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International Journal on Very Large Data Bases manuscript No. (will be inserted by the edit

International Journal on Very Large Data Bases manuscript No. (will be inserted by the edit
International Journal on Very Large Data Bases manuscript No. (will be inserted by the edit

International Journal on Very Large Data Bases manuscript No. (will be inserted by the editor)

Succinct Representation of Flexible and Privacy-Preserving Access Rights

Marina Blanton,Mikhail Atallah

Department of Computer Science

Purdue University

West Lafayette,IN47907

e-mail:{mbykova,mja}@https://www.sodocs.net/doc/4c7102768.html,

The date of receipt and acceptance will be inserted by the editor

Abstract We explore the problem of portable and?exible privacy pre-serving access rights that permit access to a large collection of digital goods. Privacy-preserving access control means that the service provider can nei-ther learn what access rights a customer has nor link a request to access an item to a particular customer,thus maintaining privacy of both customer activity and customer access rights.Flexible access rights allow a customer to choose a subset of items or groups of items from the repository,obtain access to and be charged only for the items selected.And portability of ac-cess rights means that the rights themselves can be stored on small devices of limited storage space and computational capabilities such as smartcards or sensors,and therefore the rights must be enforced using the limited re-sources available.

In this paper,we present and compare two schemes that address the problem of such access rights.We show that much can be achieved if one allows for even a negligible amount of false positives—items that were not requested by the customer,but inadvertently were included in the cus-tomer access right representation due to constrained space resources.But minimizing false positives is one of many other desiderata that include pro-tection against sharing of false positives information by unscrupulous users, providing the users with transaction untraceability and unlinkability,and forward compatibility of the scheme.Our?rst scheme does not place any

2M.Blanton,M.Atallah constraints on the amount of space available on the limited-capacity storage device,and searches for the best representation that meets the requirements. The second scheme,on the other hand,has(modest)requirements on the storage space available,but guarantees a low rate of false positives:With O(mc)storage space available on the smartcard(where m is the number of items or groups of items included in the subscription and c is a selectable parameter),it achieves a rate of false positives of m?c.

Key words Compact representation–privacy-preserving access rights–?exible access rights

1Introduction

The focus of this work is on the speci?cation of access rights that permit privacy-preserving access to a large collection of digital goods(e.g.,articles, books,magazines,multimedia objects,or any other type of digital data items).With a large number of subscription-based services available today, customers would be more willing to use such services if we could guarantee that access to the digital goods is anonymous and their preferences and access patterns cannot be tracked.That is,if customers can purchase their subscription anonymously(either by authenticating using an anonymous authentication scheme,or by purchasing the card anonymously from a pub-lic bookstore or cyber-caf′e)and further interaction with the server does not reveal customer or card-speci?c information while still allowing access to the authorized set of digital goods,then customer privacy is guaranteed.

1.1Motivation

During the con?rmation hearings of a nominee for the U.S.Supreme Court back in1988,the issue of which movies he had rented came forth.The records of which movies he had actually rented,had been obtained by a local Washington newspaper from a video rental store,by simply asking the store for them.Today the Video Privacy Protection Act(18U.S.C.2710) prevents video stores from releasing such information without the customer’s written consent,but it is nevertheless all too easy for such records to be re-leased nevertheless,either inadvertently or through a break-in,spy-ware, insider misbehavior(rogue employees),social engineering,etc.Moreover, the video-privacy bill is speci?cally about movie rentals(it does not cover, e.g.,magazine and other subscriptions).The problem is exacerbated in the online word,as it is then possible for a server to determine not only which material the customer accessed,but also how many times,when,for how long each time,etc.For example,a customer who accesses much material about a disease runs the risk of an inference being made about her hav-ing that disease(or having a lifestyle that puts her at risk for it).Some recent encryption-based digital-rights management technologies not only

Succinct Representation of Flexible Privacy-Preserving Access Rights3 reveal which encrypted material was downloaded,but also the exact times at which the user chose to view the downloaded material(as each viewing requires that the server sends a key to the client-end viewing software that is entrusted by the content-owners with decrypting/displaying the material and then destroying the key).These technologies are used for such purposes as protecting the revenue-streams of content-owners against piracy,allow-ing corporations to enforce policies on documents and emails without fear of employee non-compliance(e.g.,to remotely shred an old document or email, the server simply deletes the key associated with it,and the employees’hard drives are left with unusable encrypted material).Many of the technologies that have been deployed,or are under development,have chilling privacy implications.Even as they have such large potential for damage to privacy, these techniques have largely failed to prevent piracy,as they are typically defeatable by a determined attacker.This is why hardware-based digital rights management techniques are being deployed(they are much harder for an attacker to crack than purely software-based ones)even though they could enable more stealthy ways for software publishers to spy on users,to know what is on a user’s computer,to control what the user can and cannot execute,view,connect to the computer,print,etc.Although our schemes use tamper-resistant cards,they do not harm user privacy because at no time does a card“know”who the customer is.

The customer and regulator complaints(including lawsuits)?led against a major clickstream-information collecting company,alleging what amounts to cyber-spying,is but one example illustrating people’s sensitivity when it comes to the tracking of their online activities(even for apparently innocu-ous marketing purposes).These fears may be well justi?ed,because history is full of examples where information collected for a benevolent purpose was subsequently used for nefarious purposes(even prior to the cyber-age, e.g.,the Dutch government records that listed their citizens’religion were subsequently used by the Nazis for a horrendous purpose).The misuse need not come from the data-collecting entity:The data may simply fall in the wrong hands through a security breach–the last few years have seen an avalanche of security breaches in which private information was seriously compromised.

