Digital signature with message recovery based on factoring and discrete logarithm

There are two applications in digital signature schemes with message recovery based on a discrete logarithm problem. One is an authenticated encryption scheme, and the other is a key agreement scheme. Considering that the cryptographic assumptions will be broken in the future, the digital signature scheme with message recovery should also be designed based on two assumptions. Besides the digital signature scheme with message recovery, the authenticated encryption scheme with message linkages should also be redesigned to deal with the problem when any one of the factoring and discrete logarithm assumptions is broken. In this paper, we propose a digital signature with message recovery based on factoring and discrete logarithm and show that the scheme is secure. In comparison with Zhang ET AL.'s scheme, our proposed scheme is the most efficient one in terms of communication cost and computation complexity.