A Privacy Model for RFID Tag Ownership Transfer

The ownership of RFID tag is often transferred from one owner to another in its life cycle. To address the privacy problem caused by tag ownership transfer, we propose a tag privacy model which captures the adversary’s abilities to get secret information inside readers, to corrupt tags, to authenticate tags, and to observe tag ownership transfer processes. This model gives formal definitions for tag forward privacy and backward privacy and can be used to measure the privacy property of tag ownership transfer scheme. We also present a tag ownership transfer scheme, which is privacy-preserving under the proposed model and satisfies the other common security requirements, in addition to achieving better performance.


Introduction
RFID (Radio-Frequency Identification) technology is widespread in commercial industry such as supply chain management, inventory management, and access control for people and vehicles.A RFID application system mainly consists of tags, readers/interrogators, and back-end server.A passive tag is basically a device embedded with a small chip and a coiled antenna, in which the chip has limited computation capability and small memory to store its secret key and identifier, and the antenna communicates with its reader via radio-frequency signal.A reader is used to interrogate tags and send the data received from tags to a back-end server for product identification or inventory tracking.The back-end server stores tag's secret keys, identifiers, and the information of the items labeled by tags and executes product identification or inventory tracking.
However, the privacy issue (e.g., information leakage, location tracking, and profiling individuals) caused by RFID technology has raised grave concerns among the public.A recommendation on this issue was published by the Commission of the European Communities [1], which gave particular attention to the individual tracking and the access to personal data.Take the medicine supply chain for example, those tags attached to medicines are often transferred from one owner to another, however, the previous owner of a tag may infer the tag's track from its future interactions with a new owner, and as a result, the new owner's privacy may be infringed.Another serious scenario is that terrorists may exploit this technology to track their target who holds the RFID tags.Once those tags are distinguished at specific point (e.g., the checkpoint or toll station) by the terrorist's surreptitious devices, particular devices such as a bomb may be triggered.
The privacy of RFID tag means anonymity and untraceability [2], namely, an adversary cannot distinguish or track a tag from other tags at the protocol level.It is observed that many studies [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] on tag privacy have focused on the privacy problems caused by tag authentication or tag identification, but little attention was paid to the tag ownership transfer which may leak out tag's privacy.
Actually, a malicious owner has access to the back-end server which stores all the information of readers and tags, and he has advantage to distinguish a tag after the tag ownership transfer or inferring the past activities of a tag when getting the tag's ownership.This attack belongs to insider attack, which is serious in practice, but IND-CCA2 encryption can be employed to prevent such kind of attack [33].
Concentrating on tag ownership transfer, we propose a privacy model which introduces strong adversaries, who have abilities to obtain the full information of readers, to authenticate tags, to observe the whole transfer process, and to corrupt tags.With this model, we briefly analyze the scheme [17] which is based on public key encryption on tags.We also present a tag ownership transfer scheme, which is forward and backward privacy-preserving under our model.
The rest of this paper is organized as follows.In Section 2, we review the relevant work on tag ownership transfer, and then we describe the proposed model in Section 3. In Section 4, a recent tag ownership transfer scheme is briefly analyzed, and the proposed ownership transfer scheme is described and analyzed in Section 5. Section 6 concludes the paper.

Related Work
Soundness, correctness, and privacy are the required properties for RFID system.Briefly, soundness which is also called security in [2,9] means that a fake tag cannot be accepted by the system except with negligible probability; correctness means a legitimate tag is always accepted by the system with an overwhelming probability.Canard et al. [6] gave the definitions of soundness and correctness.
In terms of tag ownership transfer scenario, tag forward privacy means an owner of a tag   cannot distinguish   from others if   's ownership was transferred to another owner, and tag backward privacy means the current owner of   cannot link   to its previous interactions (e.g., the transcripts of authentication and ownership transfer process with its previous owner).
In Section 3, we will give the proposed privacy model, which defines tag forward privacy and backward privacy.Since our model concentrates on the privacy problem caused by tag ownership transfer, the properties of soundness and correctness will not be discussed further.However, their definitions can be combined compatibly with our model.

