LoET-E: A Refined Theory for Proving Security Properties of Cryptographic Protocols

Nowadays, more and more new cryptographic protocols are emerging, and the security analysis of emerging cryptographic protocols is increasingly important. The logic of events is an axiomatic method based on theorem proving, designed around message automation with actions for possible protocol steps; it figured out types of information transmitted in the protocols and also presented novel proof rules and mechanism. However, with the emergence of various cryptographic protocols, the logic of events lacks corresponding axioms and rules in the process of proving certain cryptographic protocols, so it needs a further extension. Based on the logical framework of protocol composition logic, this paper presents a refined theory of the logic of events called LoET-E, in which the novel rules about the freshness of nonces, the event attributes of messages, and the states of the predicate is presented; the concepts of
$Fresh$
,
$Gen$
and
$FirstSend$
is introduced; and the definition of
$has$
and the honesty axiom of LoET is extended. The refined theory can guarantee the correctness, integrity, and validity of the original axioms, ensure the consistency of event classes and basic sequences in the proof process, reduce the complexity and redundancy in the protocol analysis process, and most importantly, extend the provable range of cryptographic protocols.