RSA Signature - Multiple Use Weakness I cite from Fundamentals of Computer Security (Chapter 7 on Digital Signature, Paragraph 7.3 on RSA Signatures, page 289):


  Multiple uses of the RSA Signature scheme tend to weaken it. The way out is to make subsequent signatures dependent on those previously generated.



Why is this?
Does it affect also the RSA Encryption scheme, or is it a weakness that comes from the knowledge of the message (and therefore affects only Signature schemes)?
It's hard to say from that out-of-context statement.  It may be that they were talking about signatures with obsolete padding schemes (such as ISO 9796-1), or possibly just raw RSA (zero padding, which is even worse); it is possible with these padding, if you observe enough signatures, you could come up with a forgery.

On the other hand, there is no known weakness if you generate RSA signatures using a modern padding scheme, either PKCS #1.5 (which, I suppose, is a bit hard to call modern) or PSS.