# 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}
}
• Published 11 December 2016
• Computer Science, Mathematics
• IACR Cryptol. ePrint Arch.
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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