This paper addresses the identifier ownership problem. It does so by using characteristics of Statistical Uniqueness and Cryptographic Verifiability (SUCV) of certain entities which this document calls SUCV Identifiers and Addresses, or, alternatively, Crypto-based Identifiers. Their characteristics allow them to severely limit certain classes of denial-of-service attacks and hijacking attacks. SUCV addresses are particularly applicable to solve the address ownership problem that hinders mechanisms like Binding Updates in Mobile IPv6.