In view of the above,a customer’s trust that the data collectors will not misuse the data is only a?rst line of defense(and a rather?imsy one, based on the evidence).Privacy-conscious customers who?nd appealing a “defense in depth”that protects them from such possible mis-haps,can take steps to avoid revealing their identity to the server by,e.g.,obtaining access through anonymizing proxies,or simply from a cyber-caf′e.This,however, does not work well in the context of a for-pay access to online material,that typically requires the server to learn the identity of the subscriber through (e.g.)the entry of a login and password tied to the subscriber’s real identity through the subscription information(typically including the name,email address,and credit-card payment information).The need exists for schemes, such as presented in this paper,that support for-pay subscriptions without

4M.Blanton,M.Atallah compromising subscriber privacy,yet while preserving the content-owner’s rights.

1.2The framework

As the number and the level of maturity of services that o?er access to digital goods grow,the level of?exibility of such systems will also grow.To make access as convenient to the customers as possible,such systems might allow customers to subscribe to items of their choice with?ne granularity, and not limit their choice to a small number of prede?ned subscription types. In the most?exible setting,the system allows each customer to select a set of objects to which they wish to have access and correspondingly pay for. Depending on the structure of the data repository,a customer may be able to select individual items or groups of items based on their type,topic,or another classi?cation scheme.The customer then receives an access policy con?guration that is unique to her subscription request.

With this model in place,the service provider can no longer store a com-plete description of customer access rights at his end,because if he did,it would violate privacy requirements.A solution is to store access rights at the customer end using tamper-resistant devices such as smartcards.The main challenge is then to design a scheme that would permit the customer to ac-cess the goods to which they have subscribed and at the same time preserve their anonymity by making their transactions untraceable and unlinkable1.

Since customer policy con?guration is stored on weak devices such as smartcards,such devices are normally limited in their computational power and storage space,especially if their cost must be kept low(which is the case,for instance,with short-term orders and/or disposable cards).Limited resources,however,con?ict with our intent to provide?exible access to the items of customer choice,if the size of the data collection is very large. There is therefore a need for techniques that permit succinct representation of customer rights and avoid the use of expensive computations.

If a card that stores a customer’s subscription set does not have enough capacity to store at least one bit per item in the(potentially huge)data repository,then it becomes impossible for it to exactly represent all possi-ble subsets of the repository items.Thus,some items or subset of items will have to share the same con?guration and introduce“false positives”into the scheme—a false positive is an item that was not listed in the subscription, but which the customer is permitted to access.This model is acceptable if the probability of a false positive(PFP)is small enough.A major goal is then to design a scheme for computationally e?cient access control enforce-ment under space constraints that minimizes the number of false positives

Succinct Representation of Flexible Privacy-Preserving Access Rights5 implicit to each card.Of course,false negatives are not tolerated:a customer who has paid to subscribe to an item must always be granted access to that item.Minimizing false positives is not the only requirement:others include protection against sharing of false positives information by unscrupulous users,providing the users with transaction untraceability and unlinkability, and forward compatibility of the scheme;these,and other design goals,are stated in more detail later in the paper.

1.3Counter-indications

Our schemes are suitable for the realm of digital-rights management,in situations where a false-positive access to a document or a music is toler-able if it has a reasonably low probability of occurrence and the negative consequences would be tolerable if it were to occur.Both conditions are important because,even when the probability(call it p)of a false positive is reasonably low,if the damage(call it d)from a false positive is large enough,the expected damage p?d may be unacceptably high in some situ-ations.In view of the above,the schemes described in this paper should not be used in situations where a false positive has a catastrophic consequence, such as unauthorized access to a patient’s medical records,or the software that controls a power plant’s machinery.

But even when the probability of false positives is close to zero,and/or when the apparent and measurable damage from such a false positive is zero,there are situations where privacy-preserving techniques are not rec-ommended(any of them,not just the ones we propose).These are situations where even legitimate(not just false positive)accesses could be a cause for concern if they follow certain patterns or are done by certain individuals. Speci?cally,privacy-preserving techniques are not appropriate if the legiti-mately accessed material is of such a nature as to inherently require moni-toring or auditing by law-enforcement agencies.For example,if the on-line material is restricted-access because of its possible use to evil-doers intent on acts of violence,?nancial fraud,or disruption,then an audit trail of which authorized individuals accessed it(and when they accessed it)is needed by law-enforcement agencies to determined(e.g.)who“leaked it out”in an unauthorized fashion.The use of privacy-preserving techniques becomes obviously problematic in such a framework,as it would serve to protect the culprit.The framework we have in mind for our schemes is therefore more one involving commercially valuable but innocuous content,such as music, movies,e-books,databases of past sports events and data,historical trading transactions(stocks,bonds,commodities),and other specialized databases that are unlikely to be of use to criminal elements.

