Simulated Annealing based Optimization Model for

Rama N. et al. / International Journal of Engineering Science and Technology Vol. 2(3), 2010, 296-306

Simulated Annealing based Optimization Model for the Gossamer Protocol Rama N.#, Suganya R.* #

Department of Computer Science, Presidency College, Chennai 600 005, India

*Department of Computer Science, Meenakshi College for Women, Chennai 600 024, India and Research Scholar, Mother Teresa Women’s University, Kodaikanal 624 101, India E-mail:[email protected]

Abstract The use of low cost passive RFID tags has become very prevalent. Lightweight cryptography has evolved to address the security issues in these tags. The Gossamer protocol is a lightweight mutual authentication protocol which has guaranteed considerable security in these passive tags. As power is a major constraint in these tags, a detailed analysis of the power consumed by the Gossamer protocol was undertaken and results presented. It was determined that optimizing the power consumed by the protocol can result in substantial power savings and hence significantly enhance the performance of the RFID system. This paper proposes a new optimization model based on the simulated annealing method, that ensures the bounding of the number of power-crunching operations carried out in each run of the Gossamer protocol. The validity of the model is also established by the presentation and discussion of an experimental instance. Keywords: Gossamer; RFID; Mutual Authentication Protocol; Optimization; Simulated Annealing.

1. Introduction Radio Frequency Identification (RFID) systems have become all but ubiquitous. Yet, the severely resource-constrained nature of the components of RFID systems places several constraints on the usage of these systems [1]. The main components of an RFID system are the RFID reader and RFID tags. An RFID tag is attached to any item that needs to be tracked or monitored. The RFID reader queries the tags from time to time and keeps track of them. RFID tags are broadly classified as passive and active tags. Passive tags do not have even their own power source, and it is the RFID reader’s responsibility and prerogative to initiate the conversation. The tag draws power from the signal sent by the reader. Memory size and processing capability too are very limited in passive tags [2]. The reader and tags communicate with each other over a non-secure channel. The reader queries the tags and the tags reply with their unique identification number (ID). The ID has to be securely transmitted from the tag to the reader, lest a rogue reader gets its hands on it, as a consequence of which tags may be impersonated. However, traditional cryptographic algorithms are resourcecrunchers, and are hence irrelevant in such a resource-constrained environment. A branch of cryptography called lightweight cryptography that addresses the security issues of constrained environments has therefore evolved over the past few years [3].

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Mutual authentication is a crucial requirement that needs to be addressed in the case of RFID systems, for most applications of such systems involves the identification of the right tag by an authorized reader. Lightweight and yet secure mutual authentication protocols, therefore, become allimportant. Ari Juels proposed the scheme of minimalist cryptography for this purpose [4]. This scheme is used for authentication between the reader and the tag through the exchange of messages. Inspired by this scheme, a family of Ultra-lightweight mutual authentication protocols was proposed by Pedro Peris Lopez et al [5, 6, 7, 8], of which the Gossamer protocol is a part [9]. The suitability of the Gossamer protocol for Class 1 RFID tags (passive tags) in terms of security, number of message exchanges needed for the authentication process and the memory demanded by the protocol, has been thoroughly studied. The performance of the protocol in terms of the amount of power involved in the generation of the messages was also analyzed by the authors [10]. The impact of the power consumed on the performance of RFID systems can never be overemphasized. The lesser the power needed by the protocol the better will be the performance. As the RFID tag is drawing its power from the reader and the reader needs to energize multiple tags simultaneously, the lesser the power consumed by a single tag, the higher the number of tags the reader will be able to energize in one go. Thus, protocols proposed for mutual authentication between tag and reader as well as between tag pairs (such as those proposed by the authors [10]) will benefit to a large extent if the number of tags that can be read simultaneously by the reader increases. Optimization of the power consumed by the protocol provides a way to achieve this benefit. This paper presents an optimization model for the Gossamer protocol, based on the Simulated Annealing optimization model. The Gossamer protocol extensively uses left-shift operations. It has been found during this study that restricting the number of shift operations (shift count) to within a specific range, directly contributes to power savings. The shift operations of a particular run of the protocol is determined by the input parameters n1 and n2, random numbers generated afresh by the reader for each run of the protocol. The model proposed in this work ensures that the random numbers generated contribute to a shift count that is bounded by desired upper and lower bound values. This fixing of a range for the shift count necessarily results in power savings, and hence contributes to enhanced performance of the RFID system as a whole. However, the model props up no boundaries on the values of the random numbers themselves, thereby posing no threat to the security of the system.

