RFID Cardinality Estimation with Blocker Tags

Transcription

1 RFID Cardinality Estimation with Blocker Tags Xiulong Liu, Bin Xiao, Keqiu Li, Jie Wu, Alex X. Liu, Heng Qi and Xin Xie School o Computer Science and Technology, Dalian University o Technology, China Department o Computing, The Hong Kong Polytechnic University, Hong Kong Department o Computer and Inormation Sciences, Temple University, USA Department o Computer Science and Engineering, Michigan State University, USA National Key Laboratory or Novel Sotware Technology, Nanjing University, China {xiulongliudut, likeqiu, qhclement, xiexin}@gmail.com csbxiao@comp.polyu.edu.hk, jiewu@temple.edu, alexliu@nju.edu.cn Abstract The widely used RFID tags impose serious privacy concerns as a tag responds to queries rom readers no matter they are authorized or not. The common solution is to use a commercially available blocker tag which behaves as i a set o tags with known blocking IDs are present. The use o blocker tags makes RFID estimation much more challenging as some genuine tag IDs are covered by the blocker tag and some are not. In this paper, we propose REB, the irst RFID estimation scheme with the presence o blocker tags. REB uses the ramed slotted Aloha protocol speciied in the CG standard. For each round o the Aloha protocol, REB irst executes the protocol on the genuine tags and the blocker tag, and then virtually executes the protocol on the known blocking IDs using the same Aloha protocol parameters. The basic idea o REB is to conduct statistically inerence rom the two sets o responses and estimate the number o genuine tags. We conduct extensive simulations to evaluate the perormance o REB, in terms o time-eiciency and estimation reliability. The experimental results reveal that our REB scheme runs tens o times aster than the astest identiication protocol with the same accuracy requirement. Keywords RFID Estimation, RFID Privacy, Blocker Tags. I. INTRODUCTION RFID systems have been widely used in a variety o applications such as supply chain management and inventory control [] [7] as the cost o commercial passive RFID tags is negligible compared with the value o the products to which they are attached (e.g., as low as 5 cents per tag [8]). For example, in Hong Kong International Airport where RFID systems are used to track shipment, the average daily cargo tonnage in May was K tonnes and has been on the rise [9]. An RFID system typically consists o a reader and a population o tags []. A reader has a dedicated power source with signiicant computing capability. It transmits commands to query a set o tags and the tags respond over a shared wireless medium. A tag is a microchip with an antenna in a compact package that has limited computing capability and longer communication range than barcodes. There are two types o tags: () passive tags, which do not have their own power sources and are powered up by harvesting the radio requency energy rom readers; () active tags, which have their own power sources. The widely used RFID tags impose serious privacy concerns as when a tag is interrogated by an RFID reader, no matter the reader is authorized or not, it blindly responds with its ID and other stored inormation (such as manuacturer, product type, and price) in a broadcast ashion. For example, a woman may not want her dress sizes and a patient may not want his/her medication, to be publicly known. An eective solution to this privacy issue is to use commercially available blocker tags [], []. A blocker tag is an RFID device that is preconigured with a set o known RFID tag IDs, which we call blocking IDs. The blocker tag behaves as i all tags with its blocking IDs are present. A blocker tag protects the privacy o the set o genuine tags whose IDs are among the blocking IDs o the blocker tag because any response rom a genuine tag is coupled with the simultaneous response rom the blocker tag; thus, the two responses collide and attackers cannot obtain private inormation. This paper concerns with the problem o RFID (population size) estimation with the presence o a blocker tag. Formally, the problem is deined as ollows: given () a set o unknown genuine tags G o unknown size g, () a blocker tag with a set o known blocking IDs B, (3) a required conidence interval α (, ], and () a required reliability β [, ), we want to use one or more readers to compute the estimated the number o genuine tags in G, denoted as ˆg, so that P { ˆg g αg} β. In other words, we have a set G o genuine tags with unknown number o unknown IDs and a set B o tags with known number o known IDs, we want to estimate G with the presence o B. The two sets G and B may overlap, as shown in Fig.. This problem may arise in many applications. For example, a jewel store may want to use such an RFID estimation scheme to monitor its stock while a blocker tag is being used to protect the privacy o some precious items. Fig.. Each ID corresponds to a blocking tag Each ID corresponds to a blocking tag and a genuine tag Each ID corresponds to a genuine tag Genuine Tag IDs (unknown) Blocking IDs (known) Three types o IDs in the system containing blocker tags. To the best o our knowledge, this paper is the irst to investigate RFID estimation with the presence o a blocker tag. Although some RFID estimation schemes have been proposed [7], [], [3] [8], none o them considers the

