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IJCSNS International Journal of Computer Science and Network Security, VOL.10 No.1, January 2010 51 New Digital Multisignature Scheme with Distinguished Signing Responsibilities Luu Hong Dung and Nguyen Hieu Minh Faculty of Information Technology, Le Qui Don Technical University 100 Hoang Quoc Viet, Ha Noi, Viet Nam Summary A multisignature scheme is a digital signature scheme that allows multiple signers to generate a single signature in a collaborative and simultaneous manner. In this paper we first review of the digital multisignature schemes using elliptic curvers and elliptic curve version of the multisignature scheme with distinguished signing responsibilities. Then, we propose a new multisignature scheme with distinguished signing responsibilities. In this scheme, each group member has distinguished signing responsibility and partial contents of the message can be verified without revealing the whole message. Our proposed scheme is more efficient than the scheme reviewed and capable of application in practice. Keywords Multisignature scheme, Elliptic curve, Distinguished signing responsibilities. I. INTRODUCTION Digital signatures can be classified into two main categories: single signature and multiple signature (or multisignature). Single signature refers to the cases where only one party signs a document, while multiple signature refers to the cases where more than one party sign a single document. The digital signature schemes in use today can be classified according to the hard underlying mathematical problem which provides the basis for their security [1]: 1. Integer Factorization schemes, which base their security on the intractability of the integer factorization problem. Examples of these include the RSA and Rabin signature schemes. 2. Discrete Logarithm schemes, which base their security on the intractability of the (ordinary) discrete logarithm problem in a finite field. Examples of these include the ElGamal, Schnorr, DSA, and NybergRueppel signature schemes. 3. Elliptic Curve schemes, which base their security on the intractability of the elliptic curve discrete logarithm problem. For example, in American standard ECDSA and Russian standard GOST R 342001. The indicated problems are hard, if the used primes and elliptic curves satisfy special requirements [2, 3]. In 1983, Itakura and Nakamura [4] proposed the first multisignature scheme. It let multiple signers Manuscript received January 5, 2010 Manuscript revised January 20, 20...
IJCSNS International Journal of Computer Science and Network Security, VOL.10 No.1, January 2010
51
Manuscript received January 5, 2010
Manuscript revised January 20, 2010
New Digital Multisignature Scheme with Distinguished
Signing Responsibilities
Luu Hong Dung and Nguyen Hieu Minh
Faculty of Information Technology, Le Qui Don Technical University
100 Hoang Quoc Viet, Ha Noi, Viet Nam
Summary
A multisignature scheme is a digital signature scheme that allows
multiple signers to generate a single signature in a collaborative
and simultaneous manner. In this paper we first review of the
digital multisignature schemes using elliptic curvers and elliptic
curve version of the multisignature scheme with distinguished
signing responsibilities. Then, we propose a new multisignature
scheme with distinguished signing responsibilities. In this scheme,
each group member has distinguished signing responsibility and
partial contents of the message can be verified without revealing
the whole message. Our proposed scheme is more efficient than
the scheme reviewed and capable of application in practice.
Keywords
Multisignature scheme, Elliptic curve, Distinguished signing
responsibilities.
I. INTRODUCTION
Digital signatures can be classified into two main
categories: single signature and multiple signature (or
multisignature). Single signature refers to the cases where
only one party signs a document, while multiple signature
refers to the cases where more than one party sign a single
document.
The digital signature schemes in use today can be
classified according to the hard underlying mathematical
problem which provides the basis for their security [1]:
1. Integer Factorization schemes, which base their
security on the intractability of the integer factorization
problem. Examples of these include the RSA and
Rabin signature schemes.
2. Discrete Logarithm schemes, which base their security
on the intractability of the (ordinary) discrete
logarithm problem in a finite field. Examples of these
include the ElGamal, Schnorr, DSA, and Nyberg
Rueppel signature schemes.
3. Elliptic Curve schemes, which base their security on
the intractability of the elliptic curve discrete logarithm
problem. For example, in American standard ECDSA
and Russian standard GOST R 342001.
The indicated problems are hard, if the used primes and
elliptic curves satisfy special requirements [2, 3].
In 1983, Itakura and Nakamura [4] proposed the first
multisignature scheme. It let multiple signers
collaboratively sign the same message and the resultant
multisignature can be verified by a group of verifiers to
check whether it is valid or not. Since then, several
multisignature schemes have been proposed [57].
The application of digital multisignature can be found in
some secret sharing applications. For example, a company's
policy may require multiple managers to sign any business
contract. Digital multisignature scheme enables this internal
policy effectively. Each manager has to use his individual
secret key to sign the same document and all individual
signatures can be combined into a single multisignature.
However, to any external verifier, this multisignature is just
a normal signature that can be verified by using the
company's public key, which is a product of all public keys
of the signers. In the multisignature schemes proposed in [8],
all group members hold the same responsibility of signing
the document.
In fact, there are some applications that need to use
multisignatures with distinguished signing responsibilities.
For example, a company releases a document that may
involve financial department, engineering department and
program office. Each entity is responsible of preparing and
signing a particular section of the document. The signing
responsibility of engineering department may have no
interest to read the content prepared by the financial
department. However, the combination of all sections
represents the company's document. The company's
document should be easily verified by any outsider using
company's public key. For the sake of confidentiality, same
verifier may be restricted to access and verify only some
sections of the document.
In this paper, we first review of the digital
multisignature schemes using elliptic curvers [8] and elliptic
curve version of the multisignature scheme with
distinguished signing responsibilities [9]. Then, we propose
a new multisignature scheme with distinguished signing
responsibilities.
We will organize this paper as follows: In section II, we
will introduce elliptic curve digital schemes. Brief reviews
of the digital multisignature schemes using elliptic curvers
in [8] will be introduced in Section III. In Section IV, we
will describe the elliptic curve version of the multisignature
scheme with distinguished signing responsibilities proposed
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