2. Overview of Gossamer Protocol The Gossamer Protocol is a lightweight mutual authentication protocol designed based on the minimalist cryptographic scheme. This section gives an overview of the protocol. The basic assumptions of this protocol are as follows: • Each RFID tag has a unique identification number (ID) that is 96 bits long. • Each tag has the capability to store an IDS (Index pseudonym) and two keys k1 and k2, all of which are updated after each run of the protocol. • The RFID reader has access to a database that has the values of ID, k1 and k2, indexed through IDS for all tags in the RFID system’s scope. • The communication channel between the reader and the database is secure and only trusted readers can have access to the database. • The reader has a Pseudo Random Number Generator (PRNG) which generates two random numbers of at most 96 bits length for each run of the protocol. The following is the list of operations and the notations used: • Concatenation represented by || • XOR represented by ⊕ • Addition modulo 2m represented by + • ROT(X,Y) defined as circular left shift of X by the value (Y mod 96) This algorithm is based on generation of random numbers by the RFID reader. The tag too has to generate a few random numbers in order to secure the system further. Now Class 1 tags are highly resource-constrained and hence do not have the capability of supporting a classical PRNG. Therefore,

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a simple function called MixBits() is used to new random numbers using the random numbers generated by the reader. This is a lightweight function having its base in genetic algorithms. The protocol has the following phases (i) Tag Identification (ii) Mutual Authentication and (iii) Index pseudonym and key updating phase. In the tag identification phase, the reader sends a “hello” signal and the tag answers back with its IDS value. On receiving the IDS value, the reader uses it to index into the database and retrieves the corresponding ID and the keys k1 and k2. This marks the end of tag identification phase. Next, in the mutual authentication phase, first the reader is authenticated by the tag. This process is started off by the reader generating two random numbers n1 and n2, used extensively thereafter in that particular round of the protocol. The values n1 and n2 are encrypted into two messages A and B, which are concatenated with a third message C that reveals the identity of the reader to the tag, and sent to the tag. On receiving the message from the reader, the tag extracts the random numbers n1 and n2 from messages A and B respectively, and uses them to itself calculate C, which it then compares with the message C received from the reader. Thus, the tag authenticates the reader. Now the tag generates a message D in which it encrypts the ID and sends it to the reader, which the reader can verify. The reader thus authenticates the tag. The IDS and keys k1 and k2 are updated after each run of the protocol both at the reader and the tag ends. The updating of these values happens following the mutual authentication phase. The value of IDS, k1 and k2 of the last run of the protocol is also stored to handle synchronization problems. The equations involved in generating the messages and updating the IDS and key values are given below: Mutual Authentication Phase: Let n1 and n2 be the two random numbers generated. , (1) : , (2) , , (3) A ROT ROT IDS , , B ROT ROT IDS (4) : ROT ROT , , (5) : ROT ROT , , (6) , , (7) C ROT ROT D ROT ROT ID , , (8) IDS and Key Updating Phase: : MixBits , (9) ROT ROT IDS , , (10) IDS ROT ROT , , (11) ROT ROT IDS , IDS , (12) where c = 0x3243F6A8885A308D313198A2 (taken from π)

3. Need for Optimization The ROT() functional unit of the Gossamer protocol plays a very important role in determining the power consumed by the protocol. This is because this functional unit involves finding modulo 96, which requires repeated division, a highly demanding operation. Furthermore, repeated left-shifting is done, which also places a substantial demand on power. Over and above this, the fact is that the protocol applies this costly function twice while generating messages A, B, C and D and during each of the updates in the last phase of the protocol. A single shift operation involves as many as 1000 gate transitions. Thus optimizing the number of shift operations (shift count) will save many thousands of gate transitions. This will in turn result in a great savings in the power consumed. The number of shift operations to generate the messages varies depending on the values of the random numbers generated during each run of the protocol. A detailed analysis of this shift count range, done by varying the values of the random numbers n1 and n2 in different ranges, revealed that a desired shift count range can be fixed and values of n1 and n2 can thus be chosen to produce shift counts within the optimal range. The study revealed that it is possible to contain the shift count to within a reasonable range. Such optimization would necessarily result in significantly reduced power

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requirements for the protocol without compromising on the security, for the values of the random numbers can still be kept unbounded.

