# On Negation Complexity of Injections, Surjections and Collision-Resistance in Cryptography

@article{Miller2016OnNC, title={On Negation Complexity of Injections, Surjections and Collision-Resistance in Cryptography}, author={Douglas Miller and Adam Scrivener and Jesse Stern and Muthuramakrishnan Venkitasubramaniam}, journal={IACR Cryptol. ePrint Arch.}, year={2016}, volume={2016}, pages={192} }

Goldreich and Izsak (Theory of Computing, 2012) initiated the research on understanding the role of negations in circuits implementing cryptographic primitives, notably, considering one-way functions and pseudo-random generators. More recently, Guo, Malkin, Oliveira and Rosen (TCC, 2015) determined tight bounds on the minimum number of negations gates (i.e., negation complexity) of a wide variety of cryptographic primitives including pseudo-random functions, error-correcting codes, hardcore…

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