By Peng Zhang, Chuang Lin
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Extra info for Security in Network Coding (Wireless Networks)
0; k/ is the number of all k h matrices satisfying Condition (2). i C 1/th row to be linearly dependent on the first i rows. 0; k/ iD1 Ni . 1 hqi h C hqi h 1 / iD1 The theorem is thus proven. 1) and that of Bhattad’s  in Fig. 4. 0; k/ calculated by Eq. 9). From Fig. 4, we can see that if the size of finite field is sufficiently large, the probability of weak security can be made arbitrarily high. Moreover, our approximate result is closer to the accurate one, compared to the result given by Bhattad’s.
I;1 ; : : : ; i;NC1 / • MAC. Given x 2 i D 1; : : : ; r. x; t1 ; : : : ; tr /. FNq Fq for each i D 1; : : : ; r. Output K D . 1 ; : : : ; r /. P FNq and K, calculate a tag ti D . NjD1 i;j xj /= i;NC1 for each 30 3 Subspace Authentication for Random Linear Network Coding • Combine. Given xN 1 ; : : : ; xN l , where xN i 2 FNCr , and ˛1 ; : : : ; ˛l , where ˛i 2 Fq , q Pl output xN D iD1 ˛i xN i . P and K 0 K, calculate i D NjD1 i;j xN j C i;NC1 xN NCi , for • Verify. Given xN 2 FNCr q each i 2 K 0 .
0; k/ calculated by Eq. 9). From Fig. 4, we can see that if the size of finite field is sufficiently large, the probability of weak security can be made arbitrarily high. Moreover, our approximate result is closer to the accurate one, compared to the result given by Bhattad’s. 2 0 50 100 150 Field Size 200 250 Fig. 4 The relationship between security probability and finite field size. (a) h D 7; k D 4, (b) h D 7; k D 5, (c) h D 7; k D 6 Next we consider a more general case where a smart adversary can accurately guess some linear combinations of source messages.