2 presence o a blocker tag. Furthermore, none o them can be easily adapted to solve our problem. How about turning o the blocker tag and then using prior RFID estimation schemes to estimate the number o genuine tags? Turning o the blocker tag will give attackers a time window to breach privacy, especially or the scenarios that RFID estimation schemes are being continuously perormed or monitoring purpose. Existing tree walking based [9] and ramed slotted Aloha based [] RFID identiication schemes can be used to exactly identiy the genuine tags, and thus obtaining the genuine tag cardinality. However, they are too slow or our estimation purpose. In this paper, we propose an RFID Estimation scheme with Blocker tags (REB). The communication protocol used by REB is the standard ramed slotted Aloha protocol, in which a reader irst broadcasts a value and a random number R to the tags where represents the number o time slots in a orthcoming rame. Then, each tag computes a hash using the random number R and its ID, where the resulting hash value h is within [, ], and the tag replies during slot h. For each slot, i no tag replies, we represent it as ; i only one tag replies, we represent it as ; i more than one tag replies, the tag responses will collide, and we represent this slot as c. Note that a reader can detect i there is a collision according to the CG standard. Executing this protocol or the blocking IDs (simulated by the blocker tag) and genuine tags, we get a ternary array BG[.. ] where each bit is,, or c. As we know the blocking IDs, we can virtually execute the ramed slotted Aloha protocol using the same rame size and random number R or the blocking IDs; thus, we get a ternary array B[.. ] where each bit is,, or c. From the two arrays BG[.. ] and B[.. ], we calculate two numbers: N, which is the number o slots i such that both BG[i] = and B[i] =, and N, which is the number o slots i such that both BG[i] = and B[i] =. REB is based on the key insight that in general the smaller N is, the larger B G is and the larger N is, the larger B G is. In this paper, we show that N monotonously decreases with the increase o B G and N monotonously increases with the increase o B G. Thus, rom the observed N and N, we can estimate B G and B G. Then, we can calculate the size o G because G = B G B G. We make the ollowing three key contributions in this paper. First, we make the irst eort towards RFID estimation with the presence o a blocker tag. We propose the REB scheme jointly using N and N to achieve an unbiased estimator or the genuine tag cardinality. The key technical development o this paper is on quantitatively and statistically correlating N and B G, N and B G. Second, we conduct thorough analysis to optimize system parameters, thereby achieving the required conidence interval and reliability in the astest speed. Third, we implement REB in Matlab and evaluate its perormance through extensive simulations. The experimental results reveal that our REB scheme runs tens o times aster than the astest identiication protocol under the same accuracy requirement. The rest o this paper is organized as ollows. In Section II, we describe REB and our theoretical analysis. In Section III, we conduct extensive simulations to evaluate the perormance o REB. We discuss related work in Section IV. Finally, we conclude the paper in Section V. II. REB PROTOCOL In this section, we irst describe the system model used in this paper. Then, an eicient RFID Estimation scheme with Blocker tags (REB) is proposed to estimate the number o genuine tags by jointly using N and N observed in a time rame. We explicitly give the unctional estimator and point out that the estimation using a single time rame is hard to be accurate due to probabilistic variance. Hence, we propose to use multiple independent time rames to reine the estimation. This section urther presents rigorous theoretical analysis to investigate how many rames are needed to guarantee the desired estimation accuracy and how to avoid premature protocol termination. We also investigate the parameter settings (i.e., and p) to optimize the perormance o our REB. A. System Model For the clarity o presentation, we irst consider the RFID system containing a single reader, a single blocker tag, and a population o genuine tags. Then, we will discuss how to extend REB to the scenario that deploys multiple readers and blocker tags. We represent the set o blocking IDs as B, whose cardinality is b. The set o genuine tags is denoted as G, whose cardinality is g. We use U to denote the union tag set, i.e., B G, and U = u. The IDs in B G do not correspond to any genuine tags, whose cardinality is denoted as b, i.e., b = B G. The reader communicates with tags (including both genuine tags and virtual ones simulated by the