A COMPATIBLE IMPLEMENTATION BETWEEN IDENTITY-BASED

AND CERTIFICATELESS ENCRYPTION SCHEMES

Antigoni Polychroniadou

, Konstantinos Chalkias

and George Stepanides

Royal Holloway, University of London, Egham, Surrey TW20 0EX, U.K.

University of Macedonia, Egnatia 156, 54006, Thessaloniki, Greece

Keywords:

Compatibility, Identity-based Encryption, Certiﬁcateless Encryption, Protocol Classiﬁcation, Efﬁciency

Comparison, Compatible Implementation.

Abstract:

In this paper we put into practice the concept of compatibility and we present a classiﬁcation of two IBE-related

schemes, the Identity-Based Encryption (IBE) and the Certiﬁcate-Less Encryption (CLE). An innovative im-

plementation of a compatible IBE and CLE system was developed in order to support different encryptions

on-the-ﬂy based on the user’s needs at a speciﬁc moment. Motivated from the fact that there are numerous

theoretically efﬁcient IBE-related schemes in the literature overshadowing the beneﬁts of traditional public

key encryption (PKI) schemes, they did not, in any important way implemented into practice, as the widely-

used PKI. The question is why this is the case since IBE solves a number of problems associated with PKI.

Therefore, the controversial issue concerning the widespread use of IBE schemes into practice and the issue

of compatibility between IBE and CLE are discussed in this paper. These real problems hinder the wide use of

IBE. However, it cannot be denied that IBE, which can be extended to support a plethora of encryption models,

gains widespread adoption day by day as it solves problems within conventional public key schemes and it

results in a simpliﬁed key management, making it much more lightweight to deploy. Based on the fact that a

number of different encryption schemes stemmed from IBE, an implementation of an IBE-related compatible

system is important. Our approach categorizes known concrete constructions from two IBE-related types into

classes and analyzes similarities concerning public settings, used keys, protocol structures and provided model

of provable security.

1 INTRODUCTION

Traditional RSA (or similar) encryption is still con-

sidered the ﬁrst option for e-commerce transactions

and key exchange. This is based on the fact that cur-

rent security infrastructure in the web is mainly based

on RSA digital certiﬁcates. On the other hand, ellip-

tic curve cryptography (ECC) is considered to offer

the same level of security with RSA but with smaller

key-sizes. Unfortunately, although ECC has been pro-

posed years ago as an RSA alternative,currently, ECC

is mostly used in constrained devices and thus ac-

tual web transactions are mostly based on RSA en-

cryption and signatures. Moreover, there is no doubt

that for a new product or an idea to be applied in the

real world, compatibility with already established ap-

proaches plays the most important role, as history has

shown in the case of passing from DES to 3DES (be-

fore moving to AES) for backward compatibility rea-

sons. Therefore, we issue the compatibility between

schemes stemmed from ECC such as the ﬂexible as

well as versatile IBE schemes.

To circumvent some of the problems of conven-

tional asymmetric encryption, including the complex-

ity and the maintenance cost arised from the use

of digital certiﬁcates, the concept of IBE was pro-

posed by Shamir (Shamir, 1985) in 1984. How-

ever, it took almost twenty years for an IBE scheme

to be proposed by Boneh and Franklin (Boneh and

Franklin, 2003) in 2001. Since then, a couple of

breakthroughs have been achieved leading to new

asymmetric encryption schemes. IBE can be ex-

tended to support a plethora of encryption models

and applications including Hirerachical IBE (HIBE),

Certiﬁcateless Encryption (CLE) (Al-riyami and Pa-

terson, 2003), Certiﬁcate-Based Encryption (CBE),

Fuzzy IBE (FIBE), Timed-Release Encryption (TRE)

to name just a few. Hence, there are numerous the-

oretically efﬁcient IBE-related models in the litera-

ture which offer different advantages and properties.

On the other hand, the commercial use of IBE is not

’growing’ as fast as someone would expect and we

225

Polychroniadou A., Chalkias K. and Stephanides G..

A COMPATIBLE IMPLEMENTATION BETWEEN IDENTITY-BASED AND CERTIFICATELESS ENCRYPTION SCHEMES.

