HMN 2025: How Parallelization of cryptographic protocol analyzer Maude-NPA reduces evaluation time, makes web safer

Internet safety is a significant concern, however cryptographic protocol evaluation instruments usually require a very long time resulting from their computational complexity. Professor Kazuhiro Ogata and Assistant Professor Canh Minh Do of the Department of Computing Science at Japan Advanced Institute of Science and Technology (JAIST) have efficiently parallelized two key steps—backward narrowing and transition subsumption—in Maude-NPA, leading to what they name Par-Maude-NPA.

Par-Maude-NPA improves the runtime efficiency of Maude-NPA by about 52% on common for advanced instances, considerably decreasing evaluation time and enhancing the flexibility to investigate massive and sophisticated cryptographic protocols effectively.

This analysis is the results of a world collaboration with Professor Santiago Escobar of Polytechnic University of Valencia and Associate Professor Adrián Riesco of Complutense University of Madrid in Spain. It was published in IEEE Transactions on Dependable and Secure Computing on July 16, 2025.

Ensuring the security of web communications requires verification of design flaws and safety vulnerabilities in cryptographic protocols, similar to Transport Layer Security (TLS), which protects private data like bank card numbers from unauthorized entry throughout on-line transactions. To help the formal verification of those protocols, numerous instruments and strategies have been developed.

In addition to Maude-NPA, a number of different formal analyzers have been launched, together with ProVerif, Tamarin, and Scyther. However, till not too long ago, there had been no profitable parallelization of formal analyzers for cryptographic protocols.

Maude-NPA begins from an assault state and makes use of backward narrowing reachability evaluation to search out safety flaws in cryptographic protocols. If the preliminary state will be reached from the assault state, the attainable assault is proven. Conversely, if no such path exists, it may be concluded that the assault is infeasible. However, this system suffers from a speedy enhance within the variety of states that should be analyzed—an issue generally known as state explosion.

To deal with this, Maude-NPA introduces transition subsumption, which eliminates pointless states that may be subsumed by different beforehand explored states within the search house. In this analysis, the analysis staff parallelizes each the backward narrowing and the transition subsumption to make one of the best use of high-performance computing sources.

“Maude-NPA makes use of a breadth-first search technique to traverse the reachable state house. Starting from a set of states at layer l (representing depth l from the assault state, which is at layer 0), it performs one backward narrowing step on every state to generate their successor states at layer l+1. This operation is known as step 1,” Dr. Canh Minh Do explains.

This backward narrowing search from any given state will be carried out independently, which opens a possibility for parallelization to enhance the efficiency of Maude-NPA.

“In addition, as quickly because the successor states at every layer are obtained from step 1, Maude-NPA conducts the transition subsumption to discard pointless states that may be subsumed by beforehand explored states. This course of is known as step 2,” Dr. Canh Minh Do provides.

Although transition subsumption performs a crucial function in decreasing the state house, it’s computationally costly. Instead of checking the subsumption of every state one after the other, many states will be thought-about concurrently to enhance the runtime efficiency of Maude-NPA.

The analysis staff efficiently parallelized each the backward narrowing in step 1 and the transition subsumption in step 2 and examined throughout a wide range of advanced cryptographic protocols. Dr. Canh Minh Do feedback, “We present experimental outcomes throughout various cryptographic protocols demonstrating that Par-Maude-NPA improves the runtime efficiency of Maude-NPA by a mean of 52% for advanced case research with a lot of states at every layer.”

The case research have additionally proven that Par-Maude-NPA can successfully carry out formal evaluation of not solely typical cryptographic protocols similar to TLS, but additionally of quantum-resistant TLS, which is able to allow protected, safe, and sustainable use of the web even when large-scale quantum computer systems change into out there.