CERTIFIED PSEUDONYMS COLLIGATED WITH MASTER

SECRET KEY

Vijayakrishnan Pasupathinathan, Josef Pieprzyk

ACAC, Department of Computing, Macquarie University, Sydney, Australia

Huaxiong Wang

Division of Mathematical Sciences, Nanyang Technological University, Singapore

Keywords:

Anonymity, Identiﬁcation, Colligated pseudonyms, TPM.

Abstract:

A pseudonym provides anonymity by protecting the identity of a legitimate user. A user with a pseudonym

can interact with an unknown entity and be conﬁdent that his/her identity is secret even if the other entity is

dishonest. In this work, we present a system that allows users to create pseudonyms from a trusted master

public-secret key pair.

The proposed system is based on the intractability of factoring and ﬁnding square roots of a quadratic residue

modulo a composite number, where the composite number is a product of two large primes. Our proposal is

different from previously published pseudonym systems, as in addition to standard notion of protecting privacy

of an user, our system offers colligation between seemingly independent pseudonyms. This new property when

combined with a trusted platform that stores a master secret key is extremely beneﬁcial to an user as it offers

a convenient way to generate a large number of pseudonyms using relatively small storage.

1 INTRODUCTION

The use of pseudonyms have been proposed as a

mechanism to hide a user’s identity by providing

anonymity, while being still suitable to authenticate

the holder of the pseudonym in a communication sys-

tem (Chaum, 1985). David Chaum argued that us-

ing pseudonyms provides a way that allows a user to

work anonymously, with multiple organisations, by

allowing the user to obtain a credential from one or-

ganisation using his/her pseudonym and obtain ser-

vices using that credential from another organisation

without revealing his/her true identity (Chaum, 1981;

Chaum, 1985). To this end, Chaum and Evertse de-

veloped a pseudonym system and proposed an RSA-

based implementation while relying on a trusted cen-

tre who must sign all credentials (Chaum and Evertse,

1986). Chen extended the scheme from (Chaum,

1985) and presented its discrete-logarithm version

that relies on a trusted centre (Chen, 1995). An ad-

vantage of these schemes is that, they allow the user to

generate pseudonyms, giving n user greater degree of

control over his/her identity. However, these schemes

have a common weakness. Although the identity of

the user is hidden, the credentials (such as certiﬁcates

of his/her public key) or pseudonyms can be easily

shared (unauthorised transfer) with other users.

Based on security of preserving a high-value

(master) secret key, Canettie et al. (Canetti et al.,

2000) and Lysayanskaya et al. (Lysyanskaya

et al., 1999) independently proposed non-transferable

pseudonym systems. Though credentials obtained on

pseudonyms can be used anonymously, the authors

of (Canetti et al., 2000) assume that, certiﬁcation au-

thority (CA) grants credentials only when each user

reveals their true identity to them. This makes their

scheme prone to collusion between a CA and a ver-

iﬁer, as they can deduce the real identity associated

with the user pseudonym. The scheme from (Lysyan-

skaya et al., 1999) protectsagainst unauthorisedtrans-

fer of the user credentials, by forcing a user to reveal

the master secret key if they choose to share their cre-

dentials. But the scheme shares the same weakness as

in (Canetti et al., 2000), during the registration phase,

users are required to disclose their true identity (mas-

ter public key) to a CA.

190

Pasupathinathan V., Pieprzyk J. and Wang H. (2009).

CERTIFIED PSEUDONYMS COLLIGATED WITH MASTER SECRET KEY.

In Proceedings of the International Conference on Security and Cryptography, pages 190-197

DOI: 10.5220/0002226501900197

 SciTePress

1.1 Scope and Contribution

This paper presents a pseudonym system which is

based on the public key cryptosystem. The main idea

is to use a single trusted master secret key with many

matching public keys (pseudonyms). The proposed

system gives users the ability to generate multiple

pseudonyms (that are independent of the master pub-

lic key) from a trusted master secret key. An impor-

tant propertyof the system is that, it providesusers the

ability to generate signatures using the master secret

key, which are veriﬁable using certiﬁcates that were

issued against pseudonyms.