Tag Ownership.
A tag is often attached to an item and authenticated to its back-end server, and it would be transferred from one owner to another in its lifetime.As for a tag ownership transfer, the current owner may launch authentication procedure to authenticate or identify the tag and then transfer the tag's secret key or identifier to a new owner's server.Upon getting these secret data, the new owner has ability to authenticate or identify the tag.In this sense, these secret data used for tag authentication/identification are called ownership.In order to prevent the previous owner from authenticating or identifying the tag, the new owner will launch update procedure to make the tag and the new server refresh these shared secret data.

Tag Ownership Transfer.
Tag ownership transfer is more complicated than tag authentication to reader or their mutual authentication, because the current owner and the new owner are involved in the ownership transfer process.Moreover, tag ownership transfer is closely related to tag authentication to its reader.
Several tag ownership transfer schemes are derived from tag authentication protocols.Molnar et al. [22] proposed a scalable and delegatable pseudonym authentication protocol which enables tag ownership transfer; however, a trusted center is required.Lim and Kwon [21] proposed a robust authentication protocol enabling ownership transfer, whereas their scheme cannot achieve tag untraceability under the model in [34].Song [25] suggested a tag ownership transfer scheme, which enables authorization recovery and protects the privacy of both current and previous owners, but this scheme is vulnerable to tag location tracking, tag forward traceability, and desynchronization attack [23].Later, Song and Mitchell [26] proposed another RFID protocol and claimed it supports tag ownership transfer, tag delegation, and authorization recovery.Recently, Kardas ¸et al. [20] introduced an authentication protocol enabling tag ownership transfer with hash and XOR operation and claimed the protocol achieves tag untraceability against strong adversaries.
There are some ownership transfer schemes for the tags supporting public key encryption.Fu and Guo [27] designed a mutual authentication protocol supporting tag ownership transfer based on the SQUASH scheme [35], but the authors did not exhibit the tag ownership transfer process.Cheng et al. [17] presented an ownership transfer scheme, which employs elliptic curve cryptography (ECC) and will be briefly analyzed in Section 4.
There are some other ownership transfer schemes based on the public key encryption on readers.Elkhiyaoui et al. [18] designed a transfer scheme consisting of three subprotocols, but the scheme is vulnerable to the privacy track initiated by the tag's previous owner [36], because their definitions neglected the ability of the previous owner who ever controls the secret key of the target tag, and some revisions in [29] were presented to correct this flaw.Xin et al. [28] proposed a privacy-preserving ownership transfer scheme and claimed it guarantees privacy and other security properties; however, this scheme employed a powerful Trusted Third Party.Some researches on tag ownership transfer focus on mobile RFID environment, and the readers interested in this may refer to [30,37,38] for further investigation.

The Proposed Privacy Model
Most schemes introduced in Section 2.2 overlooked the fact that the owner may be malicious, and it lacks formal definitions to analyze the privacy property of tag ownership transfer scheme.
van Deursen and Radomirović [33] introduced the insider attack which is serious to the RFID system, because adversaries have the knowledge of readers and tags.In this section, we propose a privacy model for RFID tag ownership transfer.This model provides adversaries with abilities to get the reader's secret information, to constantly eavesdrop on the communications between reader and its tags, to corrupt tags, and to transfer tag's ownership to another owner.In the model, the goal of the adversary is to distinguish or infer the target tag from others.
3.1.Entities in the Proposed Model.For simplicity, we suppose the RFID system in the model consists of two owners denoted by  with a reader   and by  with a reader   .Because the reader and its back-end server are powerful devices and communicate via secure channel, we also suppose the back-end server is integrated with the reader.Moreover, we suppose the temporary information (e.g., the nonce generated by reader and tags) will be automatically erased when the authentication or ownership transfer process is completed.The notations used in the following sections are listed in Notations for readability.