blocker tag) under control o the backend server. The communication between the reader and tags are based on a time slotted way. Any two consecutive transmissions (rom a tag to a reader or vice versa) are separated by a waiting time τ w = 3us []. According to the speciication o the Philips I-Code system [], the wireless transmission rate rom a tag to a reader is 53Kb/s, that is, it takes a tag τ t = 8.9us to transmit bit. The rate rom a reader to a tag is 6.5Kb/s, that is, transmission o bit to tags requires τ r = 37.7us. Then, the time o a slot or transmitting m-bit inormation rom a tag to the reader is τ w + m τ t ; and the time o a slot or transmitting m-bit inormation rom a reader to the tags is τ w + m τ r. The notations used throughout the paper are summarized in Table I. B. Protocol Description Our REB uses the standard ramed slotted Aloha protocol speciied in EPC CG [] as the MAC layer communication mechanism. The reader initializes a slotted time rame by broadcasting a binary request R,, where R is a random number and is the rame size (i.e., the number o slots in the orthcoming rame). Using the received parameters R,, each tag initializes its slot counter sc by calculating sc = H(ID, R) mod and the hashing result ollows a uniorm distribution within [, ]. The reader broadcasts QueryRep command at the end o each slot. Upon receiving QueryRep, a tag decrements its slot counter sc

3 TABLE I. NOTATIONS USED IN THE PAPER Notations Descriptions G set o genuine tags. g cardinality o G. i.e., g = G. B set o blocking IDs. b cardinality o B G. i.e., b = B G. U union set. U = B G. u cardinality o U. i.e., u = B G. α required conidence interval. β required reliability. ˆg estimate o g. rame size. p persistence probability. E( ) expectation. V ar( ) variance. Z β the percentile o β. e.g., Z β =.96 when β = 95%. p probability that a slot pair is,. p probability that a slot pair is,. N # o the persistent empty slots in a rame. N # o the persistent singleton slots in a rame. by. In a slot, a tag will respond to the reader i its slot counter sc becomes. According to the occupation status, slots are classiied into three types: empty slot in which no tag responds; singleton slot in which only one tag responds; collision slot in which two or more tags respond. In the ollowing, we present how our REB estimates the number o genuine tags by observing the slots in a rame. Since the backend server gets ull knowledge o the simulated blocking IDs, it is able to predict which slots the blocking IDs are mapped to. Thus, it is able to construct a virtual ternary array B[.. ]. A bit in B[.. ] is set to when no blocking ID is mapped to this slot; when only one blocking ID is mapped to this slot; c when two or more blocking IDs are mapped to this slot (a hashing collision). On the other hand, by observing the rame, the reader could get another array BG[.. ], also consisting o bits. A bit in BG[.. ] is set to when no tag responds in this slot; when only one tag responds in this slot; c when two or more tags cause a collision in this slot. To distinguish a singleton slot rom a collision one, each tag does not need to respond with the whole 96-bit ID. For saving time, each tag responds with the RN6 (6-bit) [] that is much shorter than 96-bit ID. Two slots with the same index in B[.. ] and BG[.. ] are called a slot pair. In our scheme, the reader needs to record the numbers o the ollowing two types o slot pairs. N is the number o persistent-empty slot pairs, (i.e., B[i] = AND BG[i] =, i [, ]). N is the number o persistent-singleton slot pairs, (i.e., B[i] = AND BG[i] =, i [, ]). REB can estimate the cardinality o genuine tags by jointly using the number o persistent-empty slots and that o persistent-singleton slots. A persistent-empty slot happens only when no ID in U = B G is mapped to this index. Thus, N relects the cardinality u o U. Latter, we will show that a monotone unctional relationship can be established between u and N. REB uses this unction to estimate u rom N. Similarly, a persistent-singleton slot happens when only one ID in B G is mapped to this index. Thereore, N relects the cardinality B G (denoted as b ). Clearly, i we know u and b, we can get the cardinality g o genuine tags by calculating g = u b. It may not be suicient to satisy the required estimate accuracy by counting the numbers o N and N in a single rame. To improve the accuracy, REB requires the reader to execute k independent rames with dierent random number R. Note that, the rame size should be set no more than 5 in practice [], [9], [3] (the detailed reasons can be ound in literature [9]). I a large number o tags contend or such a short rame, most slots will become collision slots. To scale to a large tag population, we exploit the method stated in []. Speciically, the reader uses a persistence probability p (, ] to virtually extends the rame size to /p, but actually terminates the rame ater the irst slots. Fundamentally, each tag participates in the actual rame o slots with a probability p. C. Functional Estimator In this section, we derive the unctional