Let us consider an example. Consider a TPM

(Trusted Platform Module) chip that is integrated into

a computing platform (such as mobile phones, lap-

tops, etc.). The chip contains a certiﬁed public-secret

key pair. The public key is certiﬁed by its manu-

facturer and recorded on the TPM chip at the time

of manufacturing. The certiﬁed public key of the

chip can be used to authenticate the machine with the

TPM. The TPM is used to further certify public keys

of users associated with the machine. A veriﬁer can

authenticate a user based on the certiﬁcate chain con-

sisting of the user certiﬁcate, the TPM certiﬁcate and

the manufacturer certiﬁcate. But, revealing the iden-

tity of the machine to every veriﬁer would not only

compromise the anonymity of the machine but also

the anonymity of user(s) of the machine. It is pos-

sible to identify a user using their pseudonyms but,

the veriﬁer trusts only the TPM chip’s certiﬁed public

key and not the operating system of the machine or

any newly generated pseudonyms. Therefore, we re-

quire a system that gives a user the ability to generate

and control the usage of multiple identities based on

a trusted master identity (TPM’s certiﬁed public key),

where the pseudonyms should not only be indepen-

dent of the master identity (anonymity), but also there

is a relation between all pseudonyms generated

and

the trusted master secret key stored in the chip (we

call this relation colligation).

Anonymity and colligation are in some sense con-

tradictory. Anonymity requires that, it is impos-

sible (at least computationally) for an entity with

knowledge of a pseudonym, to link that pseudonym

with either the master identity or any other gener-

ated pseudonym. Whereas, colligation requires that

the prover is guaranteed that there is an underly-

To a certiﬁer it is essential that the system provides

guarantee that, all pseudonyms from a particular TPM can

be traced back to a single secret key, but a veriﬁer needs

proof of this binding between the master secret key and only

the pseudonym that he/she is currently presented with. We

do not make this distinction here.

ing link that exists between all pseudonyms (that ap-

pear to be unrelated to each other) was generated

from the trusted master secret key. Previously pub-

lished proposals like, (Damgard, 1988; Lysyanskaya

et al., 1999; Camenisch and Lysyanskaya, 2002;

Chen, 1995; Canetti et al., 2000; Chaum, 1985) that

achieved anonymity have considered a user’s iden-

tity that consists of public-secret key pair as a sin-

gle uniﬁed structure. Under a such assumption it

is unfeasible to obtain both anonymity and colliga-

tion. We aim to segregate the structure and provide

anonymity to a user but still maintain colligation be-

tween pseudonyms generated using the user’s master

secret key. The implication of this structure is that,

a user’s master secret key becomes highly valuable,

as all his pseudonyms are linked directly to the secret

key.

Based on the security requirement of non reveal-

able master public key in a TPM, Brickell et al.

proposed a method for direct anonymous attestation

(DAA) (Brickell et al., 2004) that provides anonymity

to a user based on the Camenisch-Lysyanskaya cre-

dential system (Camenisch and Lysyanskaya, 2002).

Unfortunately, the scheme (Brickell et al., 2004) does

not provide secret key linkability for identities that are

generated. Consequently, in their scheme, the TPM

needs to maintain a database of those identities and

associated secret keys. The database can get quite

large if the TPM serves a large group of users. Also,

their DAA scheme does not support identity transfer

among machines. In this paper we limit ourselves to

the problem of achieving anonymity and colligation,

and we do not address the issue of identity transfer.

1.2 Organisation

Section 2 provides the background on anonymouscer-

tiﬁcation system and cryptographic techniques em-

ployed. In Section 3 we provide our construction, and

in Section 4, we discuss its security. In Section 5, we

discuss integration of our proposal in a TPM based

setting and conclude in Section 6.

2 BACKGROUND

User anonymity and colligation between master se-

cret key and user generated identities is of paramount

importance. To provide anonymity to user gener-

ated identities (pseudonyms) our proposal will make

use of an anonymous certiﬁcation scheme, such as,

a scheme with blind signatures. An anonymous cer-

tiﬁcation system is necessary to provide anonymity

to a user and to prevent collusion between a certi-

CERTIFIED PSEUDONYMS COLLIGATED WITH MASTER SECRET KEY

191

ﬁer and a veriﬁer. To this end, we will employ a

modiﬁed blind signature scheme (refer Section 3.3)

proposed by Pointcheval (Pointcheval, 2000). Note

that any anonymous certiﬁcation scheme that sup-

ports non-transferability and revocation of anonymity

can be employed with some necessary modiﬁca-

tions. To provide colligation between the generated

pseudonyms and master secret key we can use any

one-way function. In our construction we use squar-

ing modulo a composite integer. In this section, ﬁrst

we describe the model of an anonymous certiﬁcation

scheme that is going to provide certiﬁcates for user

generated identities (pseudonyms). In the remaining

of this section we summarise the main cryptographic

building blocks that we use in our constructions.

