Energy and Communication Efficient Group Key Management Protocol for Hierarchical Sensor Networks

Transcription

1 Eery ad Commuicatio Efficiet Grou Key Maaemet Protocol for Hierarchical Sesor Networks Biswajit Paja, Sajay Kumar Madria Deartmet of Comuter Sciece Uiversity of Missouri-Rolla, Mo Abstract I this aer, we describe rou key maaemet rotocosl for hierarchical sesor etworks where istead of usi re-deloyed keys, each sesor ode eerates a artial key dyamically usi a fuctio. The fuctio takes artial keys of its childre as iut. The desi of the rotocol is motivated by the fact that traditioal crytorahic techiques are imractical i sesor etworks because of hih eery ad comutatioal overheads. The rou key maaemet rotocol suorts the establishmet of two tyes of rou keys; oe for the sesor odes withi a rou, ad the other i a rou of cluster heads. The rotocol hadles freshess of the rou key dyamically, ad elimiates the ivolvemet of a trusted third arty (TTP). We have exerimetally evaluated the time ad eery cosumtio i broadcasti artial keys ad rou key uder two sesor routi rotocols (Tiy-AODV ad Tiy- Diffusio) by varyi the umber of odes ad key sizes. The erformace study rovides the otimum umber of artial keys eeded for comuti the rou key to balace the available security ad ower cosumtio. The exerimetal study also cocludes that the eery cosumtio i SPIN [9] icreases raidly as the umber of rou members icreases i comariso to our rotocol. 1. Itroductio Sesor etworks [1] have become a imortat area of research because of their alicatios i military ad disaster relief. The most limiti factors of a sesor ode are its battery caacity ad available memory. Thus, the eery ad storae coservatio are two imortat issues at the ode level ad at etwork level. Security is oe of the most imortat issues i distributed ad hoc sesor etworks. For examle, a wireless sesor etwork uses a radio frequecy (RF) chael [10], which is ot a secure chael. It is also difficult to revet a adversary sesor ode from comromisi the security of sesor etworks because Bharat Bharava Deartmet of Comuter Sciece Purdue Uiversity, West afayette, IN bb@cs.urdue.edu of utraceable sesor odes ad less hysical rotectio [2,3,5]. To cotrol iformatio access i a hierarchical sesor eviromet, oly authorized sesors should have the crytorahic keys by which they ca decode the dissemiated iformatio. Thus, a rou key maaemet is required for such a hierarchical eviromet as it ca imlemet differet access cotrol olicies at each level ad rovide mechaisms for secure rou commuicatio by elimiati comromised odes. I the traditioal crytorahic techiques for security, every sesor ode would eed a {rivate, ublic} key air which is imractical because of hih eery cosumtio ad scalability. I this aer, we roose a rou key maaemet rotocol usi a hierarchical architecture cosisti of differet rous with a uique rou key. Usi this aroach, multi-level security ca be achieved to secure the rou of sesors at differet levels. There are two tyes of rou keys: itra-cluster, ad itercluster. The itra-cluster rou key is used for ecrytio/decrytio of messaes iside a sesor etwork rou, whereas the iter-cluster rou key is used for rous of cluster heads. The two most imortat advataes of dyamic artial keys over re-deloyed keys are that (1) sesor odes eed ot store too may keys ad (2) the dyamic key may ot be comromised because it chaes frequetly. I our roosed scheme, every sesor ode i a rou eerates a artial key dyamically, ad used it for comuti the rou key i a bottom u fashio. Oce the sesor etwork is deloyed, it is oraized i a hierarchical fashio. After that, a cluster head (leader) ets messaes from all its rou members to kow their level ad locatio i the sub-tree, ad i resose it seds a messae. It also requests the leaf odes (iitiator) to comute their artial keys. I this rotocol, the artial keys are comuted usi the fuctio associated with each ode which uses artial keys of their descedets as arumets. The key comutatio starts by leaf odes eerati radom umbers as their artial keys, because they have o descedets. The cluster head comutes the rou key usi a otimum umber of artial keys. The decisio for choosi the umber of This research is artially suorted by NSF rat EIA