4. The Proposed Optimization Model 4.1. Applying the Simulated Annealing Optimization Model The optimization model proposed in this paper is based on Simulated Annealing [12], a classical optimization model for stochastic processes. In the proposed model, a desired shift count range is identified, based on which an optimal space for the mean of the n1 values and mean of the n2 values is identified. The PRNG employed in the reader can be designed to generate random numbers n1 and n2 in such a way that the mean of their distributions falls within this optimal solution space, thus guaranteeing that the shift count lies within the desired range. Since the Gossamer protocol uses the ROT() functional unit in many of its message-generation or value-updating algorithms, any one of these algorithms may be chosen to perform the aforesaid shiftcount optimization. In this study, the message D has been chosen for the purpose, for it is this message that is generated by the resource-constrained tag. The steps involved in identifying the optimal design space for the PRNG are as follows: 1. 2. 3. 4.

Fix the desired shift count range. Generate a sample set of size 500 whose shift count range lies within the desired range. Generate sets of size 500, of random number pairs n1 and n2. Calculate the corresponding number of shifts involved (in message D in this case) for the generated sets. 5. Determine the correlation coefficient of the shift counts of the actual and desired sets of values. 6. Determine if the set is optimal or not by applying simulated annealing, the classical algorithm for which is given below.

Algorithm SIM { S := Initial solution S0; T := Initial temperature T0; while (stopping criterion is not satisfied) do { while (not yet in equilibrium) do { S’ := Some random neighbouring solution of S; ΔE:= C(S’) - C(S); P := min(1, e-ΔE/KT); q = random(0, 1); //a random number between 0 and 1 if q < P then { S := S’; } } Update T; } Output best solution; } Temperature T depends on the system parameters that need to be optimized. In the present scenario, the system parameters n1 and n2 are the factors that need to be dealt with in order to optimize

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the shift count range. The optimized system parameters as well as the solution space will therefore be expressed as distributions. In the present case, the SIM algorithm helps to generate the optimal distribution space for the mean values of n1 and n2 in order to minimize the shift count of the ROT() functional unit.

4.2. The Experimental Setup This section presents an experimental instance implemented to optimize the shift count range for the generation of message D. The process followed is detailed below: 1. 150 sets with 500 distinct pairs of n1 and n2 were generated. (The values of n1 and n2 are unbounded in these sets. The values can also be bounded depending on the specific need of the application.) 2. The corresponding shift count value, λ, was calculated for each pair. λmax, λmin and λmean, respectively the maximum, minimum and mean values of λ were determined for each of the 150 sets of values. Then, the overall mean values, viz. mean(λmax), mean(λmin) and mean(λmean) were determined. 3. Based on these three values, three different desired shift count ranges, R1, R2 and R3 were chosen in order to study the behaviour of the optimization model. They are o R1 : λmin = 40, λmax =100 o R2 : λmin = 20, λmax =150 o R3 : λmin = 10, λmax =170 4. For each desired range, one set with 500 distinct pairs of n1 and n2 that would produce a shift count within the desired range were generated. 5. The Pearson’s correlation coefficient rA giving the measure of correlation between the desired and actual shift counts was calculated. Now each of the 150 generated sets is represented by a triplet (m1, m2, rA) where m1 = mean(n1) and m2 = mean(n2). This triplet set forms the input to the SIM algorithm. 6. A desired correlation coefficient value rD was fixed, and the optimization model was used to determine whether the set under consideration would yield an optimal result. It is important to note that the optimization model makes a decision about the optimality of the set based not only on the correlation coefficient, but also on the values of n1 and n2. 7. The following are the definitions of the parameters of the SIM algorithm for the experimental setup. • ΔE = rD - rA • K = Boltzmann’s Constant = 1.3806503E-23 • T = ((1.0) * m1 + (0.8) * m2 ) * 1012 8. The result was analyzed graphically to identify an optimal range for m1 and m2 such that any distributions for n1 and n2 having their mean values in this range, would result in a shift count that is within the desired range.

5. Results, Graphical Analysis and Discussion This section presents the results of the experimental setup detailed in Section 4. The input data set and the results of the application of the proposed optimization model are presented. Based on the output of the optimization, the data of 150 sets of values (m1, m2, rA) were thus split into two sets optimal and non-optimal – for each of the ranges R1, R2 and R3 considering two values for rD, 0.999999999999 and 0.988888888888. 3-Dimensional curves were fitted on the optimal and non-optimal data sets identified for R1, R2 and R3 for each of the considered rD values (Figures 1-6). The parameters for the graphs are m1 (xaxis), m2 (y-axis) and rA (z-axis). (The z-axis cannot strictly extend beyond 1.0, for it represents the

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correlation coefficient, but has been extended in Figure 5 only to clearly display the shape of the curve.) The different colours in the graphs depict areas with different correlation coefficients. The graphs were studied to determine the optimal ranges of m1 and m2 for a desired range of correlation coefficient values, i.e. for a desired colour range, the ultimate aim being to generate distributions whose m1 and m2 values are such that the shift count would lie within the desired range of shift count values.

