SIAM Journal on Computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Computational complexity of probabilistic Turing machines
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Proofs that yield nothing but their validity and a methodology of cryptographic protocol design
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
TCC'07 Proceedings of the 4th conference on Theory of cryptography
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To formalize participants in cryptographic protocols, it is common to use probabilistic Turing machines. We point out subtleties in common definitions of probabilistic Turing machines, which imply that the common cryptographic operation of uniform random sampling in a finite set {1,...,s}@?Z is in general not possible within this model. From a technical point of view, this invalidates in particular a standard proof of the perfect zero knowledge property of the popular graph isomorphism proof system. The observed limitation appears to be relevant for other cryptographic protocol analyses as well, and we suggest one possible tweak of the definition of a probabilistic Turing machine.