DOI: 10.5220/0003975302250230

In Proceedings of the 8th International Conference on Web Information Systems and Technologies (WEBIST-2012), pages 225-230

ISBN: 978-989-8565-08-2

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

suppose that both the compatibility issue and the lack

of a complete ECC parameter standardization (includ-

ing pairing-friendly curves) are the main reasons hin-

dering the wide use of IBE. The latter is due to the

fact that the most efﬁcient and practical IBE schemes

are currently based on bilinear pairings over elliptic

curve groups for which pairing-friendly elliptic curve

groups have been proposed. The ﬁrst companies have

already started to exploit IBE commercially. Some

of them are Voltage, Trend Micro, Mitsubishi and

Noretech Microsoft etc. All in all, due to the chal-

lenges that appear in asymmetric encryption, the issue

of moving from one model to another requires much

more attention in order for new schemes, with various

interesting properties, to be widely adopted.

From the aforementioned encryption models,

CLE owns some interesting properties making it a

strong candidate to be the ‘connector’ between tradi-

tional public key encryption and IBE. In fact, a CLE

scheme could be characterized as a mixed scheme

which shares properties from both encryption mod-

els, conventional and IBE. As far as CLE and IBE are

concerned, after a thorough research we found that

there are currently at least 35 different concrete IBE

schemes and 30 concrete CLE schemes in the liter-

ature. There are also generic CLE schemes that can

be derived from IBE. Moreover, some of the existing

protocols are independent (Sun et al., 2007), (Cocks,

2001), but some of them share certain features which

allow us to put the concept of compatibility into prac-

tice. So in the following sections, we propose speciﬁc

protocols exploring IBE and CLE concepts.

We focus on practicality issues rather than techni-

cal and security details. We identiﬁed eight, competi-

tive or not, classes of IBE and eight classes of CLE. A

plethora of CLE frameworks are found to be compat-

ible with IBE frameworks. As a result, the concept of

compatibility is easier to be deployed. On the other

hand, there are classes from one model (e.g. (Baek

et al., 2005) in CLE) for which a related compatible

class does not seem to exist. Moreover, we recom-

mend the best combination of IBE and CLE for the

concept of compatibility and we offer an implemen-

tation. However, we emphasize on the fact that a key

relation and a similar construction between IBE and

CLE schemes does not automatically implies a fully

secure compatible system between them and in some

cases further security proofs are required in order to

implement a parallel encryption system with both IBE

and CLE support. Under some circumstances, the co-

existence of IBE and CLE gives an adversary more

capabilities than in a single-mode CLE.

1.1 IBE and CLE Concepts

The concept of an IBE scheme simpliﬁes the key

management, because the receiver’s unique identity,

such as an email address or a phone number, is used

to easily construct the receiver’s public key without

contacting the KGC or the receiver. When a sender

sends an encrypted message he/she merely derives re-

ceiver’s public key PK1 directly from receiver’s iden-

tity ID (usually PK1 = H(ID)), where H is a Map-

to-Point hash function. Thus, the automatic genera-

tion of public keys by everyone is considered to be

the main advantage of IBE. According to this, there

is no need for public key queries, explicit certiﬁcates

and transition of public keys. However, the receiver’s

private key d

is not generated by the receiver as in

conventional cryptography, but it is securely provided

by the KGC. The KGC owns a master secret key and

using an algorithm that takes as input a user’s ID it

outputs a private keys d

for each user. As for IBE

implementations, current IBE approaches either rely

on bilinear pairings over elliptic curve groups or on

the quadratic residue assumption and recently on Lat-

tices’ problems.

Regarding the disadvantages of IBE, they are

arisen by the fact that KGCs can generate the private

keys for each of their users. As a result, a KGC is ca-

pable of decrypting any messages. Accordingly, the

private key escrow becomes an inherent problem in

IBE. Another important problem is that IBE private

keys must be sent to the users over secure channels,

which is solved in practice using RSA-based SSL.