1.4Our contributions

Our contributions are as follows:we give two solutions that address the problem of?exible and privacy-preserving access rights.Our?rst solution

6M.Blanton,M.Atallah utilizes random permutations and does not place any constraints on the amount of storage space that should be available on the smartcard.In-stead,it searches for the best solution that meets the space requirements and satis?es the service provider.The second solution is based on the use of minimal perfect hash functions(MPHF),and di?ers from the previous solu-tion in that it is guaranteed to result in a low rate of false positives for any subscription order,but uses storage space proportional to the subscription size.More precisely,given a smartcard with O(mc)storage space,where m is the number of items or groups of items included in the subscription and c is an arbitrary parameter,this scheme achieves the rate of false positives m?c.For both schemes,we provide solutions for(i)“?at”data repositories, where the collection of documents is not organized into a data structure; and(ii)hierarchically structured collections of data items such as trees. 1.5Organization of the paper

The rest of this document is organized as follows:In section2,we review prior related literature.Section3gives a more precise problem description and lists design goals.In section4,we describe our?rst,permutation-based approach for both unstructured and structured data repositories and pro-vide its analysis.In section5,we give the second,minimal perfect hash function based approach,its analysis,and extensions.Section6compares the schemes and concludes the paper.

2Related Work

Work conducted on XML explores the problem of access control for online data repositories,which includes securing access to XML documents and using XML as a tool for specifying security policies(see,e.g.,[6–8,18,19]). Bertino et al.[5]use binary strings to represent both customer policy con-?gurations and document policies,but they allocate one bit per policy on the assumption that there will be a limited number of di?erent subscription types.Thus,their approach becomes ine?cient as the data repository grows in size and each customer chooses a customized document subscription set. The topic of digital libraries is also related to this work,but literature on digital libraries usually does not address access control.

The idea of achieving space e?ciency at the cost of a small probability of false positives was introduced in Bloom[9].Bloom?lters support ap-proximate membership queries and are widely used in a broad spectrum of applications([12,20,27],to name a few).Such data structures achieves a better space utilization than simple hash representation,but the?lter length (which in our case corresponds to the card capacity)still should be larger than the total number of items in the set to result in a reasonable perfor-mance.This is not suitable for cards of small capacity,and even customized Bloom?lters do not appear to provide acceptable results.

Succinct Representation of Flexible Privacy-Preserving Access Rights7 Other techniques for concise representation of portable access rights were used in the context of software license management[4,1].These solutions, however,do not apply to our problem,mainly because we cannot a?ord to avail ourselves of resources external to the card(as was the case in[4,1]). The more recent work in[13],on the other hand,considers the same prob-lem of portable and?exible access rights for large data repositories.In[13], the authors consider static policy assignment to all repository documents, which makes addition of new items problematic without performing peri-odic policy updates(after which all smartcards must be refreshed)and also makes it possible for dishonest users to share and use information about false positives.

Some of our solutions use minimal perfect hash functions(MPHF)as their underlying building blocks.MPHFs have received signi?cant attention, and a number of algorithms can be found in[23,22,17,21].There are MPHFs and order-preserving MPHFs(OPMPHFs)that for random m strings take the total of O(m)bits to store the functions(and this is also the lower bound).See[23,21]for more detail.

Work on unlinkability and untraceability was started by Chaum[16] and received signi?cant attention in recent years.In particular,work on unlinkability includes anonymous group authentication([2,11,15,24–26,28–30]and others)and unlinkable serial transactions[31]for subscription-based services.Prior work,however,does not account for the fact that descriptions of access rights(or service types)may be long and required to be portable, while we describe schemes that combine compact policy representation with transaction unlinkability.

3Problem Speci?cation

3.1General model

The general model used in our work is depicted in Figure1and consists of two stages.During the initialization stage—which can take place in a bookstore,at a public library,or at home—a customer chooses items of his choice,pays for the items selected,and receives a customized card that subsequently permits access to these items.During the card usage stage—which can likewise be done from a home computer,library,etc.—the customer can request access to any items from the repository.If the card permits access,it uses the built-in anonymous authentication protocol to prove its authenticity to the server and then obtains the item from the server.

Here,by“server”we do not necessarily mean a remote server.Instead, it could be a local(trusted)content player at the client end or any other mechanism used by the content owners to enforce their policies.In that case, the encrypted content is already stored at the client’s end and the server grants access by decrypting and then displaying it.Therefore the model does not necessarily assume network connectivity for data access.

8M.Blanton,M.Atallah

Initialization

1.Customer chooses m items for purchasing.

2.Server processes the order and creates a card.

3.Customer pays and receives the card.

Operation

Card Server

1.Receives from the user a re-

quest to access item i

2.Checks if access can be

granted

3.Anonymously authenticates

to the server and requests

item i on behalf of the user ?→Veri?es authentication credentials

4.←?Sends item i to the requester Fig.1General model of operation.

Throughout this paper,we assume that a card is authentic and can anonymously and at low computational cost authenticate itself to the server.

A number of solutions that range from trivial secret key schemes to more complex and provably secure schemes(e.g.,[2,25])can be used to achieve this goal.Card unforgeability is achieved through other,standard techniques described in prior literature and is out of scope of this work.

As an example of a provably secure scheme that allows users to anony-mously access the service,we show how group signatures(e.g.,[2,3,10,14]) can be used to achieve this goal.A group signature is a cryptographic con-struction that allows a member of the group to sign messages anonymously on behalf of the group.In case of a dispute,however,the identity of the originator of such a signature can be revealed by a designated authority (called group manager).The interactive version of group signatures(what is needed here)is called identity escrow,and each group signature scheme can be used in the interactive mode.In such schemes,there is a protocol that allows a user to join the group and become its member(which in our case will be done at the subscription time).As a result,user credentials for the group signature scheme and her access rights that permit access to the documents in the repository will be written on a card.Then every time a user wants to access an item at the server,she will?rst anonymously authenticate to the server using her group signature credentials and then invoke her access rights to obtain access to the document of her interest.

