## 6 Design of Seltape++
### Notations  
Table 4 contains the notations that will be used in the remainder of this study.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Name** & **Symbol** & **Description** \\ \hline Global Public Key of Server & \(GK_{pub}\) & TinyECC Public Cryptography library will be used. \\ Global Private Key of Server & \(GK_{Pri}\) & TinyECC Public Cryptography library will be used. \\ Asymmetric Signature & \(Sign_{key}(X)\) & Sign X with a key using an asymmetric algorithm (TinyECC). \\ Signature Verification & \(Verify_{SK}(X)\) & Denotes signature verification of value X with a key using an asymmetric algorithm (TinyECC). \\ Ceiling & \(\lceil x\rceil\) & Gives the smallest integer greater than or equal to \(x\). \\ Elliptic Curve Domain & \(T\) & \(T=(p,a,b,G,n,h)\). \\ ECDH Server Secret Key & \(d_{S}\) & A random number in the range of \([1,n-1]\). \\ ECDH Public Secret Key & \(d_{N}\) & A random number in the range of \([1,n-1]\). \\ ECDH Public Key of Server & \(Q_{S}\) & \(d_{S}G\) \\ ECDH Public Key of Node & \(Q_{N}\) & \(d_{N}G\) \\ Session Key & \(SK\) & \(d_{S}Q_{N}\ OR\ d_{N}Q_{S}\). It is the session key as introduced in Section 5. \\  & & in Section 5. \\ Byte Numbers of Shared Key & \(Z\) & Default is 24 = 192-bit, but for SkipJack, only \(Z=10\) bytes will be used. \\ \hline \hline \end{tabular}
\end{table}
Table 4: Notations. ECC, elliptic curve cryptography; MAC, message authentication code.  
\(\dagger\) This can be calculated using Equation (2):  
\[I=\left\lceil\frac{NPPP\times|H(.)|}{B-|MAC_{SK}(.)|}\right\rceil \tag{2}\]  
For Instance, having \(NPPP=48\) which is the default value in Deluge, \(B=92\), which is set to be the Seluge++ default payload size (discussed in Section 6.1) and \(|H(.)|=|MAC_{SK}(.)|=20\) bytes, if 160-bit SHA-1 is used for high-level security; a value of \(I\) will be populated as):  
\[I=\left\lceil\frac{48\times 20}{92-20}\right\rceil=\left\lceil 13.333\sim \right\rceil=14\;packets\]  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Name** & **Symbol** & **Description** \\ \hline Number of Hash Packets & \(I\) & Number of hash values in page 0 after MAC authentication is added to them \(\dagger\). \\ Version Number & \(V_{n}\) & Incremental number per each new version. \\ Nonce & \(N_{0}\ldots N_{n}\) & A random 160-bit number. \\ Number of Packets Per Page & \(NPPP\) & Default is 48. \\ SHA-1 Hash Bits & \(r\) & For example, \(r=160\) means SHA-1 160 bit. \\ Number of Bytes Per Packet & \(B\) & Payload size of a packet (default is 92, maximum is 102). \\ One-way Hash Function & \(H^{l}(X)orH^{l}(.)\) & Denotes the output of running a l-bit one-way hash function (H) on value X. \\  & & An l-bit one-way hash function of H on the value of V, which is repeated n times; \(H^{64}_{1}(V)=H^{64}(V)\;H^{64}_{2}=H^{64}(H^{64}_{1}(V))\;\) and so on. \\  & & This method is called message-specific puzzles and fully described in [16]. \\ Size & \(|X|\) & Denotes a size of \(X\) in bytes. \\ Symmetric Encryption & \(Enc^{l}_{sk}(X)\) & Symmetric encryption of X using an l-bit session key (SK). \\ Symmetric Decryption & \(Dec^{l}_{sk}(X)\) & Symmetric decryption of X using an l-bit session key (SK). \\ Message Authentication & \(MAC^{l}_{sk}(X)\) or & Denotes the generation of a message authentication code out of X with an l-bit shared key (SK) by using a keyed one-way hash function. \\ Packet Data & \{A,B,C\} & Means a packet with data variables of A, B and C. \\ Packet Pointer & Pkt[n] & n-\(th\) variable of a packet (\(n\geq 0\)). \\ Energy & \(E(x)\) & Denotes the energy required for an operation \(x\) to be completed on a mote in joules. \\ \hline \hline \end{tabular}
\end{table}
Table 4: _Cont._