5.1. Input Data Sets Table 1 gives the summary of the 150 input sets, each of which contains 500 sets of (n1, n2, λ). The input sets are meant to be compared with a standard set of 500 values generated for each of the ranges R1, R2 and R3. Table 1: Max, Min and Mean values of the input sets

n1

n2

λ

Max

284382378

305685985

184

Min

25

111

2

Mean

19447992

21561708

93

Max

240630915

291505003

188

Min

15

59

4

Mean

23777414

21140348

94

.....

......

............

...........

.......

44

Max

276315

244880744

188

Min

63

5251

6

Mean

39399

7913334

94

.....

......

............

...........

.......

137

Max

9913

9977

190

Min

2

18

8

Mean

4611

4355

93

.....

......

............

...........

.......

150

Max

21930007

2778544

182

Min

135

3

6

Mean

1881268

375969

92

# 1

2

For the above, mean(λmax) = 185 mean(λmin) = 4 mean(λmean) = 91 The shift count ranges R1, R2 and R3 were chosen in such a way that λmax - λmin < mean(λmax) mean(λmin), and R1, R2 and R3 are in increasing order of λmax - λmin. Following are the results obtained on comparing the 500 values of each of the 150 input data sets with a single standard data set generated for each of R1, R2 and R3.

5.2. R1: λmin = 40, λmax =100 Tables 2 and 3 show snapshots of the set of values generated for R1. Setting rD = 0.999999999999, the proposed optimization model identified only five out of the 150 sets, as optimal (Table 4). Setting rD = 0.988888888888, the optimization model identified 26 optimal sets (Table 5).

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Rama N. et al. / International Journal of Engineering Science and Technology Vol. 2(3), 2010, 296-306 Table 2: Data Set for R1

Table 3: Triplets (m1, m2, rA) for R1

#

n1

n2

λ

#

m1

m2

rA

1 2 3 4 ...... 496 497 498 499 500

4025 74 449 211626 .............. 303413 20246 206 6343 1236

259821 1556 125901 6753 ............ 9521 69417 1156 151175 1233

48 46 90 96 ............. 100 69 83 88 84

1 2 3 4 ….. 146 147 148 149 150

19447992 23777414 25360551 21079821 …………… 1605906 1738372 1773774 1829292 1881268

21561708 21140348 22913238 23629477 …………. 370644 377547 394059 401552 375969

0.985844303341463 0.978850765713698 0.986996885195985 0.989837520452073 ………………………… 0.983974430961630 0.980081353343203 0.978694550151069 0.979856049496625 0.984646942123398

Table 4: Optimal sets for rD = 0.999999999999

Table 5: Optimal Sets for rD = 0.988888888888

#

m1

m2

rA

#

m1

m2

rA

1

20300311

24105687

0.989053920957019

1

21748517

19429845

0.990574071159241

2

21907656

23446139

0.988131719871699

2

36266

8527681

0.990242985863639

3

21079821

23629477

0.989837520452073

...

............

..............

.................................

25

21769342

22512452

0.982469164471311

26

21656794

22581737

0.981646517704330

3

20029059

22216825

0.986801748019563

4

17438260

19823093

0.986800928857415

5

22385325

22801005

0.984896967632570

Figure 1 depicts the optimal region for R1 with rD = 0.999999999999, and Figure 2, the nonoptimal region for the same.

Figure 1: Optimal Sets in R1 for rD = 0.999999999999

Figure 2: Non-optimal Sets in R1 for rD = 0.999999999999

In Figure 1, • the dark green region represents optimal sets with rA [0.982, 0.984] and m1, m2 [2.0*107, 2.2*107]. •

the orange region represents optimal sets with rA [0.990, 1], m1 [2.1*107, 2.2*107], m2 [2.3*107, 2.4*107].