Oracles Provided for Adversaries.
In a realistic scenario, adversaries can exploit the following information to attack tag's privacy: (1) the secret information inside reader and tags, (2) the authentication information between reader and tags, (3) the results that adversaries launch authentication procedures with tags, and (4) the ownership transfer information between reader and tags.
We give an adversary A the following oracles to simulate his abilities to attack the privacy of a tag  id .
(1) Authenticate(,  id ) → (,  DB ,  DB ,  id ,  id , result, . ..): This oracle is provided for A to make a reader  launch authentication session with  id .If the adversary controls the secret information of  and  id , it returns , the secret information such as key and identifier pairs ( DB ,  DB ), ( id ,  id ) as well as the authentication result.Otherwise, it only returns the authentication result and the process transcripts; namely, it returns (, −, −, −, −, result, . ..).This oracle simulates the adversary's abilities to launch active attack and to get side channel information (e.g., the result whether or not a tag is accepted by its reader).
(2) Observe(,  id ) → (, result): This oracle makes  launch authentication session with the tag  id and returns the execution transcripts as well as the authentication result.The adversary can query this oracle to eavesdrop on the communication between the target tag and its reader.
(3) Corrupt( id ) → ( id ,  id , . ..):This oracle is provided for the adversary to corrupt tags.It returns the secret key, the identifier, and the other information inside  id .
(4) Transfer(  ,  id ,   ) → ( vid , ): The adversary can query this oracle to get the information of the ownership transfer process.It transfers  id 's ownership from a current owner who controls   to a new owner who controls   and returns a virtual identifier  vid for the tag as well as the transcripts of the transfer process.We denote the first four oracles by  1 ,  2 ,  3 ,  4 and the number of times that the adversary queries them by   1 ,   2 ,   3 ,   4 , respectively, and denote the set ( 1 ,  2 ,  3 ,  4 ) by .We say that an adversary A is a (, )-adversary, if the number of times that A queries the above oracles is at most ∑ 4 =1    ≤ , where  is polynomial in ℓ.
As for a tag ownership transfer process, a new owner will get the tag's secret information (e.g., the key and identifier) from the current owner and then update some information inside the tag to prevent the current owner from successfully identifying or tracking the tag.

Definition of Forward Privacy.
We denote a tag  id at time point just before its ownership is transferred by   .We also denote the advantage that A infers which

Brief Analysis for an ECC-Based Tag Ownership Transfer Scheme
Some tag ownership transfer schemes such as [18,20,26] are not based on public key encryption on tags.To achieve forward privacy or backward privacy for tags, tag owner is required to run extra tag authentication sessions in an environment where adversaries cannot eavesdrop on the authentication sessions.Such requirements do not satisfy our model in which adversaries can always eavesdrop on the interactions between the tag and its reader, in addition to corrupting the tag after the ownership transfer.
To guarantee security and privacy, a few tag authentication protocols [27,[39][40][41] are based on tags that support public key encryption, and to the best of our knowledge, the authors of [17] presented a complete ownership transfer scheme based on tags supporting ECC.We briefly analyze this scheme as follows and demonstrate that it is not forward privacy under our definitions.
This ownership transfer scheme consists of four subprotocols: tag key change protocol (P1), tag key update protocol (P2), ownership transfer protocol (P3), and controlled delegation protocol (P4); however, the authentication protocol between reader and tags is not given.Before the current owner (e.g.,   ) transfers the tag  id to the new owner (e.g.,   ),   first launches P1 to refresh the information inside  id and then runs P3 to transfer the ownership of  id to   .Finally,   launches P2 to update the information inside  id .
Under Definition 1, after querying the oracles in  at most  times, a (, )-adversary A chooses two corrupted tags ( ) and then guesses a bit  ∈ (0, 1).However, since A can corrupt  +1 id  to get its secret key   , and   is not updated throughout the whole ownership transfer process, A can always correctly guess the value of .
Under Definition 2, after querying Test( ), the adversary A will guess a bit , provided that the secret key   is given.Yet it is unclear whether or not A can link   to the previous transcripts that  −1 id  authenticates to its reader, because the authentication protocol is not given in [17].In other words, it is not ensured whether or not A can infer   from the previous authentication information.