2.1 Anonymous Certiﬁcation System

Anonymous certiﬁcation system (ACS) represents the

certiﬁcation process of a public key by a certiﬁer who

does not know the public key. This is essentially a

Chaum blind signature (Chaum, 1982) on the public

key of the user, i.e. it provides anonymity to the re-

ceiver

A typical ACS consists of four entities and three

protocols. The entities are: a user U , a veriﬁer V ,

a certiﬁer C and a trustee (tracer) T . The protocol

suites include: a certiﬁcation protocol, where U in-

teracts with C to obtain a certiﬁed pseudonym i.e. the

pseudonym is blindly signed. An identiﬁcation proto-

col, where V interacts with U to authenticate U ’s cre-

dential and provide services. A trace protocol, where

T participates and is invoked to trace the real identity

associated with U ’s pseudonym.

2.1.1 System Setting

The user, U , chooses a modulus N

, such that a N

(i)

, is a product of two distinct large primes each

congruent to 3 (mod 4), (p

(i)

, p

(i)

are Blum integers

(Blum et al., 1986)), an element g ∈ Z

whose or-

der is φ(N

) = (p

(i)

− 1)(p

(i)

− 1) and where i is the

number of pseudonyms. We also require the modulus

for pseudonyms to be different, otherwise anonymity

can be compromised trivially by just maintaining a

list of modulus. The user chooses a master secret key

∈ Z

and publishes the master public key PK

= g

mod N

(which represents the user’s true and

public identity). The certiﬁer C publishes its pub-

lic key PK

= g

mod N

while keeping the cor-

responding secret key private. The certiﬁer also pub-

Whereas, group signature schemes as employed by

(Brickell et al., 2004) provide anonymity to the source.

lishes the public key of the Trustee T , (for tracing and

revocation) which would be of the form PK

= g

mod N

, where g

∈ Z

. Every user registers with

a certiﬁcation authority to obtain a certiﬁcate of the

form

CERT

hPK

2.1.2 Protocol Certify

The certiﬁcation involves two steps: certiﬁca-

tion of the master public key and certiﬁcation of

pseudonyms. In an TPM based setting the mas-

ter public key is certiﬁed by the manufacturer,

and the following describes the certiﬁcation of the

pseudonyms.

The user, U , generates pseudonyms of the form

(PK

, ..., PK

) using the identity generation pro-

cess described in Section 3.2. The user then identiﬁes

himself/herself (using the master public key) to the

certiﬁer and engages in a certify protocol to obtain a

certiﬁcate on a pseudonym PK

. The value of PK

is never revealed to the certiﬁer. We shall express this

phase as

(PK

CERT

hPK

i) ← Certify(U , C ,

CERT

hPK

i.e. “ U engages in the certify protocol with C

using

CERT

hPK

i to obtain a certiﬁcate on PK

CERT

hPK

i”.

2.1.3 Protocol Identify

A user U who wishes to avail services offered by a

veriﬁer V , engages in a identiﬁcation protocol to con-

vince that he/she possess the necessary credentials.

We shall express this phase as

PROOF

i ← Identi fy(U , V , PK

CERT

hPK

i, PK

)

i.e. “ U engages in an identiﬁcation protocol

with a veriﬁer V using the psuedonymn PK

and

CERT

hPK

i and which contains the encryption of

the identity under the public key PK

”.

2.1.4 Protocol Trace

A veriﬁer who needs to trace the identity of the user

contacts the trustee T by providing with the transcript

from an identiﬁcation protocol h

PROOF

i. We shall

express this phase as

(PK

) ← Trace(V , T , PK

CERT

hPK

i, h

PROOF

i.e. “ V engages in the tracing protocol with T

using the values PK

CERT

hPK

i and proof of

identity use h

PROOF

i to obtain the master identity

”.

