Verified commitment schemes and reduction proofs in the lean proof assistant
Date
2026
Authors
Blacquiere, Ashley
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Abstract
This thesis presents a formalization of commitment schemes in the Lean 4 theorem prover, together with machine-checked proofs of their core security properties. Commitment schemes allow a party to commit to a value while keeping it hidden, with guarantees of binding (the value cannot be changed) and hiding (the value remains secret until revealed).
We develop a general, specification-driven framework for modelling commitment schemes and their security definitions in Lean, using a probabilistic monad to express adversarial games and reduction-based proofs. Within this framework, we formalize two canonical schemes: the Pedersen commitment scheme and the ElGamal commitment scheme. For Pedersen, we prove perfect hiding and computational binding via reduction to the discrete logarithm problem; for ElGamal, we prove perfect binding and computational hiding via reduction to the decisional Diffie–Hellman assumption.
This work contributes both concrete formalizations and reusable abstractions for cryptographic reasoning in Lean, advancing the emerging area of mechanized cryptography within the system.
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Keywords
cryptography, proof assistant, lean, commitment scheme, mechanized proof, formal verification