estimator ˆg rom N and N or the REB protocol in one rame. For an arbitrary slot pair, the probability that it is,, denoted as p, is given as ollows. p = ( p )u e up () The approximation in Eq. () holds when /p is relatively large [5], [], [3]. The number o slot pairs,, i.e., N, ollows Bernoulli(, p ). The expectation and variance o the variable N are presented as ollows. E(N ) = p = e up () V ar(n ) = p ( p ) = e up ( e up ) (3) Similarly, we use p to denote the probability that a slot pair is,, which is given as ollows. ( ) b p = ( p )( p )u b p up e () The number o, slot pairs, i.e., N, also ollows Bernoulli(, p ). The expectation and variance o the variable N are presented as ollows. E(N ) = p = b pe up (5) V ar(n ) = p ( p ) = b pe up ( b p up e ) According to Eq. (), u can be expressed as ollows. u = p Dividing Eq. (5) by Eq. (), we have: (6) E(N) ln[ ] (7) E(N ) E(N = b p ) b = E(N) pe(n ) According to Eqs. (7)(8), g is expressed as ollows. g = u b = p E(N) ln[ ] E(N) pe(n ) By substituting N or E(N ) and N or E(N ) in Eq. (9), we get the estimator o g as ollows. (8) (9) ˆg = p ln( N ) N pn ()

4 That is, Eq. () exactly speciies how to use the observed N and N to estimate the cardinality g o genuine tags. Theorem presents the expectation and the variance o the estimate ˆg, which are very important to investigate the probabilistic accuracy o the estimator. Theorem. ˆg in Eq. () is an unbiased estimator o g, that is, E(ˆg) = g. The variance o the estimator is V ar(ˆg) = (b p + b p) p. p e up Proo: To get the expectation and variance o ˆg, we use a similar method in []. Since the variance expression is dierent rom [] [], we present the detailed proving procedures or the completeness o this paper. According to Eq. (), ˆg is a unction with respect to N and N. Hence, we denote ˆg as φ(n, N ), that is, ˆg = φ(n, N ). We present the Taylor s series expansion [5] o unction φ(n, N ) around (η, η ), where η = E(N ) and η = E(N ). φ(n, N ) φ(η, η )+[(N η ) N +(N η ) N ] () We have the ollowing equation by taking expectation o both sides o Eq. (). E[φ(N, N )] =φ(η, η ) + N E(N η ) + N E(N η ) = g () So ar, E(ˆg) = g is proved, that is, ˆg is an unbiased estimator o g. In what ollows, we investigate the variance o ˆg. V ar(ˆg) = E[ˆg E(ˆg)] =E[(N η ) N + (N η ) N ] =V ar(n )( N ) + V ar(n )( N ) + Cov(N, N ) N N (3) In the ollowing, we present how to get the covariance Cov(N, N ). Since Cov(N, N ) = E(N N ) E(N )E(N ), we calculate E(N N ) below. E(N N ) = x xyp [N = x N = y] x= y= ( ( ) x = xy )(p ) x x (p ) y ( p p ) ( x y) x y x= y= ( ) =p ( x) (p ) x ( p ) x x x= ( ) = pp (p ) x ( p ) x p x x= ( )(p ) p p ( p p p x x= ( x= ) x ) (p ) x ( p ) x (p ) x ( p ) x = p p ( )(p ) p p p = ( )p p p p p () As required by Eq. (3), we also calculate the irst-order partial derivatives o φ(n, N ) as ollows. N =η N N =η = e up ( b p ) N =η N N =η = up e p (5) We have obtained E(N N ) in Eq. (), E(N ) in Eq. (), and E(N ) in Eq. (5). Thus, we can calculate Cov(N, N ) as ollows. Cov(N, N ) = E(N N ) E(N )E(N ) = p p = b pe up (6) By combining Eqs. (3) (6) (5) (6) into Eq. (3), we then get the variance o ˆg as ollows. V ar(ˆg) = up e (b p + b p) p p, (7) where and p are the used rame size and the persistence probability, respectively. D. Reined Estimation with k Frames Because o probabilistic variance, the estimate ˆg got rom a single rame is hard to meet the predeined accuracy. By the law o large number [6], we issue k independent rames and use the average estimation result ˆg k = k k ˆg j to achieve a more accurate estimate in REB, where ˆg j is the estimate o g derived rom the j th rame. We propose Theorem to investigate how many independent rames are necessary to guarantee that the average estimate ˆg k can satisy the predeined (α, β) accuracy. Theorem. The reader perorms k independent rames. The average estimate ˆg k = k k ˆg j can guarantee the required (α, β) accuracy, i the rame number k satisies k Z β gα [ up j j e p j j (b p j + j b j p j ) j ], where p j j and p j are the rame size and persistence probability o the j th rame, respectively. Proo: We deine ˆg k = k k ˆg j as the average estimate o k successive rames, where ˆg j is the estimate o the j th rame, j [, k]. The reader initializes each rame with dierent random seeds. Hence, the estimate ˆg j is independent to each other. Thus, we have E( ˆg k ) = k k E(ˆg j) = g; and V ar( ˆg k ) = k k V ar(ˆg j). Clearly, the average estimate ˆg k still converges to the actual cardinality g. Given a required reliability β, the actual conidence interval is within [g Z β V ar( ˆgk ), g + Z β V ar( ˆgk )], where Z β is a percentile o β, e.g., i β = 95%, Z β will be.96. To guarantee the required conidence α, we should guarantee: g + Z β V ar( ˆg k ) g + gα g Z β V ar( ˆg k ) g gα Substituting k k V ar(ˆg j) or V ar( ˆg k ) and solving the above inequalities, we have: k Z β k V ar(ˆg j ) (8) gα