2 artial keys to be used is based o the security ad eery cosumtio. I this aer, we modified the Tree Based Grou Diffie-Hellma (TGDH) rotocol [7] for rou key maaemet usi a eeral tree structure. I additio, Diffie-Hellma rotocol [9] is used for comuti the rou key. Usi the modified TDGH, a ew rou key maaemet scheme is reseted. The exerimets, with a sesor etwork eviromet created i NS-2 ad TiyOS are erformed usi two sesor routi rotocols (Tiy-AODV ad Tiy- Diffusio) by varyi odes, key sizes ad eery cosumtio. It is observed that Tiy-AODV is slower tha Tiy-Diffusio i terms of broadcasti the artial keys ad the rou key. Also, the Tiy-AODV takes more time to re-establish a route ad re-sed the artial keys. The exerimets for eery comutatio ad delivery of artial keys heled i selecti the otimum artial key ad rou key sizes. It is observed that a 300-bits rou key size would be reasoable cosideri memory ad commuicatio overheads. I exerimets, the otimum (eery, security) rou key size is 300 bits, which ca be comuted from 15 artial keys of 20 bits each. It is kow that decryti 300- bits rou key eeds micro secods, with the decrytio rate of 1 bit er micro secod [10]. We erformed exerimets to comute eery cosumtio ad cocluded that the rotocol cosumes very small amout of eery (aroximately joule) i the rocess of comuti 15 artial keys, broadcasti them, comuti ad broadcasti the rou key. The eery cosumtio is very small comared to the total available eery of 4,61700 joule (for 15 odes with two batteries each havi 15,390 joule er battery). The roosed rotocol coserves eery ad commuicatio with resect to SPIN [6] ad re-deloyed key rotocol. To save commuicatio cost ad eery, re-keyi of the rou is doe by the cluster head by sedi a messae to the sesor odes, which cotais iformatio for addi or removi certai artial keys to eerate the ew rou key. To uaratee that all the odes i a rou received the iformatio, they sed a rely (REP) messae. If the cluster head does ot et the REP from every ode, it re-broadcasts the messae. 2. Related work Kim et al. [7] roosed a rou key areemet rotocol called Tree Based Grou Diffie-Hellma rotocol [TGDH], which is based o the Diffie- Hellma key exchae. I this rotocol, a distributed key areemet has bee cosidered rather tha a cetralized rou key areemet. Differet rou areemet rotocols have bee roosed. I cetralized rou key distributio, oe key server eerates keys ad distributes them to the rou, while i decetralized aroaches the key is comuted dyamically. The basic requiremets for rou key areemet rotocols [1, 5] are key freshess, rou key secrecy (forward ad backward) ad key ideedece. I SPIN [6] two security cocets are used: SNEP (Secure etwork ecrytio rotocol) ad micro TESA (Time, efficiet, streami, loss-tolerat autheticatio rotocol). The advataes of SNEP are low commuicatio overhead ad sematic security. A DES-CBC chaii alorithm is used to maitai data cofidetiality i SPIN, ad a MAC is used to kee messaes ualtered. A secial couter is used to maitai the sequece of messaes. The couter value will ever be the same, so the ecryted messae is differet for the same data. The disadvataes of SPIN are that (1) it is based o oe-to-oe commuicatio but odes i sesor etworks work i rous ad (2) it does ot cosider the security i hierarchical structure ad clusteri which are imortat for sesor etwork alicatios such as i military. Escheauer et al [4] reseted a key maaemet scheme which has selective distributio ad revocatio of keys i sesor odes. Their scheme is based o the robabilistic distributio of the key, which uaratees that two eihbori odes will have at least oe commo key i their key ri. This key is used by the eihbori odes to ecryt/decryt messaes. The disadvatae of this aroach is that, re-deloyed keys are comaratively easy to fore tha a dyamic key. Also, each ode eeds more memory to store may keys, ad therefore, it is imractical 3. Hierarchical sesor etwork model I this sectio, the architecture of a hierarchical sesor etwork with multile levels cosisti of sesor odes, cluster heads, ad relay odes is described. There are two tyes of sesor rous; oe is a rou of sesor odes lead by a cluster head, ad the other is a rou of cluster heads with oe cluster head as head of that rou. Fiure 1 shows the architecture. I this model, each sesor rou collects data from a articular eorahical area ad seds the data to the earest sesor odes. If the eihbori odes are relay odes, they forward those data usi the aroriate routi ath. Fially, the cluster head areates the data ad forwards that to its uer level cluster head. Three differet tyes of idetificatios are used i this model: a uique idetificatio (ID) for each sesor ode, each cluster head ad each rou of clusters. The assimets of the IDs are doe i the followi ways: The IDs of sesor odes are ive by the cluster head of that articular rou. The IDs of cluster heads are ive by the Head of Cluster Heads [HCH] of a articular eorahical area. HCH is the cluster head, which is resosible for leadi the rou of cluster heads.