3.2Notation

In the rest of this paper we use the following notation:the data repository contains n items numbered1through n.A customer can request access to

Succinct Representation of Flexible Privacy-Preserving Access Rights9 (and accordingly pay for)m items,1≤m≤n.Access rights are stored on a card of limited capacity of k bits,where k

We use the term order to refer to a subscription order of m documents for which the customer pays and receives a card that permits access to those documents.We use the term request to refer to a request to access a document by a customer who already possesses a card and wishes to view a document.A customer subscription order of m items is denoted as {i1,...,i m},where i j uniquely identi?es a single document in the repository and1≤i1<...

3.3Design goals

The design goals that we require any solution to have are as follows:

Low rate of false positives.The probability(or rate)of a false positive (PFP)—the probability that a random document not in the set of m subscription documents is among the documents to which access is authorized—is the main evaluation criterion of any approach,and the goal of this work is to minimize such a PFP.The PFP obviously depends on the storage space available on the card.

Transaction untraceability and unlinkability.For customer privacy,we require that after a customer buys an access card and uses it to retrieve an item from the repository,it is not possible to use the data sent in the request to tell with probability signi?cantly greater than a random guess which customer is making this request.Similarly for transaction unlink-ability,we require that given two access requests it is not possible to tell with probability signi?cantly greater than a random guess whether these two requests originated with the same user.

Unique policy representation(“no sharing of false positives”).It is also a design requirement that every policy representation stored on

a card is unique.More precisely,given two subscription requests that

contain identical sets S1and S2of items to be purchased,their repre-sentations stored on access cards C1and C2will be di?erent and the false positives implicit to each card will also be di?erent.We require this property in order to eliminate the possibility of sharing information about false positives by dishonest customers.When this is not the case and a?xed set of items triggers the same set of false positives,dishonest users might share this information through public channels such as the Internet,making the scheme unusable for the data provider.

Note that this will prevent sharing of information about false positives, but not all possible forms of information sharing.That is,content shar-ing by dishonest users is always possible regardless of an access control mechanism used.Our goal here is to prevent sharing of information

10M.Blanton,M.Atallah about access rights and,more importantly,information about illegiti-mate access rights that the user should not possess.Access rights infor-mation is much more convenient to share than voluminous contents.

No additional sources of information.The schemes we design are for online data repositories that,using a card,can be accessed from a num-ber of places such as terminals at public libraries,bookstores,home workstations,and other places.Therefore,if a scheme were to require some additional information to be stored on external storage,in our sce-nario there is no reasonable place at which such information could be stored(and,as was mentioned above,no user information can be stored at the server itself by the untraceability requirement).Thus,the access card itself should contain all information necessary to perform access veri?cation.

Fast access veri?cation,fast card generation time.These parameters also serve as evaluation criteria of each scheme,and in general we re-quire card generation time to be bounded by a low-degree polynomial in n or,preferably,by a polynomial in m.Access veri?cation time should be bounded by O(k),where k is the space available on the card,because each card is assumed to be a computationally weak device.

Forward compatibility.In any proposed solution,if a card is created at time t1when the data repository contained n1documents,it also should stay operational at time t2>t1when the data repository contains n2> n1documents.In other words,the scheme should remain operational as new documents are added to the data repository.

Another important feature of a scheme that produces access right repre-sentations is Support for dynamic changes to the https://www.sodocs.net/doc/4c7102768.html,ly, every time changes to the data repository happen,previously issued cards with user access rights remain functional on the modi?ed version of the data repository.Note that the forward compatibility requirement above partially covers this feature,but,for instance,deletions from the repository are not addressed.Other changes to the repository include restructuring of the items currently present in the repository.This,however,is applicable only to struc-tured data collections such as,e.g.,hierarchies and can be handled solely using support for additions and deletions.In our design requirements we do not strictly require support for document deletions from the repository, because the scheme can be used regardless of availability of this feature. That is,if deletions are not handled automatically,the repository can be periodically“cleaned”(e.g.,once a year),removing unwanted documents all at once.We,however,analyze our solution with respect to such support and show how dynamic changes can be handled in each of the schemes.It is also worth mentioning here that a document cannot be removed from the data repository while there is at least one customer with valid access rights to that document(i.e.,documents are not likely to be removed often).

Note that the above requirements make our problem very di?erent from mere data compression.Another di?erence from data compression is that here each representation on the card must be usable“as is”without un-

Succinct Representation of Flexible Privacy-Preserving Access Rights11 compressing it?rst:There is no room in the card for decompression,and using server memory for decompression would reveal enough about the card to make pro?ling of the card’s usage patterns possible(recall that contents of two cards are di?erent even if both of them contain the same subscrip-tion set.They are in some sense an implicit ID for the card and should therefore not be revealed to the server).Client memory is not suitable for decompression either because it cannot be trusted.

4Permutation-based Approach

In this section we present our?rst solution.We?rst describe our approach to an unstructured collection of documents and provide its analysis.Structured collections of documents are addressed in section4.7.

Recall that the card’s capacity is k bits.In the rest of this section we assume that those k bits are divided into slots of log n bits each and therefore the card’s capacity is k=O( log n).

Our solution consists of generating random permutations of the docu-ments included in an order until they are clustered in such a way that the cost(in terms of false positives)of storing the permuted documents on a smart card is below a certain threshold(de?ned later).After generating a permutation of the documents,we run an evaluation algorithm to compute the cost of the optimal solution for that particular set of permuted docu-ments.If the cost is acceptable,the algorithm terminates and the solution is written to the card;otherwise,a new permutation is generated and tested. The information written on the card includes data that can be used to re-produce the permutation,as well as a number of document intervals that indicate access to which documents should be granted.The intervals include all documents from the subscription order and as few additional documents as possible.

