A simple unpredictable pseudo random number generator
SIAM Journal on Computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Stochastic lambda calculus and monads of probability distributions
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An Efficient Cryptographic Protocol Verifier Based on Prolog Rules
CSFW '01 Proceedings of the 14th IEEE workshop on Computer Security Foundations
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Efficient And Secure Pseudo-Random Number Generation
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Towards automated proofs for asymmetric encryption schemes in the random oracle model
Proceedings of the 15th ACM conference on Computer and communications security
Formal proof of provable security by game-playing in a proof assistant
ProvSec'07 Proceedings of the 1st international conference on Provable security
A framework for game-based security proofs
ICICS'07 Proceedings of the 9th international conference on Information and communications security
A modular formalisation of finite group theory
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Automated security proofs with sequences of games
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
A calculus for game-based security proofs
ProvSec'10 Proceedings of the 4th international conference on Provable security
Certifying assembly with formal security proofs: The case of BBS
Science of Computer Programming
Security protocol verification: symbolic and computational models
POST'12 Proceedings of the First international conference on Principles of Security and Trust
Verified indifferentiable hashing into elliptic curves
Journal of Computer Security - Security and Trust Principles
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Cryptographic primitives are fundamental for information security: they are used as basic components for cryptographic protocols or public-key cryptosystems. In many cases, their security proofs consist in showing that they are reducible to computationally hard problems. Those reductions can be subtle and tedious, and thus not easily checkable. On top of the proof assistant Coq, we had implemented in previous work a toolbox for writing and checking game-based security proofs of cryptographic primitives. In this paper we describe its extension with number-theoretic capabilities so that it is now possible to write and check arithmetic-based cryptographic primitives in our toolbox. We illustrate our work by machine checking the game-based proofs of unpredictability of the pseudo-random bit generator of Blum, Blum and Shub, and semantic security of the public-key cryptographic scheme of Goldwasser and Micali.