The Proposed Tag Ownership Transfer Scheme
Motivated by the slightly higher performance tags like [42,43] that support public key encryption, we propose a tag ownership transfer scheme in this section.This scheme consists of a mutual authentication protocol (AP) and an ownership transfer protocol (TP).We demonstrate it is both forward privacy and backward privacy under our model and give the security analysis in Appendix.
We suppose the database DB of the back-end server stores ( new id ,  old id , sk, . ..) for each tag  id as well as the information of the products that are labeled by tags, and DB is integrated into the reader . id stores its identifier and its reader's public key (  id , pk).In the following sections, we first describe the mutual authentication protocol and then the tag ownership transfer protocol.

The Mutual Authentication
Protocol.This protocol provides mutual authentication for the reader and tags; we give the details in Figure 1 and the interpretation as follows.
(1)  first sends a nonce  1 and an access command query to  id .
(2) Upon receiving  1 and query,  id selects another nonce  2 and responds with  1 = Enc pk ( (3) Upon receiving  After finishing the ownership transfer process,  id 's identifier is updated with a new value which is shared with   , and the public key stored in  id is replaced with   's public key; Figure 2 shows the details.
(1)   first sends its public key pk  , a nonce  1 , and the access command change to  id .
( ( = 2, . ..), because the hash value of secret nonce is employed to update the tag's identifier in our scheme.
To sum it up, according to the proposed model the advantage that a (, O)-adversary A attacks the forward privacy of the scheme is negligible.) and then guesses a bit  ∈ (0, 1), provided the identifier   id  is given.Except for guessing  with probability 1/2, A can guess  by the following ways.

Backward Privacy of the
(1) Inferring  from the relation between the interaction transcripts that   authenticates ).However, A cannot gain  2 from  1 because  1 is a ciphertext by the public key pk  ; he can only guess the secret key sk  with probability 1/ℓ to decrypt  1 .A also cannot gain   2 from  2 by inverting the one-way hash function (⋅), except to guess   2 with probability 1/ℓ  .Hence, in this way the probability that A correctly guesses  is negligible.
( Schemes Forward privacy Backward privacy Extra process [18] No No Yes [20] No No Yes [26] No No Yes [17] No is negligible.In summary, the advantage of the adversary attacking the backward privacy of the scheme is negligible according to the proposed model.

Privacy Comparison with Some Related Work.
Recently, some tag ownership transfer schemes have been proposed; we compare the privacy property between those schemes and ours in Table 1 under the proposed model.
From the table, it can be seen that our scheme enjoys privacy property.Although the schemes proposed in [17,18,20,26] are forward privacy and backward privacy under their model or their specific processes, which need extra steps to protect tag's privacy, those schemes cannot achieve forward privacy and backward privacy under our model, because in our model adversaries are permitted to corrupt tags after tag ownership transfer.Moreover, our model does not need extra processes to protect tag's privacy, and our scheme uses evolving hash value of secret nonce to update tag's identifier after each authentication or ownership transfer.

Performance Comparisons.
Since RFID reader and server support enough complex cryptographic primitives, we only analyze the computation cost on tag side and the communication cost for messages that tag sends and directly receives from reader side, and we suppose our scheme is based on ECC.
For the sake of fair comparison, we suppose an elliptic curve is defined on finite field (2 160 ), which needs 40 bytes and 20 bytes to store an elliptic curve point and an element in the field, respectively.We employ the hash scheme H-PRESENT-128 [44] with 128 bits' (16 bytes) output.We also suppose the bit length of a random number is 4 bytes and suppose the length of a tag's identifier is 12 bytes in compliance with the EPC (Electronic Product Code) Class-1 Generation-2 standard.The length of an access command sent by reader is negligible.The results listed in the table show our scheme achieves better performance on communication cost, and we explain the results as follows.The tag ownership transfer process in [18] uses ElGamal encryption scheme to encrypt tag's identification information, so we suppose the length of a prime number in the scheme is 20 bytes.The scheme in [20] runs the authentication protocol three times to finish a tag's ownership transfer, and the protocol (denoted by P2) proposed in [26] will be executed twice to complete the ownership transfer for a tag, while our scheme just runs the ownership transfer protocol only once.To finish a tag's ownership transfer, a tag in the scheme [17] receives 8 elliptic curve points and sends 4 elliptic curve points; hence it sustains the heaviest communication cost.