In order to overcome the drawback of IBE, the

essence of CLE was proposed by Al-Riyami and Pa-

terson (Al-riyami and Paterson, 2003) in 2003. CLE

retains the desirable properties of IBE without the in-

herent key escrow problem. In such a scheme the

receiver independently generates his public key PK2

and secret key x as in the case of conventional Public

Key Infrastracrure (PKI). Similarly to IBE, the KGC

computes the partial private key d

using its master

secret key and the receiver’s ID. Contrary to IBE’s

private key, receiver’s private key is a combination of

his/her secret key x and d

. As a result, the key es-

crow problem is solved since messages can only be

decrypted by the receiver (both private key parts are

required). Under some circumstances, the full private

key is just the pair (x, d

) while, in some other cases,

a more complex combination is used. When it comes

to the sender, he/she has to generate PK1 from re-

ceiver’s ID and ask for receiver’s public key PK2 in

order to encrypt a message. Bearing in mind the com-

munication between the KGC and the user during the

key generation, some classes of CLE extend IBE

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226

schemes. Current CLE schemes that evolved from

IBE depend on Bilinear Pairings. However some oth-

ers do not derive from an existing IBE scheme, such

as (Baek et al., 2005) and (Lai et al., 2009).

2 COMPATIBILITY ISSUES

This article focuses on CLE schemes derived from an

IBE variant, because our aim is to combine both tech-

nologies. What appears to be interesting when con-

sidering the above schemes is how we can connect or

modify the keys in order to make compatible imple-

mentations using a single KGC. In both schemes the

KGC provides the receiver with the d

which is used

as the receiver’s private key in IBE and as a part of

the receiver’s private key in CLE. Secondly, the pub-

lic key PK1 = H(ID) is computed in the same way in

both schemes. Hence, the partial private and the pub-

lic key of IBE schemes are generated in the same way

as in CLE. Generally speaking, all pairing-based IBE-

related schemes (CLE, TRE, HIBE) indirectly include

the ‘pure’ IBE scheme. This fact can be used in order

to achieve compatibility.

In our approach, one scenario we need to solve

is the case when a user, who uses CLE, receives a

message from a sender who used IBE for encryption.

Is it possible for a CLE-capable receiver to decrypt a

message derived from an IBE scheme? This can be

achieved by decrypting the message with the compat-

ible IBE part of the CLE, using the partial private key.

Furthermore, in case where CLE and IBE schemes

are compatible, the user is provided with the opportu-

nity to use different IBE-related schemes in parallel.

More speciﬁcally, the user can choose which encryp-

tion to use depending on the features that he expects

from a scheme (need more privacy against KGC or

not?). Emphasizing on the fact that the concept of

compatibility can be implemented in a company, it

can be ‘somehow’ compared to a HIBE scheme. More

speciﬁcally, using only one KGC with a compatible

system we offer two categories per user. The ﬁrst

category enables the KGC to check/decrypt a user’s

message decrypted using IBE encryption. The second

category achieves user’s privacy due to the fact that

the message can be encrypted using CLE encryption.

Therefore, in a company if a user needs more privacy

he/she can encrypt a message using CLE. On the other

hand, in some circumstances where the administra-

tion (KGC) needs to decrypt messages from speciﬁc

users, it allows them to encrypt using IBE encryption.

Contrary to a HIBE scheme, the proposed compatible

systems do not offer hierarchy and the user can select

which of the above aforementioned categories needs

to implement any time. Contrary to our approach, in

a Hierarchical HIBE scheme the top level user (e.g.

KGC) can decrypt all the messages from all the users

due to the hierarchy. Moreover, such a scheme de-

mands more complex keys, contrary to our compati-

ble systems. We are currently dealing with the con-

cept of a scalable compatible system without signiﬁ-

cant additional cost. In order to achieve compatibility

between IBE and CLE, we studied the key generation

algorithms of the majority of IBE and CLE concrete

schemes. Needless to say that we had to pay attention

to the mathematical problems on which the security

of every scheme depends on. Bearing in mind that if

two schemes have closely similar keys, but the prob-

lems that they depend on are different, the transfer of

a key from one scheme to another may lead to the dis-

closure of the key. Furthermore, we considered the

communication between the KGC and the user dur-

ing the key generation phase. The only compatible

schemes that we underline are based on the concept

that the user’s public key is independent of the par-

tial private key generation (e.g. BF and AP classes

etc.). The CLE schemes that are not compatible with

any IBE class are those in which the user’s public key

can only be generated after receiving the partial pri-

vate key or after a protocol interaction with the KGC

(e.g. BSS (Baek et al., 2005) class and (Lai and Kou,

2007)). Regarding the security models, as CLE im-

plies IBE, probably the security proofs are included

in the security model of CLE. Therefore, almost all

security models for CLE protect against a disclosure

of the IBE-part of the CLE private key. However, in

some cases further security proofs are required to im-

plement a parallel encryption system for both IBE and

CLE support

as the co-existence of IBE and CLE

gives an adversary more capabilities than in a single-

mode CLE. For example, the partial private key can-

not be divulged if the CLE attacker has replaced the

public key.

