Unification in primal algebras, their powers and their varieties
Journal of the ACM (JACM)
Term rewriting and all that
Completeness of many-sorted equational logic
ACM SIGPLAN Notices
RSA-OAEP Is Secure under the RSA Assumption
Journal of Cryptology
Logics for reasoning about cryptographic constructions
Journal of Computer and System Sciences - Special issue on FOCS 2003
A survey of algebraic properties used in cryptographic protocols
Journal of Computer Security
Towards automated proofs for asymmetric encryption schemes in the random oracle model
Proceedings of the 15th ACM conference on Computer and communications security
Formal certification of code-based cryptographic proofs
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Computationally sound implementations of equational theories against passive adversaries
Information and Computation
A Computational Introduction to Number Theory and Algebra
A Computational Introduction to Number Theory and Algebra
Why provable security matters?
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
A generalization of DDH with applications to protocol analysis and computational soundness
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
The security of triple encryption and a framework for code-based game-playing proofs
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Computational indistinguishability logic
Proceedings of the 17th ACM conference on Computer and communications security
Proving the security of ElGamal encryption via indistinguishability logic
Proceedings of the 2011 ACM Symposium on Applied Computing
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We consider a mild extension of universal algebra in which terms are built both from deterministic and probabilistic variables, and are interpreted as distributions. We formulate an equational proof system to establish equality between probabilistic terms, show its soundness, and provide heuristics for proving the validity of equations. Moreover, we provide decision procedures for deciding the validity of a system of equations under specific theories that are commonly used in cryptographic proofs, and use concatenation, truncation, and xor. We illustrate the applicability of our formalism in cryptographic proofs, showing how it can be used to prove standard equalities such as optimistic sampling and one-time padding as well as non-trivial equalities for standard schemes such as OAEP.