Comparisons of Communication Cost.
Comparisons of Computation Cost.We denote the running time of a scalar multiplication operation over an elliptic curve by Ecm and a hash function operation by Ha; Table 3 shows the computation cost on tag side for some recent ownership transfer schemes and ours.
Because our ownership transfer protocol TP aims at those tags supporting ECC, thus the computation cost on tag side is higher than those tags not supporting ECC [18,20,26]; however, the computation cost of the TP is superior to the schemes in [17], which is also based on ECC on tags.

Conclusions
The privacy leakage caused by RFID tags is an important issue and has drawn wide attention.Some studies focused on the privacy problem caused by authentications between reader and tags, and a few researches paid attention to the privacy problem caused by tag ownership transfer.Yet few of them take the malicious owner into account or use formal methods to analyze the privacy leakage caused by tag ownership transfer.
In this paper, we propose a privacy model, which concentrates on the privacy problem caused by RFID tag ownership transfer.This model can be used to measure the privacy property of tag ownership transfer scheme, yet it cannot be directly applied to the authentications between reader and tags.
We also designed a tag ownership transfer scheme for the tags supporting public key encryption.According to the proposed model, we demonstrate our scheme enjoys both forward privacy and backward privacy.We also give the security analysis in Appendix.Upon comprehensive consideration on privacy protection, communication, and computation cost, our scheme is superior to those compared ones, and the implementation of this scheme would be our next work.

Security of the Proposed Tag Ownership Transfer Scheme
We briefly analyze the security properties of the proposed scheme as follows.
Tag Impersonation Resistance.Note that almost all the RFID authentication protocols (including our scheme) keep tag's identifiers as secrets in order to prevent malicious parties from tracking tags.
For the AP of our scheme, upon intercepting the firstround message of a reader querying a tag  id , an adversary A should respond to the reader with the second-round message.However, A cannot correctly compute the secondround message  1 = Enc pk ( knowing the identifier   id , unless he guesses an identifier, while the probability that A correctly guess the value of   id is 1/ℓ  , which is negligible.Moreover, after each successful authentication process, a tag's identifier will be updated with a hash value of a nonce concatenating the tag's previous identifier.
We can use the same way to analyze tag impersonation resistance of the TP.Without knowing tag's identity, the probability that adversaries correctly respond with the secondround message  2 = Enc pk  (Enc pk  ( Reader Impersonation Resistance.According to the specification of AP, a reader  will first send a nonce  1 along with a command to a tag  id to launch a new session.Once receiving the first-round message, the tag generates another secret nonce  2 and responds to  with ciphertext Enc pk ( id ‖  1 ‖  2 ).It is obvious that an adversary cannot correctly decrypt this ciphertext without knowing the reader's secret key sk in order to get  2 .Hence, he cannot correctly respond to the tag with the last round message, which is a hash value directly related to  2 .In other words, if an adversary tries to impersonate a reader, the verification for the last round message by tag will be failed.
The similar analysis can be applied to the reader impersonation resistance of our TP.To sum up, without knowing reader's secret key, adversaries cannot correctly compute the last round message to pass the verification of the tag, except with negligible probability.
Replay Attack Resistance.The authentication sessions of the AP in our scheme are initiated by RFID reader, and our AP employs a secret nonce  2 and an evolved identifier  id to compute the second-round message  1 = Enc pk ( id ‖  1 ‖  2 ) and the third-round message  2 = ( 2 ‖  id ).For readability of analysis, we denote the nonce and tag's identifier in the  th session and ( + For the TP of our scheme, adversaries also cannot replay old messages in order to pass the verification of the reader/tag.On one hand, if he replays an old message  2 = Enc pk  (Enc pk  ( and forward  1 to a reader   .However, once   decrypts  1 to get the value  1 (which is not equal to the value that   has sent to the tag in the current session), the verification for  1 by   will be failed.On the other hand, if an adversary replays an old message  3 = ( 2 ) to a tag, the verification for  3 will be failed because the current nonce that the tag generates is not  2 .
Desynchronization Attack Resistance.In our scheme, the back-end database stores two identifiers for each tag.One is  old id , which is the latest synchronization identifier between the reader and the tag.The other is  new id , which is computed by the reader in the latest authentication process.
In a new session, if an adversary blocks the third-round message  2 of the AP (or the fourth-round message  3 of the TP) to desynchronize a reader with its tag, the reader can always recover synchronization with its tag in the next session using the old identifier  old id .
Man-in-the-Middle Attack Resistance.For the AP, the secondround message  1 sent by a tag  id is encrypted with its identifier, the nonces  1 and  2 .If an adversary intercepts this message and replaces it with another one to respond to a reader, the process that the reader identifies the tag will be failed with overwhelming probability.In other words, without knowing the secret identifier of a tag, an adversary cannot successfully launch the Man-in-the-Middle attack.Moreover, the third-round message  2 that a reader sends to a tag is a ciphertext of a nonce and the tag's identifier; without knowing the tag's identifier, the adversary cannot generate a valid message to pass the verification of the tag.
For the TP of our scheme, the second-round message  2 sent by a tag is also a ciphertext related to the secret identifier of the tag.Without knowing the tag's identifier, adversaries cannot compute a valid message to pass the authentication of the reader.
In summary, both AP and TP resist to the Man-inthe-Middle attack because secret identifier is employed to generate the exchanged messages.

