title: is SHA-512 collision resistant?
body: <p>According to the books that i have read, it says that S.H.A(Secure Hash Algorithm) is collision resistant.But if the input space is a 1024 bit number and the output space is a 512 bit message digest then shouldn't it be colliding for 
  (2^1024)/(2^512) times? As the range is lesser than the domain being mapped there should have been collisions. please explain where i am going wrong.</p>