5 According to Eq. (7), we have V ar(ˆg j ) = up j j e p j j (b p j + j b j p j ) j p j into Eq. (8), we have: k Z β k [ gα jp j up j e j. Substituting it (b p j + j b jp j) j ] (9) p j When the above inequality holds, the predeined (α, β) accuracy can be satisied. Ater k rames, the backend server calculates the R.H.S. (Right Hand Side) o Eq. (9). I the result is less than (or equal to) k, the estimation process terminates; otherwise, the next rame continues to be issued. Note that, we do not know the actual u, b and g. We propose to use the irst k leading rames to estimate them, as shown in Eq. (). ˆu k = k ˆb k = k ˆg k = k ˆu j = k ˆb j = k ˆg j = k [ j ln( Nj )] p j j [ jnj p jn j ] [ j p j ln( Nj j ) jnj p jn j ], () where N j and N j are the numbers o persistent empty slots and persistent singleton slots observed in the j th rame. E. Avoiding Premature Termination In the execution o REB, we can get ˆu k, ˆb k and ˆg k ater k rames. However, their estimation is inaccurate due to probability variance. I we directly use them to calculate the R.H.S. o Eq. (9), k may have a chance to be larger than it, which is not true and REB will have a premature termination (i.e., the currently achieved accuracy has not met the required one yet). In the ollowing, we propose to solve the issue o premature termination. First, we calculate the variances o ˆu k, ˆb k and ˆg k as ollows. Note that, we can obtain the variances o ˆu k and ˆb k using similar method o getting V ar(ˆg k ). V ar(ˆu k ) = k V ar(ˆb k ) = k ˆu p k j j (e j ) p j ˆu p k j e j ( ˆb k + ˆb k ) j p j V ar(ˆg k ) = ˆu p k j e j (ˆb k j p kp j + j ˆb k jp j ) j j p j () When calculating the R.H.S. o Eq. (9), we can use ˆu k = ˆu k + δ V ar(ˆu k ) to substitute u, ˆb k = ˆb k + δ V ar(ˆb k ) to substitute the irst b, ˆb k = ˆb k δ V ar(ˆb k ) to substitute the second b, ˆg k = ˆg k +δ V ar(ˆg k ) to substitute g. In Section III, simulation results demonstrate that this tactic can eectively avoid the premature termination. The three-sigma rule [7] indicates δ = 3 is large enough. F. Dynamically Optimizing p and In REB, parameters p and can signiicantly aect the protocol perormance, thus need to be optimized. We use the inormation observed rom the x leading rames to acilitate the optimization o p and in the (x + ) th rame. The optimization goal is to minimize the execution time while guaranteeing the required (α, β) accuracy. In the irst rame, we set = 5. To coarsely set p, we modiy the scheme used in [], [8], [9]. Speciically, the reader keeps issuing one-slot rames. The persistence probability ollows a geometric distribution,,, 8,, i.e., the persistence probability in the γ th single-slot rame is. This process does not terminate until an empty slot γ appears. Assuming the l th slot is the irst empty slot, we have a coarse estimation o u to be l [8]. The persistence probability p o the irst rame is simply set to / l. In what ollows, we describe how to optimize p and or the (x+) th rame (x ). Since p and are correlated to minimize the total execution time, we irst ix the value to get an optimized p. The range o is rom to 5 and its value should be,, 8,, 5, as suggested in the CG standard. Thus, we can get an optimized by comparing all possible pairs o p and (with only 9 possible values). Note that, the proposed REB is not sensitive to the coarse settings o p and, because REB will quickly converge to a near-optimal setting o p and ater a ew rames, which will be demonstrated in the simulations. ) Optimizing p: We optimize p using a binary search method or a given value. Since the smaller the estimation variance o ˆg is, the less rames will be required, that is, the less the execution time ( rame number) is. We theoretically investigate how to optimize p to minimize the estimation variance V ar(ˆg) in Eq. (7). We prove that V ar(ˆg) is a convex unction o p (, ] in Theorem 3. By virtue o the convex property, we have two claims: (i) There is an optimal p op (, ] minimizing the variance V ar(ˆg). Taking Fig. (a)(b) or example. (ii) The irst order partial derivation presented in the ollowing Eq. () satisies p (, p op ), and p (p op, ],. Taking Fig. (c)(d) or example. = e up ( b u + b + u b u p p p ) + () 3 p 3 Based on the above two claims, we propose a binary-search algorithm to get the optimal p op or the j th rame, j. In step o Algorithm, δ speciies the maximum deviation between the outputted p and its actually optimal value. Initially, p high = and p low is set to a small enough value /ˆu x. By the while loop in steps, p high and p low progressively approach the optimal p op. When the optimization derivation is less than δ, the average value o p high and p low are returned as the optimal p. The complexity o Algorithm is Θ(lg δ ). Theorem 3. V ar(ˆg) in Eq. (7) is a convex unction o p. Proo: V ar(ˆg) is a convex unction o p (, ], i and only i its second order partial derivative satisies p