Notations
,   , : The reader controlled by the owner , by owner  and in a general sense, respectively. id ,   id : A tag with identifier id and at the time point .sk  , pk  : The secret key and public key of   .sk  , pk  : The secret key and public key of   .sk, pk: The secret key and public key of . id ,  id ,   id :  id 's secret key, identifier, and the identifier at time  respectively, which are stored in  id .ID  , ID  : The set that consists of tags authenticated by   and   , respectively.DB  , DB  , DB: The database integrated in   ,   and  respectively. DB ,  DB : Secret key and identifier of the tag  id , which are stored in the database DB.  new id ,  old id : The current identifier and the previous identifier of  id respectively, which are stored in DB.

𝜏:
Interactive information like the transcripts of authentication process or ownership transfer process between reader and tags.−: The unknown information.result: The result that a reader authenticates a tag, and 1 indicates the tag is accepted by the reader, or otherwise 0. ‖: String concatenation.←, →: Assigning the right value to the left variable and returning the left value, respectively.=, ∈  : Th ee q u a lr e l a t i o n s h i pa n dt h e operation that randomly selects an element from a finite set.ℓ: The security parameter which is the length of a secret key.ℓ  , ℓ  : The length of a tag's identifier and the length of a nonce, respectively.

𝐻(𝑚):
One-way hash function with input message .Enc sk (): An encryption function with input message  and secret key sk.Dec pk (): A decryption function for a ciphertext  with public key pk.

( 5 )
Test(  id 0 ,   id 1 ) → ( +1 id , ): This oracle is provided for the adversary only once at any time.It accepts two tags and then selects a bit  ∈  (0, 1) to transfer the ownership of   id  to a new owner.This oracle returns the identifier of  +1 id  and the transcripts of the transfer process.
id and denote it by  + id ( = 1, 2, . ..) after the transfer process is finished.The transfer scheme should guarantee the previous owner cannot infer the identity of  + id ( = 1, 2, . ..) from the identity of   id .Without loss of generality, we suppose the current reader of the tag is   and the new reader is   .Definition 1. Provided with the information of   any (, )adversary A can query oracles in  at most  times, we denote the probability that A selects two corrupted tags (  id 0 ,   id 1 ) ∈ ID  for querying Test(  id 0 ,   id 1 ) and correctly guesses  by succ forward  (ℓ), with permission to query Corrupt( + id  ) ( = 1, 2, . ..).The tag is forward privacy if adv forward  (ℓ) = |succ forward  (ℓ) − 1/2| is negligible.