Consider an oversimpli?ed example where the repository has the size of 20,our card can store2intervals,and we receive a customer subscription order for documents1,5,7,9,13,and19.Suppose that after permuting the documents we obtain set{2,3,4,15,16,18},so the best option in this case is to use intervals2–4and15–18for storing the set on the card.The cost of a solution is computed as the number of false positives,and in this case the cost of the permutation is equal to1.

Both the random permutation seed and the document intervals are sub-ject to the card’s storage constraints.Since the smartcard’s capacity is O( log n),we can use it to store O( )numbers within the range{1,...,n}, or intervals.The permutation seed can also be up to O( log n)bits long.

Every interval included in a solution can be either positive,i.e.,speci?es a range of documents to which access should be granted,or negative,i.e., speci?es a range of documents to which access should be denied.In the case of unstructured data(i.e.,where the data repository is a mere collection of numbered items,not organized into a hierarchy or any other type of data

12M.Blanton,M.Atallah structure),negative ranges do not improve the result by decreasing the cost of a solution,as the lemma below shows(we,however,show later that they are necessary for structured data).

Lemma1For unstructured data,for every solution of cost C expressed us-ing both positive and negative ranges there is a solution of cost C expressed using only positive ranges,such that C ≤C.

Proof See Appendix A.

We?rst present an algorithm for producing a suitable encoding to be placed on a card(section4.1).This is a high level algorithm that tries di?erent solutions until the conditions corresponding to the policies are satis?ed.It uses two additional algorithms as its subroutines:an algorithm to produce a permutation(section4.3)and a linear-time algorithm to compute a cost of a permutation(given in section4.2).We give asymptotic bounds of our solution and also discuss possibilities for generating a random permutation. Later in this section we explore this approach in terms of its economic feasibility(section4.5),and also provide an extension that covers structured data(section4.7).

4.1Algorithm for producing a solution

To?nd a suitable encoding for a customer order,we might have to try numerous permutations of n elements until one that satis?ed certain criteria is found.These criteria can be expressed in terms of the cost of a solution (e.g.,the number of false positives for the permutation produced falls below a certain threshold),in terms of a time interval during which a solution should be computed,or some other requirements.These rules are examined in more detail in section4.5.

The algorithm we provide below takes a subscription order of m doc-uments and a set of rulesτthat tell the algorithm to stop when they are satis?ed.It runs until a suitable solution is found and returns an encoding to be stored on a smartcard,which consists of a permutation seed s and intervals that optimally represent the documents{i1,...,i m}.

Input:The repository size n,a customer order of m documents{i1,...,i m}, and a set of stopping criteriaτ={τ1,...,τt}.

Output:A seed s for generating a permutation and intervals to be stored on the smartcard.

Algorithm1:

1.Seed the permutation algorithm with a random number s.

2.Permute the m documents to get p j=πs(i j)for each document i j∈

{i1,...,i m}.

3.Sort the p i’s(O(m log(m))time).

Succinct Representation of Flexible Privacy-Preserving Access Rights13 4.Run the evaluation algorithm to?nd the cost of the permutation(O(m)

time,per section4.2).

5.Apply the evaluation rulesτto the result:if a su?cient subsetτ ?τ

of them,1≤|τ |≤t,is satis?ed,output the solution.Otherwise,go to step(1).

The asymptotic bound of a single run of this algorithm depends on the choice of the permutation function(discussed in section4.3).The total running time of the algorithm depends on the evaluation criteria and cannot be expressed as a function of the input parameters in the general case.The upper bound of the algorithm is O(n )loop invocations,but typical values are lower.This time is constrained by the space available for storing a random seed s:there are O(2 ·log n)=O(n )possible seed values that can be stored on the card.

4.2Algorithm for computing the cost of a permutation

The algorithm given in this section corresponds to step4of Algorithm1. As the input,it expects a set of m distinct permuted documents sorted in increasing order p={p1,...,p m}and computes disjoint intervals of the minimal cost that include all of the p i’s and as few other documents as pos-sible.Our algorithm works by computing distances between the documents in the set p and excluding the largest ?1of them,so that the overall cost of the covering is minimized.

Input:The repository size n and a sorted set of m elements p={p1,...,p m}. Output: disjoint intervals that contain all of the p i’s and as few other elements as possible.

Algorithm2:

1.Let x be the value of p1,y the value of p https://www.sodocs.net/doc/4c7102768.html,pute c1,...,c m?1,

where c i is the number of documents between the elements p i and p i+1 not including either p i or p i+1.That is,c i=p i+1?p i?1.

2.In O(m)time select a( ?1)th largest among c1,...,c m?1(say it is c j).

3.In O(m)time go through c1,...,c m?1and choose ?2entries that are

≥c j.Those entries and c j correspond to the ?1“gaps”between the optimal k intervals,i.e.,they de?ne the optimal intervals.

Note that the“cost”of the solution is C=c1+...+c m?1?(sum of the largest ?1c i’s),which also proves the correctness of the algorithm because c1+...+c m?1is the number of documents between positions x and y other than the elements of p,and the best that can be done is by“excluding”the large c i’s from the chosen intervals.It is also clear that the algorithm runs in O(m)time,since every step(1)–(3)runs in O(m)time.