3 Also, the IDs of the rou of sesor odes are ive by HCH. (0,0 (1,0 (1,1 evel 1 evel 2 (2,0 (2,1 (2,2 (2,3 Cluster head Geeral sesor odes Relay odes Fiure 1. Hierarchical architecture 4. Partial key comutatio I this sectio, we describe the scheme for comuti the artial key i each sesor ode. We assume that after the oraizatio, the cluster head of each rou kows the ositio (Pos <l,v> ) (level i the sub-tree) of its rou members. It sed a messae Ms(Pos <l,v> ) to let them kow their ositio. Next, the cluster head seds a messae (Re <iit,ode> ) to the leaf odes to comute the artial keys. The fuctio f(artial key of child1, artial key of child2) is used to comute the artial keys i each ode. As the leaf odes do ot have ay decedets, they eerate radom umbers as their artial keys. The, it uses a simle aroach to comute the artial keys of oleaf odes. The arets of the leaf odes comute their artial keys usi a fuctio f(). The fuctio k1 k2 is f ( k1, k2 ) mod, where is the rime umber, is the rimitive root of P ad k 1, k 2 are keys (k 1, k 2 <). The arumets of the fuctio are the artial keys of their childre. Usi a bottom u aroach, all o-leaf sesor odes ca comute their artial keys. If the tree is biary, the the fuctio for comuti the artial key K is f (K <l+1, 2v> K <l+1, 2v+1> ), where l is the level i the tree ad v is the ositio of the ode from left. For examle i Fiure 2, to comute the K <2, 0> we eed the fuctio f(k <3, 0> K < 3, 1> ). The comutatio of K <2, 1> is ot ossible usi f(k <3, 2> K < 3, 3> ) as childre ow have differet arets. If the fuctio f(k <l+1, 2v+1> K <l+1, 2v+2> ) is used the we are able to comute K <2, 1>. From this we observe that the levels l do ot chae, but the ositio v chaes deedi o the umber of childre. I a o-biary tree, the alorithm eeds to cout the siblis i the left art of the sub-tree for calculati a key for the aret ode. It the comutes m where m = siblis - 2 so the fuctio would be f(k <l+1, 2v+m> K <l+1, 2v+1+m> ). (3,0 (3,1 (3,2 (3,3 (3,4 (3,5 (3,6 (3,7 (3,8 Fiure 2. Dyamic artial key comutatio The advatae of this fuctio is that it is difficult to decode. Whe the odes kow the fuctio k1 k2 ( f ( k1, k2 ) mod ) the they do ot eed to aalyze the kow fuctio. The comlexity of the rotocol is O(lo+m), because the artial keys ad the rou key are comuted i a tree structure. For odes, it takes O(lo) time, ad comuti the m artial keys from odes takes O(m) time. A oe time symmetric key is used for eeratio ad verificatio of the MAC first time. This key is also used for ecrytio/decrytio of artial keys, itermediate keys ad rou key. Oce the rou key is comuted, the symmetric key is discarded. Fiure 3 rovides the alorithm for comuti the artial keys i a tree which is based o the ositio of the odes i that rou. Alorithm: 1. if (tree is biary) the 2. { f (K <l+1, 2v> K <l+1, 2v+1> ) } 3. else if (it is ot biary), the 4. { f (K <l+1, 2v+m> K <l+1, 2v+1+m> ) m = [ If there is sub-tree left side of ode, left siblis (umber of sub-tree)x 2 2 ] } 5. if (o sub-tree i the left side of the ode) the 6. { f (K <l+1, 2v> K <l+1, 2v+1> ) } 7. else if (sub-tree is there i the left side of the ode), the 8. { f (K <l+1, 2v+m> K <l+1, 2v+1+m> ) } Fiure 3. Alorithm for dyamic artial key comutatio

