A novel approach for anti-pollution attacks in network coding

Figures & data

Figure 1. System model: multi-cast network.

Figure 2. Message coding process.

Figure 3. Pollution threats. In Figure 3, once P is adversary, the bogus message $e_P^{\mathrm{\prime }}$ must be generated, and Q or I will receive message $e_P^{\mathrm{\prime }}$. After that, Q or I will make a combination with $e_P^{\mathrm{\prime }}$ and their own message $e_Q$ or $e_I$ to generate transmission data $c_1{e}_P^{\mathrm{\prime }}+c_2{e}_Q$(or $c_3{e}_P^{\mathrm{\prime }}+c_4{e}_I$). As the data is polluted, J(or K) can not harvest the source data.

Table 1. Notations.

Symbol	Presentation
$\tau (e)$	message e's evidence code
$I{D}_S$	Node S's public identifier
$se{c}_S$	S's secret key registered from SCS
$Seq(e)$	Message e's sequence number
$H(.)$	A hash function
$F(.)$	A mapping function that reflect the input into a subset of 1,…,ν
$\psi (se{c}_S,se{c}_Y)$	Partial information from $se{c}_S$ to Y
ν	The length of evidence code
υ	Length of $\psi (se{c}_S,se{c}_Y)$
$trun{c}_{\theta }$	Segmenting the data into θ leftmost bits
ω	Utilised for verification(e.g.ω=3)
θ	Length of evidence codes

Figure 4. With no key or illegal key attacks. Suppose M is an adversary, so when bogus data is injected to the network, R immediately advocates that the data from the node M is polluted after verifying the MACs of M.

Figure 5. With legal key attacks. Under this situation, there may exist defamation. For example, when P intends to disparage R, it send alerts to SCS and report R as an adversary. In this situation, SCS can quickly make correct judgement by verifying the transmission messages from the node R.

Table 2. Comparison.

	Ours	Homo. sig. [38]	Trapdoor [36]	Poly.time [37]
Comp.efficiency	$\ast \ast \ast$	$\ast$	$\ast$	$\ast$
Space overhead	$\ast$	$\ast \ast \ast$	$\ast \ast \ast$	$\ast \ast \ast$
Verif.info.distribution	Once	Once	Once	Repeated

Figure 6. Network delay.

Figure 7. Throughput.

Figure 8. Delay of identification.