The actual monetary damage caused by the false positives might not be linear in the number of false positives,but instead could be some other (possibly arbitrary)function speci?ed by the service provider.In this case,

14M.Blanton,M.Atallah however,the algorithm will still produce correct results,and the cost func-tion itself can be incorporated into the set of stopping rulesτ,as we explain in section4.5.

4.3Algorithms for producing a permutation

There are several well-known methods for computing random permutations. Any method that has the following properties should be suitable for our approach:

–The permutation can be speci?ed by a seed,i.e.,given a seed value,the permutation could be reproduced from it.Recall that the set of storable seeds does not“access”all possible permutations of n elements,but only

a random subset of O(n )of these permutations3.This turns out to be

enough in practical situations(see discussion in section4.5).

–The algorithm allows concurrent computing of a mapping for a single element.It is then not necessary to compute the permutation mappings for O(n)documents of the data collection at the access veri?cation time just to obtain one of them that we are interested in.We can also directly compute the mappings for the m documents included in the order during card creation time without having to generate all of the n mappings. As one example of a permutation satisfying there requirements,consider the case when n =n+1is prime,g is a generator for that prime,and a per-mutation seed is speci?ed as an integer x,1≤x≤n ?1.The permutation consists of any integer i,1≤i≤n ?1,mapping intoπx(i)=x·g i mod n . It can easily be seen that the mappingπso de?ned is a permutation(i.e., there are no collisions).Of course,the use of x as a seed means that only n of the possible permutations of the n elements are“accessible”.To extend the reachability of the seed from only n permutations to the full n allowed by the available O( log n)bits of storage,we would simply store as a seed distinct(rather than a single)such x values x1,...,x .Each x j de?nes a permutationπx

j

in the manner described above:for the j th such permuta-

tion,i maps intoπx

j (i)=x j·g i mod n .The entire permutation described

by this seed of length log n bits is then the functional composition of the

permutationsπx

1,πx

2

,...,πx

(in that order).There are n possible choices

for this permutation,as required.

In fact,any encryption function whose range and domain are[1,n],and whose key space is[1,n ],could be used for our purpose of permuting.That is,if x is the seed,thenπx(i)is simply the encryption of i using x as key. The fact that n is too small for cryptographic security is not an issue here, because we are using encryption not to hide but rather to permute.

Succinct Representation of Flexible Privacy-Preserving Access Rights15 4.4Card operation

The algorithms presented above describe card generation,but they imply a corresponding operational use of the card,which we sketch here.We as-sume that the card is tamper-resistant,so that the unforgeability constraint is satis?ed;techniques for achieving tamper-resistance can be found in the literature and are beyond the scope of this paper.Also,the card must anonymously authenticate itself to the server using a low-computation au-thentication suitable for smartcards.Policy enforcement is performed using the policy encoding placed on a card as follows.Given a document index i access to which is being requested from the server,and a card that stores a permutation seed s and intervals,the veri?cation process takes the fol-lowing steps:

–The card computes a permuted value of i as p i=πs(i).

–The card searches its intervals for p i to determine whether p i is covered by one of them.Since we can sort all intervals before storing them on the card,this step can be done in O(log )time using binary search.

–If p i is covered by one of the intervals,the card requests the document

i from the server.Otherwise,it noti?es the user about access denial. One can see from the above that the untraceability and unlinkability con-straints of our design(goals of section3.3)are satis?ed:Each card anony-mously authenticates itself and does not send any information to the server that might happen to be unique and used to link two transactions together. The card also does not require any additional sources of information to enforce proper access control and uses an e?cient method for such enforce-ment,as required.

4.5Economic analysis

This section analyzes the practicality of the scheme described above.We explore the possibility of using the scheme under di?erent settings,and examine what policies a service provider might specify in order to use the model as e?ciently as possible.We also make the“stopping criteria”that govern permutation selection process more precise.

4.5.1Values of interest As input,we are given the size of the data repos-itory n and the number of documents in a customer order m4.Other pa-rameters of use for determining what an acceptable cost is are:

16M.Blanton,M.Atallah c card(m)–the price a customer pays for an order of m documents,which

can be a possibly arbitrary function of the documents that comprise the order.

t(m)–the maximum number of requests to documents access to which was denied.Each card can count the number of attempts to view documents that were denied.When a customer requests a document not bound to the card,not only is the access denied,but also the permitted limit of unsuccessful requests is decremented.After t such attempts,the count reaches zero and the card is self-invalidated(i.e.,the policy here is“t strikes and you are out”).This is to prevent customers from probing their cards for false positives,e.g.,by trying all documents in the data repository.With this mechanism in place,each customer should be in-formed about t at the time of purchasing the card and should be given an explicit list of the documents included in his order.

m (n,m)–the number of documents that come for free with a card(i.e.,the “false positives”).This value is computed as a by-product of Algorithm 2,and implicitly re?ects the card’s capacity .

n (n,m)–the number of documents in which an attacker is interested (other than the m he ordered).This value is useful in measuring the at-tacker’s economic gain in case of discovering free accesses to documents.

In the worst case,any free document can be valuable to the attacker.In the best case,the attacker has zero interest in anything outside the m documents she ordered.

4.5.2Policy alternatives Each service provider deploying this approach might have one or more varying criteria that de?ne an acceptable“false positives”cost of a card.Below we list policies that can be used during card generation to govern execution of Algorithm1:

1.Threshold for the number of false positives m that a card con-

tains.This policy might dictate that the absolute value of the num-ber itself is constrained(e.g.,f(m )≤m max),or its ratio to the num-ber of documents in the repository or to the number of documents in the order is constrained by some threshold(e.g.,f g(m )

h(m) ≤m max,where f(x),g(x)and h(x)are arbitrary functions of argument x).We may consider a policy that lists several conditions but requires satisfying a subset of them.