4 5. Grou key comutatio We have used the multi-arty Diffie-Hellma ad TGDH rotocol [7] to roose a ew rou key comutatio method for sesor etworks. To accomlish this roositio, the leaf odes work as the iitiators ad the cluster head as the leader. Starti from the iitiator sesor odes, every sesor ode cotributes its artial key for comuti the rou key. The leader ode accumulates all artial keys for comutatio of the rou key. This is a bottom u aroach, as artial keys are accumulated from leaf odes to the aret odes. I the followi subsectio, we show the rou key comutatio with ad without usi the blid factor. The blid factor is a uique umber eerated by a sesor ode. 5.1 Grou key comutatio without blid factor We use the followi aroach for rou key comutatio without the blid factor [1]. As the leaf odes act as the iitiators, they first broadcast their artial keys. The aret odes of the leaf odes et the artial keys ad the add their ow artial keys ad rebroadcast it. As it is a bottom u aroach, the cluster head will have all the artial keys, ad it will comute the rou key usi its artial key cotributio. After that, the cluster head broadcasts the rou key. Iitially, a re-deloyed oe time symmetric key is used to ecryt ad decryt the artial keys ad the rou key. There after, oly the rou key is used for this urose. The idetificatio of the odes is attached with the ecryted artial keys. The sesor odes check the idetificatio before decryti the artial keys, as the aret odes oly eed the artial keys of their childre. I this way, they ca have early rejectio of ackets, which saves commuicatio ad comutatio overheads. The other rou members caot comute the rou key because they caot et the artial key of the cluster head, sice it does ot broadcast its artial key. I Fiure 4, the leaf odes are M 1, M 2,, M 9. To start, M 1 comutes the artial key S1 ad broadcasts it. The aret ode M 10 ets the artial keys from M 1 ad other childre. Here, is a eerator of the multilicative rou Z P * (i.e. the set {1, 2-1}, is the rime) ad S1 is a radomly chose secret umber for member M 1. ikewise, member M 2 comutes S2 ad broadcasts it, ad the aret M 10 ets the artial keys. I this way, member M 10 receives S1S2S3, ad raises the ower by S 10 to et the itermediate key (IK). Here, S10 is the artial key cotributio of M 10. I the followi ararahs, we discuss two tyes of rou keys: the itra-cluster ad the iter-cluster. The itermediate keys i M 10, M 11, ad M 12 are IK1 = S1 S2 S3 S10, IK2 = S4 S5 S6 S11 S7 S8 S9, ad IK3 = S12, resectively. The itermediate keys are ecryted usi a oe time symmetric key, as exlaied earlier. The cluster head comutes the rou key K, usi IK1, IK2, ad IK3 ad its cotributio s13. K = S1 S2 S3 S10 S4 S5 S6 S11 S7 S8 S9 S12s13 [Itra-cluster rou key] The, it ecryts the rou key usi the symmetric key. The authetic odes, which have the symmetric key, ca decryt the rou key. The cluster head broadcasts the rou key to its rou members, so that every sesor ode ets the rou key. This rou key is called the itra-cluster rou key, ad is used for ecrytio/decrytio of messaes iside the rou of sesor odes. s1 s1s2s3s10 s4s5s6s11 s1s2... s12s13 s7s8s9s12 M10 M11 M12 s2 s3 s4 s5 s6 s7 s8 s9 M1 M2 M3 M4 M5 M6 M7 M8 M9 Cluster head Geeral sesor odes Fiure 4. Itra-Cluster key comutatio For iter-cluster ecrytio/decrytio a differet rou key is comuted. The iter-cluster rou key is ot kow to the eeral sesor odes. Fiure 5 shows the comutatio of the iter-cluster rou key. The itermediate key i C 7, C 8, C 9 are IK1 iter = C1C7, IK2 iter = C2C3C8, ad IK3 iter = C4C5C6C9 The head of the cluster heads (HCH) comutes the iter-cluster rou key C usi itermediate keys IK1 iter, IK2 iter, IK3 iter, ad its cotributio c10. C = C1C7C2C3C8C4C5C6C9c10 [Iter-cluster rou key] The HCH broadcasts the iter-cluster rou key to the cluster