Security Of Symmetric Primitives Under Incorrect Usage Of Keys

We study the security of symmetric primitives under the incorrect usage of keys. Roughly speaking, a key-robust scheme does not output ciphertexts/tags that are valid with respect to distinct keys. Key-robustness is a notion that is often tacitly expected/assumed in protocol design as is the case with anonymous auction, oblivious transfer, or public-key encryption. We formalize simple, yet strong definitions of key robustness for authenticated-encryption, message-authentication codes and PRFs. We show standard notions (such as AE or PRF security) guarantee a basic level of key-robustness under honestly generated keys, but fail to imply key-robustness under adversarially generated (or known) keys. We show robust encryption and MACs compose well through generic composition, and identify robust PRFs as the main primitive used in building robust schemes. Standard hash functions are expected to satisfy key-robustness and PRF security, and hence suffice for practical instantiations. We however provide further theoretical justifications (in the standard model) by constructing robust PRFs from (left-and-right) collision-resistant PRGs.