2.Constraints on the gain from cheating.In this type of policies,we

perform analysis of cheating in terms of the attacker’s loss vs.his gain after attempting to access t out of the n?m documents not included in his order.Suppose that t >t.The expected gain from the attack in this case is the di?erence between the cost of the documents acquired for free from the list of n documents of interest,and the cost of losing the card due to this behavior.The gain is then computed as the probability of successfully getting a free access to a document multiplied by the

Succinct Representation of Flexible Privacy-Preserving Access Rights17 document cost,while the loss is computed as the probability of losing the card multiplied by the cost of the card:

E(gain) t ·c(m )

n?m

?c card·Q

t c(m )n

n?m

speci?es the probability

of not being caught,while q=1?p is the probability of begin caught. Similarly,we can compute the expected gain when the number of unau-thorized attempts is kept below the maximum,i.e.,t ≤t.In this case, the expected gain is computed based on the probability of getting free access,and there is no loss for the attacker:

E(gain) t ·c(m )

n?m

(1)

In the worst-case scenario,the attacker might be interested in and bene?t from any document acquired for free,i.e.,n =n?m,and we can also assume that t t,to maximize the gain.Then equation(1)becomes:

E(gain) t·

c(m )

n?m

≤α·c card(2) 3.Constraint on certain items being among the false positives.

The previous constraints take into account only the total number of false positives without distinguishing them,and do not account for the fact that the repository might contain a number of generally popular items.Thus,another constraint might be to lower the value of false positives for a customer by excluding such valuable items from the false positives.We refer to such items in high demand as“hot”items,and for each customer they can be either system-wide(the same for everyone), card-speci?c(based on the subscription order at card-creation time),or both.

Note that,from the privacy point of view,it is acceptable for the data owner to determine the hot items for a card based on the card’s subscrip-tion order(which must be given anyway at the time of purchase,e.g., during anonymous card purchase at a vending machine or bookstore).

Later on,as the card is used,the card does not disclose data about the subscription order or the card-speci?c forbidden hot items.

Once the set of such hot items for a subscription order is determined, the policy might state that there is a threshold on the number of such

18M.Blanton,M.Atallah items that can be among the false positives(the threshold can be stated similar to the total number of false positives in the?rst rule).Thus,if

a particular instance of a card does not satisfy this requirement,a new

instance should be generated.

4.Timeout.Under some policies,the card creation process might have to

be carried within a certain period of time.Then if no suitable permu-tation is found during that interval,the best permutation tried so far is used.

Based on the policies listed above,we create a set of stopping criteria by possibly combining two or more conditions in such a way that what the card produced always satis?es the card issuer.

4.5.3Sample policy Suppose a service provider employs a policy in which the number of attempts to access a document not included into the cus-tomer’s policy con?guration,t,cannot exceed10%of the number of docu-ments m in the customer’s order.(Recollect that each customer at the time of purchase is given a list of all documents included in the order,so that t can be kept small.)The service provider also requires that the maximal customer gain from“false positive”documents cannot exceed5%of the cost of the order.Evaluation parameters for a document permutation then can look like:t=0.1m,n =n?m,andα=0.05.Given n and an order consisting of m documents,we use Algorithm1to compute m .According to equation(2),m should satisfy the following condition:

0.1·m·c(m )

2,which is large and not di?cult to achieve for

any order of m documents.This tells us that the scheme can accommodate

a wide range of reasonable policies.

4.6Analysis of the approach

Our proposed solution is compliant with the desired design properties and minimizes the total number of false positives bound to a card.More pre-cisely,the design of our scheme ensures that goals of transaction unlinkabil-ity and untraceability,unique policy representation,no additional sources of information,and fast access veri?cation time listed in section3.3are met.The goal of forward compatibility is achieved by using unique policy

Succinct Representation of Flexible Privacy-Preserving Access Rights19 representations that“capture”the state of the repository at the time of card generation and are self-contained.As we add more documents to the repository,the old cards can still be used,for instance,to reproduce per-mutations of the documents from the previous state of the repository and provide access to the documents from customer subscriptions.

Our permutation approach also guarantees a low rate of false positives, especially if this constraint is a part of the algorithm’s termination criteria. Depending on the policies enforced by the service provider,the scheme can be evaluated on its time requirements,i.e.,how long,on average,it might take to generate a card.Thus,it might or might not comply with the goal of fast card generation.If the service provider employs a policy that includes a timeout,then in-house card generation is always achievable.If,on the other hand,he places more weight on minimizing the number of false positives, then this constraint might be relaxed.

4.7Structured data–trees

This section extends our approach to structured data collections such as trees.In many data repositories documents are stored in hierarchies,which makes it possible to utilize the repository’s structure and reduce the number of false positives in the solution computed.Since in reality many customers do not select a random set of documents,but rather are interested in certain topics(which will guide their selection of items to be included in the order), great space savings(and thus a signi?cantly reduced rate of false positives) can be achieved if instead of storing individual items we permit storing categories of items.In fact,the software that aids the user in selecting items to be included in his subscription can help to achieve space savings in cases of hierarchically structured documents.That is,it will provide the user with in option of selecting the entire section or category of documents at every level within the hierarchy,in addition to allowing selecting documents one by one.The quanti?cation of such savings,however,cannot be performed in the general case,because it heavily depends on the type of the hierarchy and user patterns in selecting documents.

