Formal Verification of ElGamal Encryption using a Probabilistic Lambda-Calculus

Game-based proofs are a common technique used to verify cryptographic constructions. Such proofs consist of a sequence of games where each transition from one game to the next can be individually verified. However, as more and more increasingly complex proofs are being published, even such transitions are often non-trivial. Moreover, games are frequently described informally or just in some ad-hoc pseudocode and may be understood differently than originally intended by the authors, or underlying assumptions may not be made explicit. For this reason, Backes et al. developed a new formal language at the chair of Information Security and Cryptography at the Universität des Saarlandes. This language supports most cryptographic primitives typically used in such games and is intended to provide a formal standard to model them. Furthermore it has been implemented on top of the proof assistant Isabelle/HOL, such that it is possible to use Isabelle’s logic to formally verify game transitions. The goal of this thesis is to provide a first application of this language to a real-world cryptographic construction by using it to formally verify the security of the well-known ElGamal encryption scheme. For this, we use the language to model the scheme as well as the desired security properties and the necessary assumptions. Next, we find appropriate game transformations in the language and formally prove their validity. Finally we show how to use these transformations to achieve a fully formalized game-based proof of the security of ElGamal.