A Novel Lightweight Algorithm for Secure Network Coding

Transcription

1 A Novel Lghtweght Algothm fo Secue Netwok Codng A Novel Lghtweght Algothm fo Secue Netwok Codng State Key Laboatoy of Integated Sevce Netwoks, Xdan Unvesty, X an, Chna, E-mal: {wangxaoxao,wangmeguo}@mal.xdan.edu.cn Abstact In the pactcal netwok codng scenao, the advesay usually has full eavesdoppng abltes. Hence, lghtweght secue netwok codng s moe sutable than the nfomaton-theoetc appoach. We popose a novel codng scheme aganst a global eavesdoppe n ths pape. In ou scheme, we utlze mappng values to andomze ognal packets nstead of locked coeffcents. It means that only one encypted symbol s eued fo a packet, whch apdly educes space ovehead and encypton volume. Meanwhle, thee s no addtonal euement at ntemedate nodes. Compaed to the exstng schemes, ou scheme s moe effcent n space ovehead and encypton volume wth appopate computatonal complexty.. Intoducton Keywods: Netwok Codng, Lghtweght Secue, Eavesdoppng Attacks Netwok codng [] allows ntemedate nodes to mx the ncomng packets befoe sendng out, whch s dffeent fom the tadtonal stoe-fowad mechansm. Lnea netwok codng [2] showed that t could acheve the multcast capacty n a suffcent lage feld. Fo the opeaton convenence and smple algebac stuctue, much of the eseach focuses on the lnea netwok codng. Moeove, when the feld sze s lage than 2 8 o 2 6, andom lnea netwok codng (RLNC) [3] could also acheve the multcast capacty wth pobablty exponental appoachng wth code length. In RLNC, the ntemedate nodes ndependently select codng coeffcents andomly ove fnte feld, whch s a decentalzed mechansm, and easy to mplemented n pactce. Koette and Medad [4] poposed the algebac famewok fo netwok codng and gave an algebac chaactezaton of the multcast poblem. Netwok codng had many applcatons, such as weless mesh netwok [5-6] and coopeatve communcaton [7] etc. Secue netwok codng was fst consdeed n [8] to acheve pefect nfomaton-theoetc secuty, whch s aganst that advesaes could only wetap a lmted numbe of netwok lnks. Feldman et al. [9] showed that makng a secue lnea netwok code s euvalent to fndng a lnea code wth genealzed dstance popetes and ponted that f we gve up a small amount of oveall capacty, then a andom code acheves secuty by usng a much smalle feld. Rouayheb et al. [] pesented a constucton of secue netwok codes by usng secue codes fo wetap channel Ⅱ.Nga et al. [] extended the genealzed Hammng weght [2] fo lnea eo coecton codes to lnea netwok codes. Weakly secue netwok codng was poposed n [3] such that advesay s unable to get any meanngful nfomaton about the souce messages, ths s moe pactce than the pefect nfomaton-theoetc secuty. Stongly secue lnea netwok codng s poposed by Haada and Yamamoto [4], they showed that stong secuty n fact contans weak secuty as a specal case. Unvesal secue netwok codng was poposed n [5] based on ank-metc codes, and t has the unvesal popety that can be appled on top of any netwok wthout po knowledge o any modfcatons on the lnea netwok code. Jan [6] studed the elaton between secuty and netwok topology. A necessay and suffcent condton was deved unde whch souce messages can be tansmtted wth pefect secuty. In eal scenaos, the wetap capablty s unlmted and computatonally bounded. Moeove, netwok capacty and compute esouce ae pecous. To solve the poblem, the moe pactcal scheme was poposed n [7-9] that combnes cyptogaphc appoaches wth netwok codng to aganst global eavesdoppe and keeps andom netwok codng unchanged at ntemedate nodes. A mnmum ovehead scheme (MOS) was poposed n [7] to acheve pefect secuty, but wth hgh encypton volume because the whole message s encypted. The scheme n [8] (P-Codng) utlzed pemutaton encypton functon to aganst eavesdoppng attacks wthout ovehead, but t s also wth hgh Advances n nfomaton Scences and Sevce Scences(AISS) Volume4, Numbe2, Nov 22 do:.456/aiss.vol4.ssue