heads. The cluster heads use this rou key for ecrytio/decrytio of messaes amo the cluster heads Grou key comutatio usi blid factor We ca comute the rou key usi a blid factor. The advatae of usi a blid factor is that a attacker will ot be able to et the rou key whe the cluster head broadcasts the rou key. I Fiure 4, the itermediate keys are IK1 = S1 S2 S3 S10 S4 S5 S6, IK2 = S11 ad IK3 = S7 S8 S9 S12. After comutatio of IK1, IK2, ad IK3 the aret odes M 10, M 11, M 12 broadcast the itermediate keys. The childre of M 10, M 11, ad M12 are iterested i those keys, as they eed to

5 remove their cotributio from the IK. The they isert a radomly chose blid factor B. The keys, after iserti blid factor, are as follows. IKB1 = B1 S2 S3 S10, IKB2 = S1 B2 S3 S10, ad IKB9 = S7 S8 B9 S12. The cluster head ets the broadcasted keys IKB1,, IKB9. The cluster head the comutes the rou key K, usi IKB1 IKB9 ad its cotributio s13. B1 S2 S3 S10 S4 S5 S6 S11 S7 S8 S9 S12s13 K = After the rou key comutatio, the cluster head broadcasts the rou key with blid factor. Now the authetic sesor ode ca recoize its blid factor. Each member remove its blid factor that it received from the cluster head. They reisert their oriial cotributio S i (i = 1...) for etti the rou key. The same method is used to comute the iter-cluster rou key. A symmetric key is used for ecrytio ad decrytio of artial keys. The cluster head uses the same symmetric key for ecrytio of the rou key. C10 c4... c9c10 c1c7 c2c3c8 c4c5c6c9 C7 C8 C9 c1 c2 c3 c4 c5 c6 C1 C2 C3 C4 C5 C6 Cluster head Fiure 5. Iter-Cluster key comutatio 5.3. Udati a rou key Our key maaemet rotocol rovides a scalable aroach for udati rou keys for lare dyamic rous. Sectio 3 shows that lare dyamic rous, rekeyi the rou o each membershi chae becomes usustaiable. Oe of the aroaches to kee the key fresh is by re-keyi the rou at fixed itervals; this aroach is comutatioally exesive as the artial keys ad the rou key will be comuted aai. Aother aroach for udati the key would be to sed a messae from the cluster head to its rou members cosists of istructios to remove or add a certai artial key from the rou key i order to et the ew rou key. The rou key K, which is described i Sectio 5.1 is: K = S1 S2 S3 S10 S4 S5 S6 S11 S7 S8 S9 S12s13 [Old rou key] For examle, the cluster head seds a ecryted messae to its rou member for removi S10 from their rou key. The ew rou key K would be: K = S1 S2 S3 S4 S5 S6 S11 S7 S8 S9 S12s13 [New rou key] To uaratee that all the sesor odes received the messae to udate the art of the rou key, odes sed a ackowledmet (ACK) messae to the cluster head. If the cluster head receives the rely (REP) from all the odes, the it seds the ext messae that the ew rou key is i effect ow. If the cluster head does ot receive the rely messae REP from all its rou members, the it reseds (broadcast) the messae util it ca et a rely messae or it ca come to kow evets, such as a articular sesor ode does ot have battery ower left for commuicatio. To kee track of all the artial keys, the cluster head ca use a rimary idex by sorti the IDs of its rou member odes Aalysis: Eery ad security level with resect to key size This subsectio exlais the aalysis of balaci the eery cosumtio verses security level by choosi the aroriate key sizes i the roosed rotocol. Notatios: eaf level odes i the hierarchy f vt eaf level K Partial keys i the leaf odes P k Pre-deloyed key i the etwork, ca be symmetric or asymmetric K Paret key of the sub-tree P Paret odes of each sub-tree v evels i the hierarchy as i fiure 1 f ( ) Fuctio with the artial keys of childre as arumets E Eery cosumtio (joule) P total Total eery i the etwork (joule) Pcosumed Cosumed eery for rou key comutatio G Grou of sesors i the etwork N Number of rous i the etwork S Size of key Number of levels i each rou C Number of artial keys cosidered for the rou key V Battery voltae (volt) C Caacitace (farad) f Frequecy (Hz)

