A Formal Security Analysis of the $p\equiv p$ Authentication Protocol for Decentralized Key Distribution and End-to-End Encrypted Email

Abstract

To send encrypted emails, users typically need to create and exchange keys which later should be manually authenticated, for instance, by comparing long strings of characters. These tasks are cumbersome for the average user. To make more accessible the use of encrypted email, a secure email application named $p\equiv p$ automates the key management operations; $p\equiv p$ still requires the users to carry out the verification, however, the authentication process is simple: users have to compare familiar words instead of strings of random characters, then the application shows the users what level of trust they have achieved via colored visual indicators. Yet, users may not execute the authentication ceremony as intended, $p\equiv p$ ’s trust rating may be wrongly assigned, or both. To learn whether $p\equiv p$ ’s trust ratings (and the corresponding visual indicators) are assigned consistently, we present a formal security analysis of $p\equiv p$ ’s authentication ceremony. From the software implementation in C, we derive the specifications of an abstract protocol for public key distribution, encryption and trust establishment; then, we model the protocol in a variant of the applied pi calculus and later formally verify and validate specific privacy and authentication properties. We also discuss alternative research directions that could enrich the analysis.