2 A Novel Lghtweght Algothm fo Secue Netwok Codng encypton volume. Lghtweght secue scheme (SPOC) was pesented n [9], whch only encypts a much shote exta codng vecto nstead of the whole packet, so t educed encypton volume but nceased capacty ovehead. In ths pape, we popose a moe effcent scheme aganst global eavesdoppe that acheves secuty wth mnmum ovehead and encypton volume wthout changng the mplement at the ntemedate nodes o eung a lage feld. The key dea of ou novel scheme s to utlze some mappng values to geneate a souce pecodng matx nstead of exta codng vectos, whch educe the length of the andom keys. 2. Poblem Fomulaton We epesent a communcaton netwok by an acyclc dected gaph G V, E, whee V and E denote the set of nodes and edges, espectvely. Each edge n the netwok s able to tansmt a packet ove fnte feld wthout eo. Souce node S wshes to send a lage fle M to all the eceves n a geneaton and M s spltted nto data packets by S. Each data packet s denoted by n x ( x,, xn),, whee. Intemedate nodes andomly choose codng coeffcents ove fo ts nput packets and fowad a lnea combnaton of nput packets at each outgong edge. Snk nodes can ecove M wth Gaussan elmnaton afte ecevng at least lnea ndependent packets. Thee s a global eavesdoppe n the netwok. We assume the advesay s able to choose a subset of ndependent edges, whch means that the global codng vectos of wetap edges ae ndependent. 3. Poposed Scheme In ths secton, we popose a pecodng scheme fo lghtweght secue netwok codng wth gnoed space ovehead. 3. Pecodng at Souce As descbed n the pevous secton, a lage fle M was spltted nto packets, and we choose an n appopate mappng functon h( x): fo these packets, whch maps packets to dffeent values. Then, we constuct a pecodng matx P by mappng values h( x ),. h( x) h( x2) h( x ) h( x) h( x2) h( x ) P h( x) h( x2) h( x ) () Obvously, matx P s a Vandemonde matx and t s an nvetble matx that could be used to pe-encode ognal packets x, x. x x x2 x2 P x x n n (2) Then souce S concatenates packet x ( x,, xn, h( x)). x wth coespondng mappng value h( x ) to be a pe-encoded 676

3 A Novel Lghtweght Algothm fo Secue Netwok Codng Fo secuty, S must hde the last symbol h( x ) of x fom advesay, so that the advesay can not get nfomaton about ognal packet by wetappng attacks. We encypt h( x ) usng AES cyptosystem and obtan Ehx ( ( )). Then we get a new packet x ( x,, xn, E( h( x))). Afte that, S ceates an augmented packet as follow, new m (,,,,,,, x ) ( n),,,. At last, the augmented packets ae tansmtted nto the netwok and the ntemedate nodes employee RLNC. 3.2 Decodng at Snks When a snk node eceves at least ndependent message packets, t can begn to decode as follows. new new T Step : Usng Gaussan elmnaton to ecove the new message packets [ x,, x ]. new new T Step 2: We decypt the last column of [ x,, x ] wth AES to get [ x,, x ] T and h( x ). Step 3: Constuct the pecodng matx P by h( x ),,,. Compute the nvese matx P, and emove h( x ),, h( x ) T fom [ x,, x ] T to obtan [ x,, x ] T. T T Step 4: At last, we obtan the ogn data packets by [ x,, x ] P [ x,, x ]. 3.3 Secuty Analyss new We assume the advesay has full knowledge about the stuctual chaactestcs of P, and mappng functon h() s also known to t. Howeve, t s computatonally bounded, whch means that gven a ha mappng value b, t s computatonally nfeasble to fnd nput a such that b. The element of P s keep secet to advesay, snce we andomze the ognal packets x, by P. Euvalently, the ognal packets ae encypted by P. Theefoe, the advesay only gets the new lnea combnaton of x,. Futhemoe, the advesay s able to eavesdop at least ndependent edges to decode new new x,, x. The subset of wetap edges s denoted by W, and R {( h x ),,} denotes new new mappng value set. The advesay tes to obtan the ogn packets x,, x fom x,, x by the followng euaton system, h( x) xh( x2) x2 h( x) x x h( x) xj h( x2) x2j h( x) xj xj (4) h( x) xn h( x2) x2n h( x) xn xn thee ae ( n ) euatons wth ( n ) unknown vaables x,, xn and h( x),, h( x ) n (4). It s easly known that h( x ),, h( x ) has P possbltes, because h( x ), has possbltes. So the numbe of total possbltes s ( ) ( 2) ( ) P. Theefoe, the soluton to (4) s an affne subspace wth cadnalty as follow, That means, ( n) P ( n) P (3) 677