6 et f vt ad v =1, 2,. [ v = 0 is the root]. The aret key K is comuted from the fuctio f( K, K 1 ) where f ( k) k mod. The eery remaii i each sesor ode is comuted usi their levels i the architecture. It is kow that the eery cosumtio i a circuit is : Power P = V 2.f. C If the ower (eery) cosumtio at each level is P the the total ower i all rous is: Total ower = P v N Eery remaii = Ptotal - P v N The eery required at each level will comute the total eery eeded i the comutatio of the rou key, ad is ive by P v v 1 By cosideri the artial keys at each ode level ad at their aret level eery cosumtio would be: P f ) K k ( v P If artial keys are cosidered to form the rou key the the eery cosumtio with resect to key size would be: P cosumed = ( K ) C E The eery cosumtio for the rou key must be less tha the total available eery. Thus, ( K ) C E Ptotal E N It is assumed that there exists more tha oe rou i the etwork. If the artial key size varies from 20 to 100 bits the the eery cosumtio would be: E 100 ( K S 20byte ) C S The artial key sizes are based o the rou key size, the umber of artial keys cosidered for the rou key ad the available eery. The eery cosumtio for comuti the artial keys ad the rou key roortioal to the security requiremet i terms of key sizes ca be exressed as follows: C G,, K C ( K ) E Sec where Sec is the time to the decryt the key at a decrytio rate of 1 bit er micro secod. It is observed that, as the key size icreases the security ad eery cosumtio would icrease, ad it is ot ossible to have P P. cosumed total ( f E) ( vt E) If P cosumed 1, the the cluster head ca choose the artial keys from the leaf odes. From the above, we ca fid the umber of artial keys to be used for balaci the security requiremet based o key size verses the eery cosumtio. 6. Performace evaluatio ad observatio For erformace aalysis, we have imlemeted the rou key maaemet rotocol i TiyOS ad NS-2. As NS-2 is ot develoed for sesor etwork, a sesor etwork eviromet is created i NS-2 by lui i sesor aet, eery model, ad multichael model develoed by the Uited States Navy. The cluster head comutes the rou usi the method as described i Sectio 5. It chooses a certai umber of artial keys i order to comute the rou key. It also stores the idetificatio of the odes alo with the artial keys so that it ca save memory by discardi the artial keys received earlier. I order to measure how fast the artial keys are delivered to the cluster head, we did exerimets usi two sesor routi rotocols: Tiy-AODV ad Tiy- Diffusio. The sesor odes, which do ot fall i a 10 meters rae, eerate artial keys so that the cluster head ca et the artial keys from differet reios i its rou. The, they establish a route to the cluster head usi the routi rotocol ad sed the artial keys usi that route. The reasos for restricti the umber of sesor odes ad broadcasti the artial keys are to reduce commuicatio overhead, ad eery cosumtio. Fiure 6 shows the time take by the etwork to sed the first 25 artial keys to the cluster head usi the Tiy-AODV ad Tiy-Diffusio routi rotocols. The alorithm for eerati ad broadcasti artial keys ad comuti the rou key was ket the same i both cases. Routi Protocols Tiy-AODV, Tiy- Diffusio Area 2000 x 2000 meter Number of odes er 50 rou Chael Sile (wireless) Simulatio time 160 sec Trasmitti mw ower Receivi ower mw Idle 0.0 W Iitial eery 0.5 Joule Sesi ower mw Table 1. Parameters for simulatio

