Digital signature with a subliminal channel

A subliminal channel is a covert communication channel to send a message to an authorised receiver; this message cannot be discovered by any unauthorised receiver. There are some applications that can take advantage of this by hiding secret messages in this subliminal channel. For example, a credit card provider can hide the card holder´s credit history and credit limit in a digital signature for an issued credit card. G.J. Simmons (1985) found that El Gamal-type digital signature schemes can be easily used to establish a subliminal channel owing to their low information rate. Simmons also found (1993) that in all broadband subliminal channels devised thus far the receiver needs to know the transmitter´s secret signing key; subliminal channels that do not require the transmitter to entrust its secret key to the subliminal receiver are generally narrowband. This limits the practical usefulness of the subliminal channel. The paper shows how to construct a digital signature scheme with a broadband subliminal channel that does not require the subliminal receiver to share the transmitter´s secret signing key. The subliminal channel can be constructed in either the p-channel or the q-channel, where p and q are two large primes as used in the RSA scheme. To any outsider, forging a legitimate signature requires solving both the factoring problem and the discrete logarithm problem. Implementation of the signature scheme based on the Lucas function is proposed to achieve greater efficiency