SECRYPT 2009 - International Conference on Security and Cryptography

192

2.2 Assumptions

Our system relies on the following assumptions:

• Assumption 1 (Factoring). A probabilistic

polynomial-time algorithm G exists which on in-

put 1

|N|

outputs N, where N is a composite of two

prime number, p

and q

, such that for any prob-

abilistic polynomial time algorithm A , the prob-

ability that A can factor N is negligible i.e. the

probability of success is smaller than

poly(|N|)

• Assumption 2 (Square Root). A probabilistic

polynomial-time algorithm A which on input N

and a, where N is a composite of two prime

numbers, p

and q

and a ∈ QR

is a quadratic

residue, the probability that A can output b, such

that b

≡ a mod N is negligible, i.e. the probabil-

ity of success is smaller than

poly(|N|)

• Assumption 3 (Square Decisional Difﬁe-

Hellmann). The square decisional Difﬁe-

Hellman (SDDH) problem is deﬁned as follows.

Distinguish between distributions of the form

(g, g

, g

) from (g, g

, g

), where r is random and

uniformly chosen integer from {1, . . . , N −1}. We

assume that there is no probabilistic polynomial-

time algorithm G that can solve a random

instance of the SDDH problem with probability

poly(|N|)

We also use the Chaum and Pederson construction

(Chaum and Pedersen, 1992) as a sub-protocol for

a interactive proof of knowledge for the discrete log

problem (DL-EQ). Their protocol (Chaum and Peder-

sen, 1992) was designed for the case when group of

the exponents has prime order, whereas in our proto-

col the group of the exponents have composite order.

But as suggested by (Camenisch and Michels, 1999),

the proof of knowledge of discrete logarithm from

different groups (DL-EQ) holds even when working

over a cyclic sub-group of Z

∗

. We combine the DL-

EQ with El-Gamal encryption over a composite mod-

ulus (Franklin and Haber, 1993) to encrypt the master

identity of the user under the public key of the trustee,

veriﬁable by the certiﬁcation authority.

3 PROTOCOLS

We shall now present our scheme that consists of four

phases: identity generation, certiﬁcation, identiﬁca-

tion and trace.

3.1 System Setting

The system involves four entities. A user U who

holds a long term certiﬁed public key PK

(we shall

call it the master public key), and wishes to hide his

identity from a veriﬁer V . The public keys are certi-

ﬁed by a certiﬁcation authority C and a trustee T re-

sponsible for tracing the pseudonym used by the user.

The U master public-secret key-pair is generated

as in Section 2.1.1. U then obtains a certiﬁcate on the

master public key PK

from a certiﬁcation authority

C , which represents the U ’s true identity.

The public key of the certiﬁcation authority is

= g

and the trustee is PK

= g

, where

and SK

are the corresponding secret keys for

the certiﬁcation authority and the trustee respectively.

3.2 Identity Generation

U generates new identities using the following key

generation process, which takes the inputs, N

, g, a

counter value i (indicating the total number of new

identities being generated), identity level l (number

of identities generated previously) and the master

secret key SK

I-Generation

(g,i,l,SK

)

For

j = l,.. .,i

= g

mod N

EndFor

Return

(PK

,...,PK

)

During the ﬁrst run the value of identity level l

would be 1 and counter value i is the number of new

identities U requires. Further calls to the key genera-

tion, the identity level would be the counter value that

was used during the previous run (l

′

= i). An implicit

requirement is that, U should keep track of the values

i and l as long as the master public key remains valid.

We could (and do) treat the identities generated as

public keys, that are of the form (PK

,...,PK

) =

, . . . , g

)

3.3 Certiﬁcation

The newly generated public keys (PK

, ..., PK

)

are required to be certiﬁed by C before they can be

used. It is possible to use a normal certiﬁcation pro-

cedure as currently employed in public key crypto-

systems, where the public key PK

is signed by U

using the master secret key SK

and sent to C for

certiﬁcation. C veriﬁes the signature using the master

public key PK

, on a successful veriﬁcation C dig-

itally signs using his private key SK

and sends the

certiﬁcate to U . This method is quite straightforward,

CERTIFIED PSEUDONYMS COLLIGATED WITH MASTER SECRET KEY

193

Certiﬁer User

r ∈

x = PK

−−−−−−−−−−−→

β, γ, s ∈

(X, Y ) = EncElg

P K

(P K

, s)

α = x · g

β−SK

· P K

−γ

δ = IHI(PK

k(X, Y )kα)

e = δ − γ

←−−−−−−−−−−−

y = r − eSK

−−−−−−−−−−−→

= g

y+SK

P K

ρ = y + β

Figure 1: Modiﬁed Blind Certiﬁcation Protocol of

(Pointcheval, 2000) - The signature on PK

is (α, δ, ρ) and

a receiver can verify using the relation α

= g

but certain applications (e.g. applications based on

TPM) require the new identities to be protected even

from the certiﬁer. So, we propose a modiﬁcation to

the certiﬁcation scheme based on a blind signature

scheme using a composite modulus by Pointcheval

(Pointcheval, 2000). The blind signature scheme now

includes the master public key of the user which is

used by the certiﬁer to form the commitment and is

later veriﬁed by the user.