7 We observed that the Tiy-AODV takes aroximately 54 secods to deliver the first 25 artial keys to the cluster head; whereas Tiy-Diffusio takes almost 15 secods. This exerimet is erformed to determie the effectiveess of routi rotocols i terms of how fast the artial keys ca reach the destiatio. After that, the rou key is comuted by the cluster head. The it is broadcasted to all its rou members. We foud that both routi rotocols take a comarably small amout of time for broadcasti artial keys. Fiure 7 shows the time take by the etwork to broadcast the rou key eerated based o the collectio of artial keys usi the Tiy-AODV ad Tiy-Diffusio routi rotocols. From exerimets, it is observed that the rou members whose IDs are 1 throuh 25 receive the rou key i aroximately 7.57 secods if Tiy-AODV is used whereas if Tiy- Diffusio is used the it takes aroximately secods. The reaso is that, Tiy-Diffusio uses a routi table for creati routes ad therefore, it takes more time to deliver the iitial ackets comared to Tiy-AODV because of its roactive features. There is a very small time differece i broadcasti the rou key usi Tiy-AODV ad Tiy-Diffusio. Thus, deliveri the artial keys (as show i Fiure 7) to the cluster head usi Tiy-AODV takes more time tha Tiy-Diffusio because of the artial key broadcast from every ode, ad the deliveri it to the cluster head requires may-to-oe commuicatio. I Fiure 8, we reset the results for time take i broadcasti artial keys of size 20 ad 30 bits. The rou key i the cluster head is comuted usi the first 15 artial keys. The rou key size would be 300 ad 450 bits, resectively. We observed that the time take to accumulate artial keys of size 300 ad 450 bits remais almost same. Theoretically, the time required to decryt 300 bits key size is micro secods, at a rate of 1 bit decryt er micro secod. Therefore, the forery time for size of 300 bits rou key is quite hih. Partial key delivery time (msec) Tiy-AODV Tiy-Diffusio Number of odes Fiure 6. Partial key delivery to the cluster head Grou key delivery time (msec) Tiy-AODV Tiy-Diffusio Number of odes Fiure 7. Broadcasti rou key We erformed aother exerimet to aalyze the eery cosumtio i the roosed model. As a remider, the ower cosumed by the sesor odes for trasmissio ad recetio is set at 175 mw, for sesi mw, ad the iitial eery of the eeral sesor odes is 0.5 joule. The cluster head cosumes the same ower for trasmissio ad recetio with its iitial eery is set to 2.5 joules. Fiure 9 shows the eery cosumtio rah for eerati 20 artial keys ad deliveri those to the cluster head. This also icludes the eery cosumtio for commuicatio before deliveri the artial keys. From this exerimet, we observe that chai the umber of seders has imact o the eery cosumtio, ad this exerimet hels to decide the umber of artial keys that should be chose i order to balace the eery cosumtio ad security. The otimum umber of artial keys is 15 with resect to the curret cofiuratio. Althouh the total ower cosumtio for eerati artial keys, deliveri, comuti the rou key ad broadcasti back is ot show i the fiure, it is aroximately joule. Oe way to rotect the etwork from itruders is by udati (re-keyi) the rou keys frequetly so that a itruder caot et