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In Figure 2, however, the graph is a collection of vertical strands. In each strand the colour varies [0.970, 0.999]. The implication of this is that the from blue to orange corresponding to rA distributions of random numbers n1 and n2 that have mean values m1 and m2 in the range plotted, will not always result in distributions which have the desired shift count range. An instance from the graph is, when m1 [0, 5.0*106] and m2 [2.4*107, 2.5*107] the resulting distribution will not always be optimal. Figure 3 shows the optimal values of m1 and m2 with rD = 0.9888888888. Since the rD value has been lowered, the number of data sets that are identified as optimal by the optimization model, naturally increases. This can also be gleaned from the area covered by the curve. For instance, when m1 [5.0*106, 1.5*107] and m2 [2.0*107, 2.4*107], we get rA [0.995, 0.998] which means rA > rD. This is the orange region of the graph. Figure 4, the representation of non-optimal values of m1 and m2 when rD = 0.9888888888, clearly shows that for the plotted values, the shift count distribution will not always be optimal.



5.3. R2: λmin = 20, λmax =150 Tables 6 and 7 show snapshots of the set of values generated for R2. For rD = 0.999999999999, the proposed optimization model identified only 26 optimal sets out of the given 150 sets (Table 8). For rD = 0.988888888888, the optimization model identified all 150 sets as optimal. Table 6: Data Set for R2


#

n1

n2

λ

#

m1

m2

rA

1 2 3 4 ..... 496 497 498 499 500

11136 119194 2238 81446 .............. 124105 6682 41787 6092 73862

43418 3472950 24533 531 .............. 487 32781 20223972 7872 1751775

58 114 142 75 .......... 86 87 126 66 123

1 2 3 4 ….. 146 147 148 149 150

19447992 23777414 25360551 21079821 …………… 1605906 1738372 1773774 1829292 1881268

21561708 21140348 22913238 23629477 …………. 370644 377547 394059 401552 375969

0.997546268676425 0.995528385993785 0.997477800811463 0.998280018961295 ………………………… 0.996075218229694 0.995488956227832 0.995853333987828 0.994390885601899 0.997073835597999

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Rama N. et al. / International Journal of Engineering Science and Technology Vol. 2(3), 2010, 296-306 Table 8: Optimal sets for rD = 0.999999999999

#

m1

m2

rA

1

41330

6953692

0.998492238269985

2

21079821

23629477

0.998280018961295

3

21958317

21464575

0.998164043161518

...

..............

...............

................................

25

21980517

22194863

0.995433670587354

26

22070903

20457930

0.995103104627828

R2 is larger than R1 and maps more closely to the shift count range of the input sets. This considerably increases the number of sets that qualify as optimal, whereby the permissible range of values for m1 and m2 becomes wider. Figure 5 gives the graph depicting the optimal region for R2, where rD = 0.999999999999. Figure 6 represents the non-optimal regions for the same. In Figure 5 • the yellow region corresponds to the highest correlation and is obtained when rA [1, 1], m1 [2.0*107, 2.5*107], m2 [2.0*107, 2.2*107]. •

the bright blue region represents the lowest correlation and is obtained when rA [0.985, 0.990], m1 [6.0*106, 1.0*107], m2 [2.0*107, 2.5*107].



In Figure 4, we have rA [0.960, 1.000] and we have a jagged distribution. Thus, for instance, for m1 [0, 5.0*106] and m2 [1.0*107, 1.0*107] the resulting distribution will not always yield shift counts within the stipulated range. Clearly, since all the input distributions considered have rA > 0.988888888888, when rD is set to 0.988888888888, the result is that all inputs sets are optimal in R2.

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5.4. R3: λmin = 10, λmax =170 Tables 9 and 10 show snapshots of the set of values generated for R3. For rD = 0.999999999999 itself, the proposed optimization model identified all 150 sets as optimal. Table 9: Data Set for R3


#

n1

n2

λ

#

m1

m2

rA

1 2 3 4 ..... 496 497 498 499 500

11544 2440 14583 77398 .............. 176938 918 2354 429 304

158077 250 156910 1544 ........... 1123 47942 1959 109767 1390

95 134 119 88 .......... 101 100 57 114 125

1 2 3 4 … 146 147 148 149 150

19447992 23777414 25360551 21079821 ………….. 1605906 1738372 1773774 1829292 1881268

21561708 21140348 22913238 23629477 ………… 370644 377547 394059 401552 375969

0.997246073280999 0.996230884557808 0.997650264703144 0.998413071420934 ……………………. 0.996325855732489 0.996295473052837 0.996061273070142 0.996208183080908 0.996726478973797

R3 is a closer approximation to the shift count range of the input sets, than R2. As a consequence of this, all input sets were found to be optimal at both rD = 0.999999999999 and rD = 0.988888888888.