The certiﬁcation process is represented by:

(PK

CERT

hPK

← Certify(U , C ,

CERT

hPK

, (X, Y)i)

where,

CERT

hPK

i is the valid blind signature

(PK

, α, δ, ρ) by C on PK

and (X, Y), accom-

plished by the three-pass protocol depicted in Figure

1. The security proof of the modiﬁed protocol triv-

ially follows the proof presented in Pointcheval’s pa-

per (Pointcheval, 2000).

3.4 Identiﬁcation

The Identiﬁcation protocol (Figure 2) is based

on Pointcheval optimised identiﬁcation scheme

(Pointcheval, 2000) of Girault’s identiﬁcation scheme

(Girault, 1991), but it now also includes the DL-EQ

log

X = log

Y. In this protocol a user U uses his

certiﬁed pseudonym to identify himself/herself with a

veriﬁer V and at the end of the protocol the veriﬁer

obtains an undeniable proof of U participation in the

protocol. The identiﬁcation process is represented by

PROOF

i ← Identi fy(U , V , PK

CERT

hPK

i, PK

)

3.5 Tracing

The trace protocol (Figure 3) is invoked by a veri-

ﬁer V after U has misused a pseudonym and runs

User Veriﬁer

k, w ∈

= g

; a

= (PK

· PK

)

h = IHI(g

)

h,(a

),(X,Y )

−−−−−−−−−−−→

∈

= IHI(X, Y, a

, a

)

←−−−−−−−−−−−

= 2

− c

· SK

= w − s · c

,CERT

hP K

−−−−−−−−−−−→

Verify CERT

hP K

and obtain (α, δ)

′

= IHI(PK

k(X, Y )kα)

= g

; a

= PK

= IHI(g

P K

)

Figure 2: Identiﬁcation Protocol.

between the veriﬁer V and the trustee T . To trigger

the protocol V has to provide proof of protocol par-

ticipation by U . We shall express this phase as

(PK

) ← Trace(V , T , PK

CERT

hPK

i, h

PROOF

Veriﬁer Trustee

σ = SIGN

hc, z, hi

σ,α,δ,ρ,PK

,PK

−−−−−−−−−−−→

CERT

hP K

VERIFY

hσi

= IHI(g

)

= g

Verify CERT

hP K

Obtain (X, Y ) from hPROOF

P K

= DecElg

(X, Y )

Figure 3: Tracing Protocol.

4 SECURITY

4.1 Adversary Goals

We assume an active adversary A , who is capable of

eavesdropping and injecting messages in the commu-

nication medium. We also assume that an adversary

may be also be a legitimate (but dishonest) participant

in a protocol, i.e. either the certiﬁer or the veriﬁer or

both may be dishonest.

As in (Damgard, 1988; Lysyanskaya et al., 1999),

we want our pseudonym system to be secure against

the following attacks, i.e. an adversary’s goal is to

mount any of following attacks:

• Pseudonym forgery: An adversary tries to forge a

pseudonym for some user, possibly in association

with other participants, including the certiﬁer.

That is the attack can be either:

SECRYPT 2009 - International Conference on Security and Cryptography

194

1. An adversary in possession of a valid proof

tuple (PK

CERT

hPK

i) issued to an-

other user or for a tuple of the form

(PK

CERT

hPK

i) is successfully able to ex-

ecute an identiﬁcation protocol with a veriﬁer

identifying as U

2. An adversary successfully identifying him-

self/herself by executing an identiﬁca-

tion protocol with a tuple of the form

(PK

CERT

hPK

i).

• Identity compromise: An adversary in association

with other participants tries to obtain information

regarding the user’s master public-secret key-pair,

i.e. and adversary with the knowledge of all user

generated public keys (PK

, ..., PK

), it should

be computationally infeasible for an adversary to

either obtain the master public key PK

• Pseudonym linking and colligation: An adver-

sary tries to obtain information that links a pair of

pseudonyms to the same user or to a user’s master

public key. The goal is that even with the knowl-

edge of all user generated public keys (PK

, ...,

), it should be computationally infeasible for

an adversary to prove that any of the PK’s in the

set (PK

, ..., PK

), are related.

