Message Authentication Codes (MACs).

A function family $\{f$_k}k∈ (where $$ is the key length, taken to be the security parameter) is a secure MAC family if any adversary $A$ (whose resources are bounded by a polynomial in $$) succeeds in the following game only with negligible probability. A random $$-bit key $k$ is chosen; next $A$ can adaptively choose messages $m$₁,&ldots;,m_n and receive the corresponding MAC values $f$_k(m₁)&ldots;f_k(m_n). $A$ succeeds if it manages to forge the MAC, i.e., if it outputs a pair $m,t$ where $m\ne m$₁,&ldots;,m_n and $t=f$_k(m). See [2] for more details.