Now we present our approach for building user cards in case of hier-archically structured repositories.Suppose we are given a tree of n docu-ments and a subscription order of m documents.The card’s capacity is still k=O( log n)bits or O( )records,but in this case each record,in addition to two numbers that specify a range,might contain some other information. We consider both positive and negative ranges for encoding documents on a card.We also consider two di?erent types of placements:when a positive or negative assignment is placed on a node v,it can either a?ect the entire subtree rooted at v–we denote this case as recursive–or a?ect only the node on which the assignment is placed–we denote this assignment as local. The case where a depth parameter can be stored at v,so as to limit the depth of the subtree included,will be considered later in this section(such

20M.Blanton,M.Atallah

a depth parameter limits the depth of the nodes in?uenced by that range,

so that nodes that are farther than that depth below v are not a?ected). When two ranges overlap,the more speci?c range(i.e.,lower in the tree)is used.As before,the word“cost”is used as the“cost of the false positives”

(not the dollar cost paid by the customer).

Throughout our algorithm,we use the following notations.For each

node v,a cost of the subtree rooted at v can be computed in two di?erent contexts:positive and negative.If a node v is evaluated in the positive context–the cost is denoted by C+(v),–this means that a positive range

has been speci?ed at its parent or above the parent in the tree.In this case,

if no new range is placed at v or below,the entire subtree will be included in

the?nal solution.In this context,only negative ranges placed at v or below

have e?ect.Similarly,if a node v is evaluated in the negative context–the

cost is denoted by C?(v),–then it means that a negative range has been

speci?ed at its parent or above,and by default the entire subtree will be excluded from the solution.If no context has been speci?ed,we start in

the negative context and assume that no nodes are included in the solution unless explicitly speci?ed.

Our solution uses dynamic programming techniques;and as with any dynamic programming approach,the cost of an optimal solution at any

given node v needs to be calculated for several cases that di?er in the number of encoding slots available.Thus,we use C+(v,j)and C?(v,j)

to mean the cost of encoding the tree rooted at v in positive and negative contexts,respectively,with j storage slots available,where0≤j≤ .

Here we provide an algorithm for binary trees,which can naturally be extended to work for more general t-ary trees with t≥2.When working with binary trees,we typically use nodes u and w as child nodes of v.In order to compute a cost of a subtree rooted at node v,we need to consider two cases: computation of C+(v,j)and C?(v,j),which we describe subsequently.Let

us consider non-leaf nodes?rst and then proceed with leaves of the tree.

Time complexity of the algorithm for both binary and arbitrary t-ary trees

is given later in this section.

4.7.1Non-leaf nodes

Case of C+(v,j):When the cost is computed in the positive context,we need to consider three di?erent cases.

Case1:No record is placed at v.Then C+(v,j)is computed as:

C+(v,j)=min{C+(u,i)+C+(w,j?i)+c1|0≤i≤j}, where c1is1if v is not in the order,and0otherwise.

Case2:A negative recursive record is placed at v.This case cannot happen if v is included in the order.We compute the value as:

C+(v,j)=min{C?(u,i)+C?(w,j?i?1)|0≤i≤j?1} Case3:A negative local record is placed at v.This case also cannot happen if v is included in the order.To compute C+(v,j),we use:

C+(v,j)=min{C+(u,i)+C+(w,j?i?1)|0≤i≤j?1}

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身高 (cm)
衬衣尺码 (领围 cm)
西服尺码夹克尺码西裤尺码
(肩宽 (胸围 (腰围
cm)
cm)
cm)
西(腰裤围尺寸码) T
恤尺码
毛衣尺码 内裤尺码 统计比例
160 37(S) 44(S) 80(S) 72
28
S
S
S
0
165 38(M) 46(M) 84(M) 74,76 29
M
M
M
1
170 39(L) 48(L) 88(S) 78
30
L
L
L
2
175 40(XL) 50(XL) 92(M) 80
31
XL
XL
XL
3
180 41(2XL) 52(2XL) 96(L) 82
32
2XL
2XL
2XL
3
185 42(3XL) 54(3XL) 100(XL) 84,86 33
3XL
3XL
3XL
2
190 43(4XL) 56(4XL) 104(4XL) 88
34
4XL
4XL
4XL
1
195 44(5XL)
90
35
5XL
5XL
5XL
0
2、衬衫尺寸(除个别款尺寸,买前询问)
平铺尺寸 M
XL
胸围 97cm 99cm 101cm
肩宽 43cm 44cm 45cm
衣长 67cm 68cm 69cm
袖长 62cm 64cm 65cm
3、裤装尺码为: 26 代表腰围为:“尺” 28 代表腰围为:“尺” 30 代表腰围为:“尺” 32 代表腰围为:“尺” 34 代表腰围为:“尺” 38 代表腰围为:“尺” 42 代表腰围为:“尺” 50 代表腰围为:“尺” 54 代表腰围为:“尺”
27 代表腰围为:“尺” 29 代表腰围为:“尺” 31 代表腰围为:“尺” 33 代表腰围为:“尺” 36 代表腰围为:“尺” 40 代表腰围为:“尺” 44 代表腰围为:“尺” 52 代表腰围为:“尺”
4.女装尺码对照表
上装尺码
“女上装”尺码对照表(cm)
S
M
L
155/80A
160/84A
165/88A
XL 170/92A

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