We now present our claims on the security of our

proposal.

Claim 4.1. If the Square Decisional Difﬁe-Hellman

(SDDH) problem is hard, then public keys generated

from the master public key are indistinguishable.

The public keys generated are of the form g

where, i ∈ 0, . . . , l. For an adversary A to distinguish

between a newly generated public key from a master

or another newly generated public key, A should solve

the square Difﬁe-Hellman decision problem, i.e., ef-

ﬁciently distinguish between two distributions of the

form (g, g

, g

) and (g, g

, g

), which is assumed

to be hard.

Claim 4.2. It is computationally infeasible to obtain

the master public key of a user by an adversary even

with the knowledge of all newly generated public key.

Proof (Sketch) : For an adversary to obtain the

master public key (PK

) from a pseudonym (PK

)

presented, the adversary needs to solve, ﬁrst the dis-

crete log problem to obtain SK

and then solve the

square root problem to obtain the value i. This vio-

lates our security assumptions. It is also a well known

fact that, assuming the factoring of Blum Integers is

intractable, the function f

= SK

mod N

is a trap-

door (one-way) permutation (Goldreich, 1999).

Claim 4.3. It is computationally infeasible to obtain

the master public key of a user by a veriﬁer or a cer-

tiﬁer even if the certiﬁer and veriﬁer collude.

Proof (Sketch) : Both C and V have knowl-

edge of the public parameters. In addition, C has

the knowledge of the user’s master public key PK

whereas, a veriﬁer has the knowledge of the cipher-

text obtain from the El-Gamal encryption (X, Y), the

pseudonym of the user PK

, the signature value on

both the pseudonym and the cipher-text (α, ρ, δ, PK

For a dishonest certiﬁer

C and a dishonest veri-

ﬁer

V to obtain the master public key PK

of a user,

either independently or in collusion, any one of the

following cases need to be satisﬁed.

Case 1. The blind signature protocol during the certi-

ﬁcation process leaks information about the iden-

tity of the user.

Case 2. A veriﬁer is able to deduce the master iden-

tity from the pseudonym presented during the

identiﬁcation protocol.

Case 3. The certiﬁer and a veriﬁer with their com-

bined knowledge, are able to identify the colli-

gation that exists between a pseudonym and the

master secret key.

The security of Case 1 trivially follows the proof

of security of blind signature protocol by Pointcheval

in (Pointcheval, 2000). For Case 2, a veriﬁer can

obtain the master public key if the proof of DL-EQ

log

X = log

Y leaks any information regarding the

master public key. A way of proving the security

of the scheme is via the oracle replay technique for-

malised by Pointcheval and Stem (Pointcheval and

Stern, 1996). In particular, the Schnorr signature with

composite modulus has been proved secure in the ran-

dom oracle model (Bellare and Rogaway, 1993) by

Poupard and Stem (Poupard and Stern, 1998). They

showed that if an adversary is able to forge a signa-

ture under an adaptively chosen message attack, then

he/she is able to compute discrete logarithms in G.

The security of Case 3 is based on the inability

V and

C to obtain any information that links the

user when he/she interacts in the identiﬁcation and

the certiﬁcation protocols. There are only two pos-

sibilities which can identify a user that he/she partici-

pated in both the protocols. (a) The pseudonym leaks

value about the true identity and (b) the El-Gamal

cipher-text (X, Y) which is used in both the certiﬁ-

cation and identiﬁcation protocols can be linked to

. If

C and

V in collusion are able to identify

that the same (X,Y) which was presented in the iden-

tiﬁcation protocol was used in the certiﬁcation pro-

tocol, then they can positively establish a connection

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195

between the pseudonym presented during the identi-

ﬁcation protocol with the master identity used in the

certiﬁcation protocol.

From Theorem 4.2, we can conclude that it is

computationally infeasible for

V or

C to obtain the

master identity from a given pseudonym. As for pos-

sibility two, the hash value δ computed with cipher-

text (X, Y), the pseudonym PK

and the value α as

inputs, is blindly signed and never revealed to the cer-

tiﬁer.

Claim 4.4. If the El-Gamal encryption is secure, then

only the corresponding trustee can obtain information

about the user from the encrypted cipher-text.

