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On-line/Off-line signatures are used in a particular scenario where the signer must respond quickly once the message to be signed is presented. The idea is to split the signing procedure into two phases. The first phase is off-line: in this phase, the signer does some preparing works before the message to be signed is presented. The second phase is on-line: once the message to be signed is known, the signer utilizes the result of the pre-computation and takes a very short time to accomplish the signing procedure.
In most of these schemes, when signing a message $m$, a partial signature of $m$ is computed in the off-line phase. We call this part of signature the off-line signature token of message $m$. In some special applications, the off-line signature tokens might be exposed in the off-line phase. For example, some signers might want to transmit off-line signature tokens in the off-line phase in order to save the on-line transmission bandwidth. Another example is in the case of on-line/off-line threshold signature schemes, where off-line signature tokens are unavoidably exposed to all the users in the off-line phase.
This paper discusses this exposure problem and introduces a new notion: divisible on-line/off-line signatures, in which exposure of off-line signature tokens in off-line phase is allowed. An efficient construction of this type of signatures is also proposed. http://eprint.iacr.org/2008/447
