A potentially serious problem with current digital signature schemes is that their underlying hard problems from number theory may be solved by an innovative technique or a new generation of computing devices such as quantum computers. Therefore while these signature schemes represent an efficient solution to the short term integrity (unforgeability and non-repudiation) of digital data, they provide no confidence on the long term (say of 20 years) integrity of data signed by these schemes. In this work, we focus on signature schemes whose security does not rely on any unproven assumption. More specifically, we establish a model for unconditionally secure digital signatures in a group, and demonstrate practical schemes in that model. An added advantage of the schemes is that they allow unlimited transfer of signatures without compromising the security of the schemes. Our scheme represents the first unconditionally secure signature that admits provably secure transfer of signatures.