# Extending the Quality of Secure Service Model to Multi-Hop Networks
## 2 Related Work
Rather than quantify confidentiality directly, the probability of confidentiality is quantified as a surrogate. The probability of confidentiality, \(P(C)\), is related to another new metric, the probability of leakage, \(P(l)\), as follows:  
\[P(C)=1-P(l). \tag{1}\]  
For leakage to occur, a listener must intercept a message, decrypt it (if applicable), and decode the data contained in the message. The probability of interception, \(P(int)\), quantifies the probability that a listener with channel access will receive the message. The probability of decryption, \(P(dcr)\), quantifies the probability that the adversary will decrypt it. Finally, the probability of decoding, \(P(dco)\), quantifies the probability that an adversary will decode the message. Similarly, the probability of integrity is quantified instead of attempting to quantify integrity directly. The probability of integrity, \(P(I)\), is related to the probability of corruption, \(P(c)\), as follows:  
\[P(I)=1-P(c). \tag{2}\]  
According to [19], and followed in [4], corruption is considered to have three components: noise, active data injection, and data suppression. The probability of noise occurring in a message, \(P(n)\), is the probability that a message will be adversely affected by noise. Noise is a natural phenomenon that happens regardless of the transmitter's capability. The probability of injection, \(P(inj)\), quantifies the probability that an adversary will inject false or misleading data into the message. Finally, the probability of suppression, \(P(s)\), quantifies the probability that an adversary will actively suppress or jam the message, thus preventing the receiver from getting the message. This point is somewhat unconventional with respect to the generally accepted concept that suppression, specifically DoS attacks on a network, influence the availability of a network. While true that a DoS attack on a network affects the availability of the network, the active adversarial contamination of a network by injecting so much false data to disable communications, as is the case with a traditional DoS attack, or to overtly jamming a network signal with a false signal, as is the case for a traditional RF jamming attack, relates more directly to the definition of corruption. Therefore, using this approach, all forms of jamming, to include DoS attacks, are considered attacks on the integrity of the data or message, not as an attack on the availability of the network. Conveniently, this groups all adversarial influences under the metrics for confidentiality and integrity. For the QoS model, the metrics used to describe availability are already conveyed in QoS metrics. This is reflected as \(A=QoS\), where \(QoS\) is the set of metrics that include  
Figure 1: A Network Configuration with Multiple Logical Channels. cost, jitter, latency, bandwidth, and bit rate, which already provide a repeatable method of measuring availability. These metrics reflect the basic network characteristics without adversarial influence. The probability of leakage for each channel within a communication architecture is defined in [4] as:  
\[P(I)=\frac{P(int)\cdot P(dcr)\cdot P(dco)\cdot\sigma}{n}. \tag{3}\]  
This equation considers the number of listeners, \(\sigma\), that may be accessing the network and the number of channels, \(n\), between the transmitter and receiver. The number of channels also directly influences the Average Channel Loading (\(AL\)) and Duplication Factor (\(DF\)) for a communication system, specifically whether the message is fragmented across the \(n\) channels, what size those fragments may be, and how many times those specific fragments are duplicated, either on one channel or across multiple channels. The probability of corruption for each channel, \(n\), between the transmitter and receiver in a communication architecture is defined as:  
\[P(c)=\frac{ \begin{pmatrix}\left(1-P(n)\right)P(int)AL+\left(P(n)+\frac{P(c)}{ DF}\right)-\left(P(n)\right)\frac{P(c)}{DF}\end{pmatrix}