The first digital signature scheme with a (t, l) threshold subliminal channel was proposed by Lee et al. However, according to our analysis, it is found that Lee et al.'s scheme is low efficient in practice. At the same time, Lee et al.'s scheme is not secure against resending attack. Then, a randomized RSA signature scheme is proposed. The proposed randomized RSA signature scheme can be proved to be secure under adaptive chosen-message attacks in the random oracle model. Based on this signature scheme, by using the Lagrange interpolating polynomial and distributing the secret shadows of the RSA exponent among n subliminal receivers, a new digital signature scheme with a (t, l) threshold subliminal channel is proposed, which overcomes all the shortcomings of the scheme proposed by Lee et al. The new scheme is secure and efficient in practice.
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