2.1 Classiﬁcation

Taking into consideration the similarities, as well

as the differences of numerous IBE and CLE pro-

posals, we tried to organize them into classes.

As a result, eight IBE classes have been mod-

eled which are the BF(Boneh and Franklin, 2003),

the COCKS(Cocks, 2001), the SK(Kasahara, 2003),

the KW(Katz and Wang, 2003), the Waters(Waters,

2005), the Gentry(Gentry, 2006), the BB1(Boneh

and Boyen, 2004)(a) and the BB2(Boneh and Boyen,

2004)(b) classes. Note that the classes can be

In fact, changes in the security proofs of CLE are re-

quired as they typically extend IBE, but not vice versa.

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generalized into less classes since Gentry, SK and

BB2 classes belong to the Exponent-inversion fam-

ily. Moreover, Waters and BB1 classes derive from

the commutative-blinding framework and KW class

stems from a full-domain-hash IBE. We pointed out

which of them are useful or not. The representative

scheme of each class is the ﬁrst proposed scheme in

the literature. Therefore, the names of the classes de-

rived from the corresponding authors’ names of the

initial paper of each approach which does not auto-

matically mean that these schemes are or are not the

best performed paradigms in their class. This clas-

siﬁcation depends on the structure of the keys. Fur-

thermore, we had to pay attention to the mathemat-

ical problems (security assumptions) on which the

security of every scheme depends on. In addition,

in an attempt to standardize the closely related CLE

with IBE proposals we classify the CLE schemes

into eight classes which are the AP03(Al-riyami and

Paterson, 2003), the AP05(Al-riyami and Paterson,

2005), the LQ(Libert and jacques Quisquater, 2006),

the CCLC(Cheng et al., 2007)(a), the BSS(Baek et al.,

2005), the PCHL(Park et al., 2007), the DLP(Dent

et al., 2008) and the LDLK(Lai et al., 2009) classes.

In Tables 1 and 2, we can see the representative

classes of schemes belonged to BF or AP05 classes

where Msk is the master secret key of KGC, Pub is

the user’s public key, Priv is the user’s private key and

Gener is a speciﬁed generator. Our implementation

is a compact compatible system based on these two

classes. We will see later why we chose these two

compatible classes.

2.2 Compatibility

Considering the structure of the keys derived from

CLE classes we set the IBE compatible classes. Table

3 shows the CLE classes corresponding to their IBE

compatible class. By taking into consideration the

competitive and compatible useful classes, the com-

patibility can be put into practice. If the Random Or-

acle Model and of course the Weak-Types of Adver-

sarial Security Models are considered practically se-

cure, according to our performance analysis, the SK

(Kasahara, 2003) class has the best efﬁciency perfor-

mance, followed by BB2 and Gentry classes which

are proven secure in the standard model. In CLE,

among the useful classes, the best performed class

is the LQ(Libert and jacques Quisquater, 2006) class,

followed by AP05 and CCLC classes. The LQ(Libert

and jacques Quisquater, 2006) class is compatible

with SK-IBE class. Depending on their keys and on

the security assumptions they lead to a mixed CLE-

IBE system. Both classes support the simplest im-

Table 1: CLE Classes.

AP05(Al-riyami and Paterson, 2005)

KEYS

Msk: s ∈

←−Z

, P

pub

= sP ∈ G

Secret: x ∈ Z

Pub: P

= xP ∈ G

,ID ∈ {0, 1}

∗

Partial: d

= sQ

∈ G

where

= H

(ID) ∈ G

Priv: s

= (d

, x) ∈ G

× Z

Gener: P ∈ G

Table 2: IBE Classes.

BF(Boneh and Franklin, 2003)

KEYS

Msk: s ∈

←−Z

, P

pub

= sP ∈ G

Pub: ID ∈ {0, 1}

∗

Priv: d

= sQ

∈ G

= H

(ID) ∈ G

Gener: P ∈ G

The used hash function is modeled as: H

: {0, 1}

∗

→ G

∗

Table 3: Compatible Classes.

