What is the weakness, if there is any, of using the same message space for different public exponents (assuming e changes everytime)?
Imagine I have a message space [0,n] where n is a 1024 bit number and several public exponents of 1024 bit each as well, does that somehow have an impact on my RSA system?
Edit: assume I don't have access to n in this scenario (unless "message space" refers to n. However, in this case we assume that the given message space is a composite number with > 6 prime factors)