# SIMECK-T: An Ultra-Lightweight Encryption Scheme for Resource-Constrained Devices
## 2 Methodology
### Implementation
This level of protection is not achievable on the default 51-byte keystream size; a minimum of 1 KB is recommended according to the NIST statistical tests [24]. ### Performance Evaluation on Raspberry PICO

The PBKDF2 function with 65.000 iterations takes 7.572 milliseconds to run. For 30.000 iterations, it takes 3.494 milliseconds. For 10.000 iterations, it takes 1.165 milliseconds, and for 1.000 iterations, it takes 0.116 milliseconds. A single encryption in counter mode takes 0.00873 milliseconds and in electronic codebook mode 0.00327 milliseconds. By modifying the number of SIMECK rounds to five and the number of internal TEA rounds to seven, the following results are obtained:

A single encryption in counter mode takes \(1.038\times 10^{-2}\) milliseconds and in electronic codebook mode \(3.31\times 10^{-3}\) milliseconds. The PBKDF2 function with 65.000 iterations takes 10.422 milliseconds to run. For 30.000 iterations, it takes 4.810 milliseconds, and for 10.000 iterations, it takes 1.603 milliseconds. ## 5 Discussion

[PERSON] [94] estimates the strength of a key size based on the cost of breaking a DES [95] cipher key. The original name of this cipher is LUCIFER [96], having a key size of 128 bits. This key was reduced to 56 bits. Sufficient protection is defined as the cost involved in breaking the DES cipher in 1982, where \(y\) is the current year and \(\lambda\) is the key length. \[y(\lambda)=1982+\frac{3(\lambda-56)}{2} \tag{24}\]

\[\lambda(y)=56+\frac{2(y-1982)}{3} \tag{25}\]

Although outdated, [PERSON]'s law [97] is taken into account. According to Equation (24), \(y(80)=2018\), which means that 80-bit keys should no longer be used, starting with 2019. Equation (25) predicts that, for 2025, a minimum key size of \(\lambda(2025)=85\) bits is required. However, an 80-bit key can be accepted as a decent security level for IoT devices, as shown in the following analysis. The power of TOP500 [98] contains exascale-capable supercomputers. For a cryptographic cipher designer, this means, in the worst-case scenario, that such a machine can be used to brute force more than 1 quintillion passwords per second. For an 80-bit key size, this means that it can be recovered theoretically in \(2^{80}/2^{18}=2^{62}\) seconds. The measured performance in TOP500 [98] is for floating point operations in double precision. Simple operations like ARX ciphers can reasonably be expected to happen orders of magnitude \begin{table}
\begin{tabular}{c c c} \hline \hline
**Rounds** & **64 bit Blocks** & **Time (s)** \\ \hline
1 & 1,048,576 & 8.97 \\
2 & 1,048,576 & 17.84 \\
3 & 1,048,576 & 28.34 \\
4 & 1,048,576 & 35.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: TErrestrial Trunked RAdio (TETRA) TEA3 cipher performance across rounds with a keystream size of 1 KB. faster, and specialized hardware can be designed for even faster brute-forcing capacity. But the costs for such a computation simply outweighs any hopes for finding a needle in a \(2^{80}\) space. However, for such a key length to offer protection, the key values need to be random. The ASCII table has 95 printable characters, which means that, if the key is 10 bytes, each byte will be covered by 95 symbols instead of the full 256. A 95 symbol byte for a key size of 80 bits is 95\({}^{8}\) which lies between \(2^{52}\) and \(2^{53}\) practically reducing the key size to something easy to brute force. This is true when the symbols are placed with equal probability. If not, the actual search space for the key is smaller. A 96-bit key with 95 symbols means 95\({}^{12}\) possibilities which lie between \(2^{78}\) and \(2^{79}\) when the symbols have the same probability of appearing in the password. As a consequence, a tunable password derivation function is required to mitigate brute-force attacks. The number of rounds in the password derivation function could increase depending on the quality of the password and the current year [34].