CLE Classes compatible with IBE Classes

AP03 and AP05 −→ BF

LQ −→ SK

DLP −→ Waters

PCHL −→ Gentry

CCLC −→ BB1

BSS -

LDLK -

- BB2

- COCKS

- KW

plementations. A drawback of these classes is that

the security depends on a strongest q-BDHI assump-

tion compared to other classes. We highlight though

that our measurements took under consideration the

case of a single KGC, otherwise some other pairing-

based classes could be beneﬁted from the bilinearity

property when multiple KGCs are to be used. We are

currently investigate the case of multiple KGCs and

its effect on the compatibility and on the performance

of IBE and CLE schemes. In a multiple KGCs ap-

proach, we need to split the master secret key into ad-

ditive or polynomial shares to avoid single points of

failure. On the other hand, a less time efﬁcient com-

mutative blinding BB1 scheme is extremely ﬂexible

as well as versatile to implement extensions of IBE

followed by BF schemes. Thus, another mixed CLE-

IBE system could be derived from BB1 and CCLC

classes sacriﬁcing some of its efﬁciency. The combi-

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nation of BF and AP classes are quiet efﬁcient but a

practical drawback in terms of security is their high

dependency on random hash functions. Therefore,

based on the fact that the majority of companies that

use IBE, such as Voltage, implement the BF scheme,

we constructed compatible systems companying BF

and AP05 compatible classes. Using the IBECrypto

library(Anastasios Kihidis, 2010) which is an open

source implementation of BF scheme we can success-

fully implement a compatible scheme in which users

as well as administrators choose whether they want to

use IBE or CLE on-the-ﬂy.

3 CONCLUSIONS

This article raises the importance of compatibility

between IBE-related schemes in order to exploit all

aspects from each IBE-related scheme (CLE, Time-

released, hierarchical IBE, etc) since IBE can offer

a lot of extensions. More speciﬁcally, we consider

compatibility as the ability to use different asymmet-

ric encryption constructions in parallel. If someone

uses an IBE scheme and someone else uses another

scheme (e.g. CLE) derived from this speciﬁc IBE

scheme, under certain circumstances, they can com-

municate to each other. Our focus is on CLE due

to the fact that it is theoretically the most general

scheme, in which the structure of its keys shares prop-

erties from both IBE and conventional PKI. For this

reason we conducted an extended and analytical sur-

vey of the majority, if not all, existing concrete IBE

as well as CLE schemes. We constructed eight, com-

patible or not, classes of IBE and CLE in order to

achievecompatibility. Then we identiﬁed the compat-

ible classes, from which we can beneﬁt from utilizing

IBE and CLE in a whole compatible system with a

single KGC. The categorization in classes allowed us

to specify a compatible system for example in a com-

pany where the users are provided with the opportu-

nity to select between CLE(privacy) and IBE(no pri-

vacy) encryptions depending on the needs of the com-

pany. With the concept of compatibility and its im-

plementation we can achieve some intresting proper-

ties. We can use only one KGC for both encryptions,

increase the security of an IBE scheme at any time

by using a secret key as in CLE. In addition, we can

decrypt an IBE message using the IBE part of CLE,

bearing in mind that it is impossible to achieve this

if the user’s public key in CLE is certiﬁed in the par-

tial private key. The concept of a compatible system

ﬁrstly reduces the problems of PKI avoiding the use

of digital certiﬁcates, and secondly it offers the best

aspects of both CLE and IBE schemes. Even better,

although it comes in contrast with the characteriza-

tion certiﬁcateless, the user’s public key PK2 could

in some schemes be signed, for backward compati-

bility with traditional PKI. Under this assumption, a

CLE user would be able to encrypt in IBE, CLE and

traditional PKI settings in an ideal system. In addi-

tion, considering other IBE-related encryptions such

as the TRE, the Role-based Access, the HIBE, the

Fuzzy IBE and the Attribute-based Encryption, we

can develop a ’global’ compatible system supported

numerous IBE-related concepts in which a user will

be provided with the opportunity to choose between

the desired IBE-related encryption on-the-ﬂy.

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