## 3 Benchmark Results
### Digital Signature Algorithms
#### 3.5.2 Energy Costs  
Figure 6 shows the energy costs of digital signature algorithms. The form of the graphic is the same as Figure 5 of temporal costs. We have measured the average consumed power induced by asymmetric cryptography operations and it is about 10% lower than that of symmetric cryptography. Thus, we conclude that the processor is not working so intensive. A study on how to better fit the code for ARM processors and improve the performance of asymmetric cryptography on PDAs can be successful, although it is out of the scope of this work. Results of other studies are coherent with ours in the sense that the relationship between the performances of the algorithms in each device is quite similar to what we have obtained in our target PDAs. However, in absolute values, results are very different due to the use of different processors. [PERSON] _et al._[5], using a StrongARM SA-1110 processor at 206 MHz, get: 546.5 mJ for RSA-1024 signature generation and 15.97 mJ for verification; 313.6 mJ for DSA-1024 signature generation and 338.02 mJ for verification; and 134.2 mJ for ECDSA signature generation and 196.23 mJ for verification. The only significant difference with our measurement is in ECDSA, where [5] get comparatively better results because they use a different elliptic curve over a binary field. Table 7 shows the expense of energy in MB/J of the analyzed signature algorithms. All the computations required to perform a signature and a verification over a message are included \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Sign**} & \multicolumn{3}{c}{**Verify**} \\ \cline{2-7}  & \(\Delta\) & MB/s (files I K) & MB/s (files I M) & \(\Delta\) & MB/s (files I K) & MB/s (files I M) \\ \hline
**RSA-512** & \(1.33\cdot 10^{-2}\) & \(1.50\cdot 10^{-1}\) & \(13.73\) & \(1.38\cdot 10^{-2}\) & \(5.33\cdot 10^{-1}\) & \(14.67\) \\ \hline
**RSA-1024** & \(1.08\cdot 10^{-2}\) & \(4.05\cdot 10^{-2}\) & \(11.06\) & \(1.38\cdot 10^{-2}\) & \(3.51\cdot 10^{-1}\) & \(14.47\) \\ \hline
**RSA-2048** & \(5.79\cdot 10^{-3}\) & \(9.56\cdot 10^{-3}\) & \(5.94\) & \(1.35\cdot 10^{-2}\) & \(1.84\cdot 10^{-1}\) & \(13.96\) \\ \hline
**DSA-512** & \(1.36\cdot 10^{-2}\) & \(2.22\cdot 10^{-1}\) & \(14.14\) & \(1.36\cdot 10^{-2}\) & \(2.05\cdot 10^{-1}\) & \(14.07\) \\ \hline
**DSA-1024** & \(1.25\cdot 10^{-2}\) & \(8.62\cdot 10^{-2}\) & \(12.88\) & \(1.22\cdot 10^{-2}\) & \(7.47\cdot 10^{-2}\) & \(12.60\) \\ \hline
**DSA-2048** & \(8.24\cdot 10^{-3}\) & \(1.88\cdot 10^{-2}\) & \(8.45\) & \(7.41\cdot 10^{-3}\) & \(1.49\cdot 10^{-2}\) & \(7.59\) \\ \hline
**ECDSA-112** & \(1.07\cdot 10^{-2}\) & \(3.90\cdot 10^{-2}\) & \(10.94\) & \(1.06\cdot 10^{-2}\) & \(3.87\cdot 10^{-2}\) & \(10.92\) \\ \hline
**ECDSA-160** & \(9.89\cdot 10^{-3}\) & \(3.03\cdot 10^{-2}\) & \(10.14\) & \(9.52\cdot 10^{-3}\) & \(2.71\cdot 10^{-2}\) & \(9.76\) \\ \hline
**ECDSA-224** & \(9.32\cdot 10^{-3}\) & \(2.55\cdot 10^{-2}\) & \(9.56\) & \(8.47\cdot 10^{-3}\) & \(2.00\cdot 10^{-2}\) & \(8.69\) \\ \hline
**BLS** & \(4.81\cdot 10^{-3}\) & \(5.90\cdot 10^{-3}\) & \(4.92\) & \(3.84\cdot 10^{-3}\) & \(4.51\cdot 10^{-3}\) & \(3.94\) \\ \hline
**BB** & \(1.98\cdot 10^{-2}\) & \(1.98\cdot 10^{-2}\) & \(20.24\) & \(6.11\cdot 10^{-3}\) & \(6.11\cdot 10^{-3}\) & \(6.25\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Digital Signature Performance (MB/s) in Hx2790. in the depicted graphics. The energy cost associated with the hash algorithm used in BLS is (\(165.81+0.03\cdot x\)) mJ, and the compression algorithm is 9.81 mJ. The most efficient signature algorithm is the BB short signature, closely followed by DSA and RSA algorithms using keys of 512 bits. The least energy-consuming verification algorithms are RSA using keys of 512 and 1,024 bits. Comparing with the energy costs of symmetric algorithms (see Figure 2) asymmetric cryptography is more expensive. In iPAQ3970 it is better working with asymmetric algorithms if input data is above 200 KB, while in the Hx2790 it should be above 400 KB.