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RESEARCH PAPER

SCIENCE CHINA

Information Sciences

September 2014, Vol. 57 092110:1–092110:10

doi: 10.1007/s11432-014-5139-z

 Science China Press and Springer-Verlag Berlin Heidelberg 2014 info.scichina.com link.springer.com

DNA-chip-based dynamic broadcast encryption

scheme with constant-size ciphertexts and

decryption keys

FANG XiWen & LAI XueJia

∗

Department of Computer Science and Engineering, Shanghai Jiao Tong University,

Shanghai 200240, China

Received February 16, 2014; accepted April 18, 2014

Abstract In this paper we present DNA-DBE, a DNA-chip-based dynamic broadcast encryption scheme. In

our scheme, new users can join dynamically wi thout modiﬁcation of other users’ decryption keys. Either the

ciphertext or the decryption key is of constant-size. Backward secrecy is achieved in DNA-DBE: if new users join

the system dynamically, they will not be able to retrieve past data. The security of our scheme relies on hard

biological problems, which are immune to attacks of new computing technologies in the future. T here exists a

special feature in DNA–based cryptosystems, i.e. the set of encryption keys and the set of decryption keys have

a many-to-many relationship. The i mplementation of more complicated DNA cryptosystems taking advantage

of this special feature has been previously lef t as an open problem. Our DNA-DBE system is a solution to this

open problem, which is also the ﬁrst exploration of DNA based group-oriented encryption system.

Keywords DNA cryptography, dynamic broadcast encryption, group oriented cryptography, DNA chip,

cryptology

Citation Fang X W, Lai X J. DNA-chip-based dynamic broadcast encryption scheme with constant-size cipher-

texts and decryption keys. Sci China Inf Sci, 2014, 57: 092110(10), doi: 10.1007/s11432-014-5139-z

1 Introduction

Since Adleman’s pioneering research that showed DNA can be used to solve the Hamiltonian path problem

[1], many researchers have explored the ability of biological mole c ule s to perfor m computation. Later,

the enormous storage capability and parallel computability of DNA molecules were also introduced into

cryptogr aphy: Clelland et al. demonstrated an approach to hide messages in DNA microdots [2]. Gehani

et al. proposed two DNA one-time-pad encryption schemes [3]. Based on the encoding technique presented

in Lipton [4], Boneh et al. proposed a scheme breaking the Data Encryption Standard (DES) [5]. All of

these re searches demonstrated that it is a viable way to constr uct cryptosystems or perform cryptanalysis

based on DNA technology.

DNA chip (microarray) is one of the hottest areas in biological research today. DNA chips consist

of a la rge number of spots embedded on a solid surface. Each sp ot contains multiple copies of probes.

Using this technology, massive parallel operations can be achieved, and this is how DNA-chip-based

cryptosystems came into being:

∗

Corresponding author (email: lai-xj@cs.sjtu.edu.cn)

Fang X W, et al. Sci China Inf Sci September 2014 Vol. 57 092110:2

In Ref. [6], a DNA symmetric-key cryptosystem based on DNA chip technology (DNASC) was pro-

posed, which is the ﬁrst exploratory study of DNA-chip-based cryptosystem. In this system, both en-

cryption and decryption keys ar e DNA probes, while its ciphertext is embedded in a specia lly designed

DNA chip (microarray). The plaintext can be retrieved by hybridizing the encrypted chip with the secret

key probes. Later an asymmetr ic enc ryption system DNA-PKC was proposed in Ref. [7]. These two

systems demonstrated that it is viable to implement cryptosystems taking advantag e of the DNA chip

technology.

In terms of security, there exist essential diﬀerences between conventional modern cryptosystems and

DNA-based crypto systems. The security of conventional modern cryptography is based on hard com-

putational problems, such as discrete logarithm problem and prime factoriz ation. However, with the

development of co mputing technology, if the computational problems we assume hard can b e solved ef-

ﬁciently in the future, the crypto systems that rely on these computational problems can be broken. By

contrast, the security of DNA cryptography relies on hard biological problems. Such a s cheme is immune

to attacks of new computing technologies in the future, thus providing another level of sec urity.

It has been demonstrated that the set of encryption keys and the set of decryption keys in DNA based

cryptosystems have a many-to-many r elationship [7], i.e. each of the encryption key might be associated

with many decryption keys and vice versa, which implies that a system with more complicated functions

could be implemented. Such feature can be used to construct a broadcast encryptio n system which allows

the center to encrypt a message and send it to a group of users.

Broadcast encryption scheme, ﬁrst explored by Fiat and Nao r [8], enables a center to communicate

securely with some subse t of users authorized to receive messages. Only the us e rs in a certain set S can

use their private key to retrieve the plaintext. A system is said to be fully collusion resistant when even

if all users o utside of S collude, they can not decrypt the broadcas t messag e. If new users can join a

preexisting system without modiﬁcation of user decryption keys nor ciphertext siz e, the scheme is said

to be dynamic broadcast encryption [9].

A typical broadcast encryption system is made up of the following algorithms:

Setup (n) takes as input the number of receivers n. It outputs n private keys dk

, dk

, . . ., dk

for the

receivers.

Encrypt (S, m) takes as input the set of receivers S, the plaintext m. It outputs the cipher-text C

Decrypt (S, C

, i, dk

) takes as input the set of receivers S, a user id i and the private key dk

for user

i and the cipher-text C

to output message m iﬀ i ∈ S.

The sec urity of a broadcast encryption scheme consists of two requirements: all of the users in S

are able to retrieve the plaintext m and none of the users outside of S could get information about

the message. In conventional schemes, one has to construct se veral par ticular expressions elaborately

according to S and a certain framework, eg. q-BDHE problem [10], (t, n)-GDHE problem [9]. Therefo re

by computing these expressions, all users in S co uld recover the message.

Our contribution. Based on the DNA cryptosystem proposed in Refs. [6,7], in this paper we present

a DNA-chip-based dynamic broadcast encryption system, which is the ﬁrst exploration of DNA-based

group-oriented encryption scheme. By introducing the special feature of DNA-chip-based cryptosystem,

the requirements of broadcast encryption could be met naturally.

As one encryption key can be associa ted with many decryption keys in DNA-chip-based cryptosystem,

if a certain encryption key is used to encrypt a given message, then all of the corresponding decryption

keys can be used to decry pt the ciphertext. Thus we can construct a DNA broadcast encryption system

using this feature.

As one decryption key can also be associated with many encryption keys, if a new user wants to join

the system, the broadcas t center could assign the new user a certain decryption key who se corresponding

set of encryption keys share some common elements with other users’, i.e. the broadcast center can still

encrypt the mes sage without implying modiﬁcation of preexisting decryption keys. Thus taking adva ntage

of the special feature of DNA-chip-based cryptosystem, a dynamic broadcast encryption sy stem can be

implemented.

In our scheme, either the ciphertex t or the decryption key dk

possessed by user u

is of constant

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