3. 4 . 1 )
Definition of Backward Privacy.After the ownership of the tag   id has been successfully transferred to a new owner, the transfer scheme should guarantee the new owner cannot link the information of  + id ( = 1, 2, . ..) to the previous activities of the tag.With the same way to define tag forward privacy, we define tag backward privacy as follows.Definition 2. Provided with all the information of   any (, )-adversary A queries oracles in  at most  times, we denote the probability that A chooses uncorrupted tags (  id 0 ,   id 1 ) ∈ ID  for querying Test(  id 0 ,   id and then correctly guesses  by succ backward  (ℓ) with being given the identifier of   id

Figure 1 :
Figure 1: The proposed mutual authentication protocol.

Figure 2 :
Figure 2: The proposed tag ownership transfer protocol.
Proposed Scheme.Under Definition 2, a (, )-adversary A receives all the information of   and queries oracles in  in the first stage.A selects two uncorrupted tags ( 1 ,  decrypts it to get   id ,   1 ,   2 .If (  1 =  1 ) does not hold,  interrupts this process.If (  1 =  1 ) holds,  then retrieves   id in its DB.If both (   assigns another nonce to the variable  2 .Otherwise,  assigns the hash value (  2 ‖   id ) to  2 and updates  old id with  new id if   Finally,  sends back  2 to  id .(4) Upon receiving  2 , if ( 2 = ( 2 ‖  This protocol transfers  id 's ownership from the current owner of   to the new owner of   .Before the transfer process,   and   should authenticate to each other and setup a secure channel, and then   sends  new id ,  old id and the other information of  id to   . id equals  new id . also updates  new id with the value (  2 ).
) Once receiving pk  ,  1 and change,  id selects another nonce  2 and assigns the value Enc pk  (  id ‖  1 ‖  2 ) to  1 and then sends  2 = Enc pk  ( 1 ) to   .assigns the value of (  2 ) to  3 and updates  old id with  new id if   id equals  new id .alsoupdatesnew id with (  2 ‖   id ).Finally,   sends back  3 to  id(5) If  3 is equal to ( 2 ),  id replaces pk  with pk  and updates  Forward Privacy of the Proposed Scheme.According to Definition 1 of the proposed model, an (, )-adversary A obtains all the information of   and queries oracles in  in the first stage.A selects two corrupted tags ( , respectively, in order to determine the value of .However, since A does not hold the secret key sk  , the probability that he decrypts   1 with a random secret key is 1/ℓ.In other words, the advantage that A correctly guesses  is 1/ℓ in this way.(2)Inverting the one-way hash function (⋅) to get the nonce   2 from  3 = (  2 ) and then calculating ( 2 ‖   id 0 ) and ( 2 ‖   id 1 ) to compare the results with  +1 id  .However, as we all know, it is hard to invert one-way hash function so far, and the adversary can only guess the value of   2 .Hence, the probability A correctly guesses  is 1/ℓ  in this way.However, it is difficult to invert the one-way hash function, and A can only guess a value as the input of the hash function.As a result, the probability that A correctly guesses  is 1/ℓ  .Finally, the adversary could keep on corrupting  + id  ( = 2, 3, . ..) in the future interactions between the tag and its reader.However, this does not help A link (3) Upon receiving  2 ,   decrypts it to get   1 and then forwards   1 to   .(4) Upon receiving   1 ,   decrypts it to get   id ,   1 , and   2 .If (  1 ̸ =  1 ) holds,   interrupts this process.If both (  id ̸ =  new id ) and (  id ̸ =  old id ) hold,   assigns a nonce to a variable  3 ; otherwise, )

Table 1 :
) Inferring  from the test transcripts (pk  ,  1 , change,  2 ,   1 = Enc pk  (  is not related to (pk  ,  1 , change) and  3 , which is a hash value of a nonce.Moreover,  2 is the result of the encryption for 1 , and   1 is the ciphertext of  1 ,  2 , and  Comparisons of privacy property.

Table 2 :
Comparisons of communication cost.

Table 3 :
Comparisons of computation cost.
1) th session by