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A Signcryption Scheme
Based on Secret Sharing Technique
Mohamed Al-Ibrahim
Center for Advanced Computing
Department of Computing
Macquarie University
Sydney, NSW 2109, Australia
ibrahim@ieee.org
Abstract.
Signcryption is a cryptographic primitive that performs sign-
ing and encryption simultaneously, at less cost than is required by the tra-
ditional signature-then-encryption approach. In this paper, a new sign-
cryption scheme is proposed for the open problem posed by Zheng, and
is based on Secret Sharing technique. The scheme is an “all-in-one” se-
curity approach: it provides privacy, authentication, integrity and non-
repudiation, all with less computational cost as well as communication
overhead. Yet, the scheme is not restricted to any particular cryptosys-
tem and could be designed with any cryptographic cryptosystem.
1
Introduction
Zheng [14] in Crypto 1997 introduced a new cryptographic primitive termed
digital signcryption
. He addressed the question of the cost of secure and authen-
ticated message delivery: whether it is possible to transfer a message of arbitrary
length in a secure and authenticated way with an expense less than that required
by signature-then-encryption. There, the goal was to provide simultaneously en-
cryption and digital signature in a single step and at a cost less than individually
signing and then encrypting. Their motivation was based on an observation that
signature generation and encryption consumes machine cycles, and also intro-
duces “expanded” bits to an original message. Hence, the cost of cryptographic
operation on a message is typically measured in the message expansion rate and
computational time invested by both sender and recipient. With typical stan-
dard signature-then-encryption, the cost of delivering a message in a secure and
authenticated way is essentially the sum of the cost of digital signature and that
of encryption. The answer to the question in [14] was proposed by an approach
based on the discrete logarithm problem of a shortened form of El-Gamal based
signatures. There, the secret key
k
was divided into two short sub-keys
k
1
and
k
2
;
the first was used for encryption, and the latter for signing. They left as an open
and challenging problem the design of other signcryption schemes employing any
public-key cryptosystem such as RSA, or any other computationally hard prob-
lem. Later, in [13], they introduced another signcryption scheme based on the
problem if integer factorization. Also, other studies by Bellare
at. el
. [2,3], An
