Abstract
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Fresh$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Gen$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$FirstSend$ </tex-math></inline-formula> is introduced; and the definition of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$has$ </tex-math></inline-formula> 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.
Highlights
The security of cryptographic protocols plays a vital role in the information security field, but most existent cryptographic protocols have vulnerabilities and defects that have been discovered or not, in some safety-critical areas, we need a set of cryptographic protocols which is rigorous and can truly implement the security properties it claims
Assuming that principal A is honest, and A sends the encrypted information containing b, it can be inferred that A has received the encrypted information containing (a, b), so honest rules are introduced. This part redefines the ownership of the private key and signature, extend the honesty axiom that describe the behavior of honest principals, reduce the complexity and redundancy in the protocol analysis process
This rule RuleF2 means that after the principal A generates a nonce, if one of the subsequent send event e2 is not send a for the first time, it can be judged that there is a send event e3 on the principal A to send the nonce for the first time, where e3 occurs before e2 and after the event e1 that generated the nonce. During this period, there are no other send event containing freshness of the nonce, that is, the above mentioned FirstSend. This part introduces the concept of Fresh, and derives two definitions of Gen and FirstSend based on the Fresh into LoET, presents two rules related to this three new concepts
Summary
The security of cryptographic protocols plays a vital role in the information security field, but most existent cryptographic protocols have vulnerabilities and defects that have been discovered or not, in some safety-critical areas, we need a set of cryptographic protocols which is rigorous and can truly implement the security properties it claims. LoET is an axiomatic method based on theorem proving and this logic is designed around a message automation with actions for possible protocol steps [3], [6]. This theorem ensures that any well-typed protocol is robustly safe under attack while reasoning only about the actions of honest principals in the protocols [3]. PCL (Protocol Composition Logic) is a logic for proving security properties of network protocols [7] and is mainly used to verify the authentication and secrecy of the protocols under the public key encryption system.
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