6 x 6 x 6 3 x 5 x 7 in Eq. (7) Var(ĝ) 8 6 Optimal p Var(ĝ)in Eq. (7) 5 3 Optimal p in Eq. () V ar(ĝ) Optimal p in Eq. () V ar(ĝ) 5 5 Optimal p persistence probability p (a) persistence probability p persistence probabilityp persistence probability p (b) (c) (d) Fig.. b =, b = 5, g =, = 5. (a) The variance V ar(ˆg) against p [., ]. (b) Magniied plot o (a), p [.,.]. (c) The irst order partial derivation o V ar(ˆg) against p [., ]. (d) Magniied plot o (c), p [.5,.]. ˆg (, ], >. We get its second order partial derivative as ollows. ˆg up =e ( b u + b u + u b u 3 p p b + u + 6 p 3 p ) } {{ } denoted as R 6 p (3) As shown in Eq. (3), we denote ( b u + b u+u 3 p b u p b +u p p ) as R. In what ollows, we irst prove R is always larger than. R =(b u p + b u p + u p b u p 3 b 3 p u 3 p + 6 )/( 3 p ) =[(b up up) + ( b up ) + 6 () 3 + ( up 3 3 ) + ( b u b ) 3 p]/( 3 p ) Since u > b in Eq. (), we have R >. Using the ourth-order Taylor series expansion, we have e up > + up + u p + u3 p u p 3. According to Eqs. (3)(), we have: ˆg up = e R 6 p >( + up + u p + u3 p u p 6 )R 3 p = ( u 3 p u3 b p 3 ) + 5u6 p 5 + p 5 5 (u b u3 + 3 ( u 3 p 3 3 ub 8 ) + u 3 3 (b u ) + u3 b p + u5 b p 3 u b + > 6 6 p 3 ) (5) ˆg >, which is a Eq. (5) indicates that p (, ], necessary and suicient condition to prove that V ar(ˆg) is a convex unction o p (, ]. ) Optimizing : We optimize or the (x+) th rame. Considering CG standard and practical constraints [], should take a value rom,, 8,, or 5. To improve the time-eiciency, it is reasonable to minimize the expected remaining execution time. We denote the minimum rame number that needs to be urther executed as y, our goal is: Minimizing ( + ) y (6) Algorithm : Optimizing p x+ or the (x+) th rame. Input: ˆu x, ˆb x, ˆg x, and. Output: The optimized p x+ or the (x + ) th rame. : δ =.; : p low = ˆu x ; 3: p high = ; : while p high p low > δ do 5: p = (p low + p high )/; 6: Calculating in Eq. (); 7: i ( > ) then 8: p high = p; 9: else : p low = p; : end i : end while 3: p x+ = (p low + p high )/; : return p x+ ; In Eq. (6), + means a slot or transmitting protocol parameters is ollowed by an -slot rame. According to the termination condition in Eq. (8), the value o y should satisy the ollowing inequality: x + y Z β x V ar( ˆg j) + yv ar(ˆg) (7) gα By solving the above inequality, we know that the minimum rame number y that needs to be urther executed is: Z β V ar(ˆg) x+ [ Z βv ar(ˆg) x x] g α g α + Z β V ar(ˆg j) x g α Here, V ar( ˆg j ) = up j jp e j j (b p j + j b j p j ) j p j (8), j [, x], V ar(ˆg) = p e up (b p + b p) p. g, u, b can be approximated by ˆg x, ˆu x, ˆb x, respectively. For any {,, 8,, 5}, we can use Algorithm to get the corresponding optimal p. Given each pair (, p), the smallest y can be obtained rom Eq. (8). Thus, we can get the optimal rom Eq. (6). The calculation complexity o optimizing p and is bounded by Θ(9 lg δ ).

7 G. REB with Multiple Readers and Blocker Tags In practice, a single reader cannot probe all the tags due to the limited communication ranges []. Similarly, a single blocker tag cannot protect all privacy-sensitive tags that may be distributed across the a large area. A solution is to deploy multiple readers and blocker tags with overlapping regions to cover the whole monitoring area. We assume all the readers and blocker tags are well synchronized by the excellent scheduling schemes [8] [3]. All parameters, p, R involved in REB are the same across all readers. In what ollows, we present how to distributively construct the global BG[.. ]. For an arbitrary slot s in a rame, i all the readers observe an empty slot, the backend server sets BG[s] = ; i no reader senses a collision and all the received RN6s are the same, the backend server sets BG[s] = ; i at least one reader senses a collision or dierent RN6s are observed by dierent readers, the backend server sets BG[s] = c. Based on these rules, the reader is able to generate a global actual array BG[.. ]. Logically, all the readers co-work like a super reader that is able to cover the whole area. The rest o REB in multi-reader scenarios is the same as what ormer sections have described. III. PERFORMANCE EVALUATION In this section, we conduct simulations to evaluate the perormance o REB in a large scale RFID system that contains thousands o tags. The simulators were implemented using MATLAB. Since REB in the multi-reader scenario is logically the same as that in the single reader scenario, this paper only simulates a single reader ollowing prior literature [7], [], [6], [3]. The setting o slot length is based on what we speciied in Section II-A. In the ollowing, we irst veriy the eectiveness o our optimization methods on and p. Then, we conduct simulations to evaluate the actual estimation reliability o REB and its time-eiciency. We run each simulation times and report the average results. A. Veriying the Optimized and p The setting o parameters and p is important to the perormance o REB. To achieve the overall optimal and p, it is necessary to know the values o u, b and g beore the execution o REB, which, however, are what we want to estimate. Using the simulation conditions shown in Fig. 3, the overall optimal is 8, and the overall optimal p is.75, which are calculated by the actual values o u, b and g. In the simulations corresponding to Fig. 3, we aim to veriy the convergence o and p to their overall optimal values. Results in Fig. 3 (a) demonstrate that about 8.5% o the independent simulations correctly take the overall optimal = 8 in the 3 rd rame. And this ratio reaches 5.5% in the th rame, that is, our REB has a good chance to take the overall optimal just ater the 3 rd rame. The simulation results in Fig. 3 (b) demonstrate that the persistent probability p approaches its overall optimal value rame by rame. The value o p taken in the th is very close to the optimal value.75. All in all, and p approach their overall optimal values rame by rame. The underlying reason is that more rames increase the estimation accuracy o u, b and g, which eventually acilitates the optimization o and p. Ratio o the taken rame size % =56 =5 =3 =6 =8 % % % % 9% =8 =56 =5.