6. Conclusion The optimization model proposed in this paper is a new approach to achieving reduction in power consumed by fixing an optimal range for the number of shift operations performed in the Gossamer protocol. Highlights of the optimization model proposed in this work are: • The desired shift count range can be fixed depending on the security levels needed for the application. • The equation for T can be fine-tuned to produce a larger or smaller design space. • The design space for the PRNGs can be identified more precisely by generating a larger number of samples. • The decision on how well the actual set needs to correlate with the desired set is left open to the designer. • The model can also be applied to applications where the values of m1 and m2 are bounded. Thus PRNGs can be designed to generate numbers with fixed word length which in turn reduces the hardware complexity and increases the processing speed at the reader end too. The reduction in power consumption by the protocol results in improved performance of the RFID system. Since the parameters that are to be optimized are stochastic in nature, the Simulated Annealing method has been employed. The model has been detailed and its usage has also been demonstrated through examples. Detailed analysis of the graphical representations of the optimal sets and how it leads to fixing up the design space for PRNG is also presented. Thus this model proves to be a successful optimization model that achieves significant reductions in the number of shift operations involved in the ROT functional unit of the Gossamer protocol. The beauty of this novel proposal is that such reduction is achieved without compromising on the security of the protocol, for the pseudo random numbers n1 and n2 are still left unbounded. Only the mean of these random numbers is restricted to fall within a standard distribution, causing the number of shift operations to become restricted to within certain boundaries.

References [1] Joaquin Garcia-Alfaro, Michel Barbeau, and Evangelos Kranakis. Security Threat Mitigation Trends in Low-cost RFID Systems. 2nd SETOP International Workshop on Autonomous and Spontaneous Security, September 2009.

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Rama N. et al. / International Journal of Engineering Science and Technology Vol. 2(3), 2010, 296-306 [2] Class-1 Generation-2 UHF air interface protocol standard http://www.epcglobalinc.org/standards/ (last accessed on 10.01.2010).

version

1.0.9:

"Gen2",

2005,

url:

[3] Denis Trcek and Pekka Jappinen. Non-Deterministic Lightweight Protocols for Security and Privacy in RFID Environments. RFID and Sensor Networks: Architectures, Protocols, Security and Integrations, Auerbach Publications, 2009. [4] Ari Juels. Minimalist cryptography for low-cost RFID tags. Proceedings of SCN’04, vol. 3352 of LNCS, pages 149– 164, 2004. [5] Pedro Peris-Lopez, J. C. Hernandez-Castro, J. M. Estevez-Tapiador, and A. Ribagorda. LMAP: A real lightweight mutual authentication protocol for low-cost RFID tags. Handbook of RFIDSec’06, 2006. [6] Pedro Peris-Lopez, J. C. Hernandez-Castro, J. M. Estevez-Tapiador, and A. Ribagorda. M2AP: A minimalist mutualauthentication protocol for low-cost RFID tags. Proceedings of UIC’06, Vol. 4159 of LNCS, pages 912–923, 2006. [7] Pedro Peris-Lopez, J. C. Hernandez-Castro, J. M. Estevez-Tapiador, and A. Ribagorda. EMAP: An efficient mutual authentication protocol for low-cost RFID tags. Proceedings of IS’06, Vol. 4277 of LNCS, pages 352–361, 2006. [8] Chien H.Y., SASI. A New Ultralightweight RFID Authentication Protocol Providing Strong Authentication and Strong Integrity, IEEE Transactions on Dependable and Secure Computing, vol. 4(4), pp. 337–340. Oct.-Dec. 2007. [9] Pedro Peris-Lopez, Julio Cesar Hernandez-Castro, Juan M. E. Tapiador, and Arturo Ribagorda. Advances in Ultralightweight Cryptography for Low-cost RFID Tags: Gossamer Protocol, Workshop on Information Security Applications, Vol. 5379 of LNCS, pages 56-68, 2008. [10] Rama N. and Suganya R. Power Analysis of the Gossamer protocol for Passive RFID tags. Accepted for publication in International Journal of Wireless Communication and Networks March 2010. [11] Rama N. and Suganya R. A Family of Gossamer-Based Mutual Authentication Protocols for Tag Pairs in RFID Systems. Reviewed and accepted for presentation and publication in the proceedings of ICMCS International Conference on Mathematics and Computer Science 2010, Loyola College, Chennai. [12] Kirkpatrick S., Gelatt C. D., Jr,.Vecchi M. P, Optimization by Simulated Annealing, Science, New Series, Vol. 220, No. 4598. (May 13, 1983), pp. 671-680

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