Conditional Digital Signatures and Signing in the Future M.Klonowski, M.Kutylowski, A.Lauks, F.Zagorski We consider conditional digital signatures (CDS for short): According to this scheme a creator of a CDS signature, say Alice, signs a message M1 conditioned by a signature under M2 of an another user, say Bob. The string created by Alice can be transformed into a digital signature of Alice under M1, once we are given a signature under M2 produced by Bob. Until the moment of creating a signature under M2 by Bob, the signature under M1 by Alice DOES NOT EXIST. This differs from the previous solutions where merely a condition about M2 has been included into a message signed by Alice. The key feature of our scheme is that Alice prepares the CDS signature before Bob actually signs M2. We propose two CDS schemes -- the first one prohibits checking that a signature of M1 has been prepared by Alice until Bob signs M2. In the case of the second scheme Alice can prove interactively that the string created by Alice hides a signature of M1 conditioned upon Bob's signature under M2. CDS signatures can be used for various purposes. For instance, they seem to be very useful in computer systems with a modular or layered architecture, and allow one process to sign something in advance in a secure way. Similar scenarios can occur in many business and legal situations. CDS schemes can be used to build a system in which a signature can be retrieved at a given FUTURE date. This feature requires a public institution signing periodically the current time. In a similar way one can provide possibility of conditional decryption -- in such a case one can decrypt a ciphertext only after signing a particular document by a third party (for instance a public body).