%.6% %.3% =3 =6.7% =8 =56 = % 8.5% %.8% =3 =6 5.5% 6.53% % =8 =56 =5.97% % =3 =6 Persistence probability the j th rame the j th (b) rame (a) actual persistence probability optimal persistence probability Fig. 3. Veriying the optimized settings o and p. B G = 5, B G = 5, G B = 5. α = %, β = 9%. (a) Veriying the optimized. (b) Veriying the optimized p. B. Estimation Reliability One o the most important perormance metrics or estimation protocols is the actual reliability. In an arbitrary simulation, i the estimate ˆg is within [g( α), g( + α)], we reer to it as a successul estimation. We record the success times among independent simulations. The ratio, i.e., success times/, is treated as the actual reliability. Simulation results in Fig. reveal that REB (δ = ) does not always meet the required reliability (i.e., β = 95%). The reason lies in the variances i directly using ˆu k, ˆb k and ˆg k to determine the termination condition. By taking their variances into consideration, the proposed δ-sigmabased termination tactic eectively avoids the premature termination. Simulation results in Fig. reveal that the actual reliability o REB (δ = ) and REB (δ = ) is always higher than the required one. Estimation Reliability δ δ δ 8 5 Estimation Reliability 3:: :3: :: Premature termination :: :: ::3 :: Cardinality o tag set U Tag ratio o B G B G G B (a) (b) Fig.. Evaluating the reliability o REB. α = 5%, β = 95%. (a) Tag ratio B G : B G : G B is ixed to : :, and u varies rom 3 to. (b) u is ixed to 9, and tag ratio varies. C. Time Eiciency Besides the estimation reliability, another important metric is time-eiciency. In this subsection, we evaluate the time-eiciency o the protocols given the same estimation accuracy. No existing estimation protocols can correctly approximate the cardinality o genuine tags in an RFID system with the presence o blocker tags. The only possible solution, to the best o our knowledge, is to perorm the comprehensive identiication protocols to identiy the tags in the system. Hence, we compare REB with two representative identiication protocols: one is the Tree Hopping

8 (TH) protocol [9]; the other one is the Enhanced Dynamic Framed Slotted ALOHA (EDFSA) protocol []. TH protocol terminates ater it traverses the whole tree. TH can identiy not only the IDs in (B G) (G B) when a queried preix is ollowed by a successul read, but also the IDs in B G when a preix whose length is equal to tag ID but still ollowed by a collision read. Then, we can get the set G, by calculating [(B G) (G B) B] (B G). The cardinality g is got upon getting G. As or EDFSA protocol, it executes rames round by round. In a round, only the IDs in (B G) (G B) have chance to be identiied. We denote the set o identiied IDs as S ident. Since the reader does not know whether all IDs in (B G) (G B) are completely identiied or even what percentage o them are identiied, EDFSA cannot terminate by itsel. For the sake o EDFSA, we assumes it can intelligently terminate once [ (B G) (G B) S ident ] < G α. ) Impact o Tag Cardinality: To investigate the impact o tag cardinality on the protocols execution time, we ix the tag ratio B G : B G : G B to ::, and vary u (indicating the system scale) rom to 5. The simulation results in Fig. 5 demonstrate that our REB signiicantly outperorms HT and EDFSA. For example, when u = 5, REB (δ = ) runs about times aster than EDFSA, and nearly 9 times aster than TH; while REB (δ = ) runs 33 times aster than EDFSA, and 68 times aster than TH. Moreover, the execution time o HT and EDFSA grows linearly as u increases. In contrast, our REB has a stable execution time, which reveals its good scalability against tag cardinality u. Execution time (s) Cardinality o tag set U 5 5 Fig. 5. Evaluating the time-eiciency o protocols with varying u. Tag ratio o B G : B G : G B is ixed to : : and α = 5%, β = 95%. ) Impact o Tag Ratio: The dierent tag ratio o B G : B G : G B may have signiicant impact on the execution time o protocols. Here, we ix u = 3, and evaluate the execution time o protocols with varying tag ratio. The simulation results in Fig. 6 demonstrate that our REB still outperorms the existing protocols by signiicantly reducing the execution time. Moreover, the results in Fig. 6 clearly show the perormance trend o the protocols with varying tag ratio, which are elaborated below. The results in Fig. 6 (a) reveal