4 A Novel Lghtweght Algothm fo Secue Netwok Codng P x,, xyw (5) P whee Y W denotes the message packets whch ae caed n W. Hence, the advesay cannot ecove x,, x wthout h( x),, h( x ). That s, the ogn data packets ae secue. 3.4 Compason In ou scheme, thee ae ogn data packets n a geneaton whch ae n -length, and get n - length pe-encoded packets afte souce codng. That means the space ovehead of one packet s. The last symbol of the pe-encoded packet s used to constuct the locked coeffcent, so that only one symbol s needed to be encypted. As mentoned pevously, the space ovehead and encypton volume ae ndependent of the packets, whch ae sgnfcant educed by ou scheme. Howeve, SPOC encypts n -length ogn data packets wth -length global encodng vectos. These global encodng vectos ae encypted by shaed keys and placed n the heade of the coespondng peencoded packets, whch ae called locked coeffcents. 8 In ode to gve a smple compason, we consde a feld wth sze 2, and thee ae 2 packets n a geneaton. The maxmum packet sze s 5 bytes as [9] mentoned. Ou scheme esults n a space ovehead ato of.667%, because of only one symbol s placed n the heade of a packet. Howeve, thee s 2-length locked coeffcent placed n the heade by SPOC, so that the space ovehead ato s 3.3% fo SPOC. Futhemoe, ou scheme yelds encypton volume of 2 bytes n a geneaton and coespondng to 4 bytes by SPOC. Table. Compason wth othe schemes Schemes Encypton Volume Space Ovehead Computaton Cost Adel [7] n Zhang [8] Vlela [9] Ous n 3 ( ) 3 ( ) The compason between ou scheme and othe schemes s gven n Table. and Fgue, the ed cuve n Fgue s ou esult. And the blue cuve s ovelappng to the puple cuve, whch means the encypton volume geneated by Vlela scheme s almost same as tadtonal scheme. We can see fom Table. that ou scheme causes a tny space ovehead and Fgue shows that ou scheme sgnfcantly educes the encypton volume compaed to othes. In addton, the computatonal cost of ou scheme s 3 ( ), whch s the same as SPOC. The man computatonal cost conssts of the nvese of pecodng matx P and othe matx opeaton. The scheme poposed n ths pape s an effcent algothm whch has smalle space ovehead and lowe encypton volume wth appopate computaton cost. 678

5 A Novel Lghtweght Algothm fo Secue Netwok Codng Tadtonal Vlela Ou Zhang Adel Encypton volume Data sze Fgue. The compason of encypton volume 4. Concluson We poposed a novel lghtweght scheme aganst eavesdoppng attacks based on computatonal secuty n ths pape. The basc dea of ths scheme s to utlze keys, whch ae espectve to ogn data packets, to geneate a Vandemonde matx as pecodng matx. Snce encypted mappng value s embedded at the end of pe-encoded packets and then tansmtted ove the netwok, the space ovehead s mnmzed, and the encypton volume s educed as well. The secuty analyss shows that fo the same secuty euement, ou scheme s moe effcent. 5. Acknowledgements Ths wok s suppoted by the Natonal Natual Foundaton of Chna unde Gants No.6832 and The authos also would lke to thank all the evewes fo the had woks. 6. Refeences [] Rudolf Ahlswede, Nng Ca, Shuo-Yen Robet L, and Raymond W. Yeung, Netwok nfomaton flow, IEEE Tans. Inf. Theoy, Vol. 46, No.4, pp , July. 2. [2] Shuo-Yen Robet L, Raymond W. Yeung and Nng Ca, Lnea netwok codng, IEEE Tans. Inf. Theoy, Vol. 49, No. 2, pp , Feb. 23. [3] Tacey Ho, Muel Medad, Ralf Koette, Davd R. Kage, Mchelle Effos, Jun Sh and Ben Leong, A andom lnea netwok codng appoach to multcaost, IEEE Tans. Inf. Theoy, Vol. 52, No., pp , Oct. 26. [4] Ralf Koette and Muel Medad, An algebac appoach to netwok codng, IEEE/ACM Tansactons on Netwokng, Vol., No. 5, pp , Oct. 23. [5] Jn Q,, Shuny Zhang, Shujng L,, Lu Cao, "A Random Lnea Codng Algothm fo Cogntve Weless Mesh Netwoks", JCIT, Vol. 7, No. 6, pp. 2-2, 22. [6] Yafe Hu, Fangmn L, Xnhua Lu, "On Netwok Codng fo Qos Impovement n Weless Mesh Netwoks", AISS, Vol. 4, No. 7, pp. -3,

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