eouh time to fore the rou key. I our model, we udate the rou key usi the techique described i Sectio 5.3. As exlaied earlier, i order to save commuicatio ad comutatio cost, istead of re-comuti the artial keys ad the rou key, the cluster head seds a messae to its rou members for removi or addi certai artial keys from the rou key to obtai the ew rou key. I Fiure 10, the eery cosumtio by SPIN ad our key maaemet rotocol are comared. Thouh SPIN is used for oe-to-oe ode commuicatio, here it used for rou commuicatio. It is observed that SPIN takes more time for commuicati withi a rou. We observed that the eery cosumtio of

8 SPIN icreases exoetially with the icrease of the umber of odes i a rou. Time (msec) Partial key size 20 bit Partial key size 30 bit Number of artial keys Fiure 8. Time take for differet key sizes Eery cosumtio (Joule) Eery cosumtio Partial keys Fiure 9. Eery cosumtio verses the umber of artial keys Eery cosumtio (joule) Dyamic key maaemet rotocol SPIN Number of odes Fiure 10. Comariso of dyamic key maaemet rotocol with SPIN 7. Coclusios I this aer, we have described a rou key maaemet rotocol where the artial keys are comuted dyamically, istead of usi re-deloyed keys. A rou key is eerated based o the artial keys of the rou members. The dyamic artial keys have some advataes over re-deloyed keys, as may re-deloyed keys eed to be stored to rovide secure commuicatio, which is ot feasible i sesor odes because of the limited memory. It is easy to recomute the artial keys as each ode uses a fuctio with the artial keys of its childre as arumets of the fuctio to comute its artial key. Usi a detailed simulatio study it is show that the roosed rotocol is able to comute the artial keys ad the rou key withi a very small time eriod. We observed that the eery cosumtio for eerati the artial keys ad the rou key is very small comared to the total available eery. It is also sow by a exerimet that the eery cosumtio of SPIN icreases exoetially as the umber of rou odes icrease, but our roosed rotocol cosumes a very small amout of eery after the first rou key comutatio. 8. Refereces [1] David W. Carma, Peter S. Kruus, ad Bria J.Matt. Costraits ad aroaches for distributed sesor etwork security. NAI abs Techical Reort #00-010, Setember [2] H. Cha, A. Perri, ad D. So. Radom key redistributio schemes for sesor etworks, i IEEE Symosium o Security ad Privacy, Berkeley, Califoria, May [3] Welia Du, Ji De, Yuhsia S. Ha, Shia Che ad Pramod Varshey. A Key Maaemet Scheme for Wireless Sesor Networks Usi Deloymet Kowlede. To aear i IEEE INFOCOM, [4]. Escheauer ad V. D. Glior. A key-maaemet scheme for distributed sesor etworks, i Proceedis of the 9th ACM cofereceo Comuter ad commuicatios security, Washito, DC, USA, [5] Welia Du, Ji De, Yuhsia S. Ha, ad Pramod Varshey. A Pairwise Key Pre-distributio Scheme for Wireless Sesor Networks. I Proceedis of the 10th ACM Coferece o Comuter ad Commuicatios Security (CCS), Washito DC, October 27-31, [6] A. Perri, R. Szewczyk, V. We, D. Culler, ad J.D. Tyar. SPINS: Security rotocols for sesor etworks. I Proceedis of Mobicom, [7] Michael Steier, Gee Tsudik, Michael Waider. Key Areemet i Dyamic Peer Grous. IEEE Trasactios o Parallel ad Distributed Systems 11(8): , [8] A. Shamir. How to Share a Secret Commuicatios of the ACM, 22(11): , [9] Whitfield Diffie ad Marti E. Hellma. Privacy ad autheticatio. A itroductio to crytorahy. Proceedis of the IEEE, 67(3): , March [10] William Stallis. Network Security Essetials Alicatios ad Stadards.