that the larger the ratio o tags in B G is, the larger the execution time o our REB scheme is. The underlying reason is that more tags in the set B G will incur more intererences to the process δ δ o estimating genuine tags. We make another two main observations rom Fig. 6 (b) which shows the execution time o the protocols with varying ratio o tags in B G. First, the perormance o identiication protocols deteriorates as the ratio o tags in B G increases. The reason is that more tags in B G will cause more blocking collisions, which seriously interere the tag identiication process. Second, the larger the ratio o tags in B G is, the smaller the execution time o our REB scheme is. The underlying intuitive reason is that larger ratio o tags in B G leads to smaller ratio o tags in B G, which decreases the intererence o tags in B G to the process o estimating g. Because o a similar reason, the results in Fig. 6 (c) reveal that the execution time o REB also decreases as the ratio o tags in G B increases. Execution time (s) Execution time (s) (a) the ratio o tags in B G varies (b) the ratio o tags in B G varies (c) the ratio o tags in G B varies Fig. 6. Evaluating the time-eiciency o protocols with varying tag ratio. u is ixed to 3, and α = 5%, β = 95%. IV. δ Execution time (s) RELATED WORK In the inant stage o RFID study, a great deal o attention was paid to the problem o tag identiication that aims to identiy the exact tag IDs. Generally, there are two types o identiication protocols: Aloha-based protocols [3] and Tree-based protocols [9]. Fundamentally, the Alohabased protocol is a kind o Time Division Multiple Access (TDMA) mechanism. A tag ID can be successully identiied in a slot when only one tag responds in this slot. As or tree-based protocols, the reader broadcasts a / string to query the tags. A tag responds with its ID once it inds that the querying string is the preix o its ID. A reader can successully identiy a tag ID when only one tag responds. Clearly, the execution time o identiication protocols is proportional to the tag population size. What is worse, in the RFID system with presence o blocker tags, the perormance o identiication protocols will urther deteriorate because o the blocking collisions caused by IDs in B G. To ast report the tag cardinality or various purposes such as timely stock monitoring, a great eort has been made to study the problem o tag estimation [5], [7], [], [3] [8], [3], [33] [35]. These estimation protocols leverage the observations rom Aloha/Tree protocols to statistically estimate the tag cardinality. For example, M. Shahzad et al. proposed the Average Run based Tag estimation (ART) by observing the average length o sequences o consecutive non-empty slots []. To the best o our knowledge, all these estimation protocols cannot address the problem o genuine tag estimation because they cannot exclude the intererence rom blocking tags. RFID privacy is o great importance but suers the threat rom malicious scanning. Ari Juels et al. proposed the blocker tags to protect the privacy-sensitive tags rom δ

9 malicious scanning []. Every coin has two sides. Ehsan Vahedi et al. indicated that the blocking technique causes a new threat to the RFID system. Speciically, a malicious blocker tag can prevent the valid reader rom reading the tags. An eicient scheme was proposed to detect the existence o an attacker in the RFID system [36]. Following the original purpose o proposing blocker tags, this paper still leverages the blocker tags to protect the privacy o genuine RFID tags. V. CONCLUSION This paper ormally deines a new problem o genuine tag cardinality estimation with the presence o blocker tags. To eiciently address this practically important problem, we propose the RFID Estimation scheme with Blocker tags (REB), which is compliant with the commodity EPC CG standard and does not require any modiications to othe-shel RFID tags. REB provides an unbiased unctional estimator which can guarantee any degree o estimation accuracy speciied by the users. Using REB, a retailer can timely monitor the product stock while blocker tags are being used to protect the privacy o some important items. Extensive simulation results reveal that REB is tens o times aster than the astest identiication protocol with the same accuracy requirement. ACKNOWLEDGMENT This work is supported by the National Science Foundation or Distinguished Young Scholars o China (Grant No. 65); the State Key Program o National Natural Science o China(Grant No. 63); NSFC under Grant nos. o 6736, 6736, 677, 6387, 6389, 63798, 63799, 678, 639 and 6756; HK RGC PolyU G-YM8; NSF grants ECCS 36, ECCS 89, CNS 38963, CNS 65, and CCF 867; the Jiangsu Future Internet Program under Grant No. BY395--8, and the Jiangsu High-level Innovation and Entrepreneurship (Shuangchuang) Program. REFERENCES [] K. Finkenzeller, RFID Handbook: Fundamentals and Applications in Contactless Smart Cards, Radio Frequency Identiication and Near-Field Communication, Wiley,. [] L. Yang, Y. Chen, X.-Y. 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