspect bit-level linear relationships between the input and the output of the cipher. An interesting pattern in Table 8 would require finding a bias that is not close to zero--no interesting pattern has been found, suggesting that the encryption scheme is resistant to linear trails. A randomly generated key is kept constant during statistical searches, so that any pattern has a sufficiently large collection of pairs to surface. #### 4.2.3 Differential Cryptanalysis

The results in Table 9 show the frequency of appearance and the respective percentage for differential trails using different attack strategies. For an ARX cipher, rotational, additive, and XOR-based differences are expected to trigger a pattern. However, our results show that OR- and AND-based operations are more susceptible to producing trails. This may be due to the external rounds of SIMECK, but we expect that most trails are canceled by performing the XOR operation with a constant inside the TEA inner rounds.