The proof of this theorem directly follows the

proof in (Franklin and Haber, 1993). The authors

showed that the security of the composite El-Gamal

reduces to computing quadratic residue over a com-

posite modulus that is a product of two primes. And

since the master public key is encrypted using the pu-

bic key of the trustee, only the trustee can successfully

decrypt the cipher-text.

Remark 1. The protocol also provide guarantees of

honest participation of a user. The cipher-text con-

taining the master public key is signed (blindly) by

the certiﬁer. A veriﬁer computes the hash value of

the cipher-text (X, Y), the pseudonym and α again to

verify against the signed hash value in the blind cer-

tiﬁcate, thus conﬁrming that the user has performed

an El-Gamal encryption over the same values, which

was used during the certiﬁcation process.

5 APPLICATION

In this section, we present a brief summary about how

the protocols can be applied in an Trusted Platform

Module (TPM) based setting. We are considering a

TPM setting because of tamper resistant protection

offered to the master secret key, but the protocols can

be applied to other structures like directory based ser-

vices (e.g. active directory, LDAP).

The Trusted Platform Module (TPM) is the basis

of trusted computing, promoted by the Trusted Com-

puting Group. A TPM consists of an unique endorse-

ment key (EK) pair, that is built into the hardware

module during manufacturing. The public part of EK

is certiﬁed by the manufacturer and the secret part is

sealed inside the TPM and is never revealed to the

outside. A primary function of the TPM is attestation

i.e. the TPM provides guarantees to a remote service

that the platform is not tampered with and therefore

secure. A TPM can also provide other security ser-

vices like secure boot and sealed storage. We refer

the reader to (TCG, 2001; TCG, 2007) for more in-

formation about TPMs.

The deployment of TPM raises some valid pri-

vacy concerns. Authentication based on directly us-

ing the TPM’s EK, will compromise anonymity of

the module as all transactions performed by the same

TPM can be linked. Further more, it will compro-

mise the anonymity of the user associated with the

module. Privacy protection in TPM currently involves

two mechanism: Privacy CA based attestation (TPM

v1.1) (TCG, 2001) and Direct Anonymous Attesta-

tion (TPM v1.2)(Brickell et al., 2004; TCG, 2007).

We do not propose a replacement to current TPM au-

thentication standards. We merely wish to highlight

the use of TPM as an application for our proposal, and

as mentioned before our protocols can be integrated

into other systems like directory based services.

TPM BASED SETTING: The endorsement key

(EK) in a TPM will be of the form (PK

,SK

). The

EK is certiﬁed by the manufacturer and embedded

into the TPM. A user who wishes to obtain services

from an application software on a machine generates

a pseudonym of the form (PK

,SK

) as described in

Section 3.2. The application software and the TPM

then perform an identiﬁcation protocol as in Section

3.4. At the end of the identiﬁcation protocol the ap-

plication software is provided a guarantee on the iden-

tity of the user and the associated TPM, but the system

still protects the identity of both the TPM and the user

associated with it.

6 CONCLUSIONS

The aim of a pseudonym is to hide the identity of

legitimate users by providing conﬁdentiality to the

identity, thereby providing anonymity. A pseudonyms

also need to be traced in case of misuse and therefore

needs to provide only restricted anonymity. In this pa-

per, we have presented an pseudonym system by us-

ing the property of preserving a high value secret key.

The system not only provides restricted anonymity

but also supports colligation between a trusted high

value secret key and generated pseudonyms.

Compared to other pseudonym schemes, our

scheme has an efﬁcient identiﬁcation protocol, thus

computation can be carried out on a devices that are

constrained of processing power. Computations may

be performed on the module itself, whereas the DAA

scheme (Brickell et al., 2004; TCG, 2007) requires

computation to be distributed among the TPM and the

host computer. Our scheme is also ideally suited for

storage constraint devices. Because, there are no new

secret key to be generated for each pseudonyms, only

SECRYPT 2009 - International Conference on Security and Cryptography

196

counter values of the pseudonym, thus there is no ap-

preciable increase in storage requirement even when

the number of pseudonyms required are high.

Finally, in terms of anonymity, our proposal pro-

vides a excellent beneﬁt to users, as not only appli-

cations on a single computer can be associated with

a different pseudonym but also every web based ap-

plication used by a user can be associated with a

pseudonym.

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