# Bivariate Polynomials Modulo Composites and their Applications

@article{Boneh2014BivariatePM,
title={Bivariate Polynomials Modulo Composites and their Applications},
author={Dan Boneh and Henry Corrigan-Gibbs},
journal={IACR Cryptol. ePrint Arch.},
year={2014},
volume={2014},
pages={719}
}
• Published 7 December 2014
• Mathematics, Computer Science
• IACR Cryptol. ePrint Arch.
We investigate the hardness of finding solutions to bivariate polynomial congruences modulo RSA composites. We establish necessary conditions for a bivariate polynomial to be one-way, second preimage resistant, and collision resistant based on arithmetic properties of the polynomial. From these conditions we deduce a new computational assumption that implies an efficient algebraic collision-resistant hash function. We explore the assumption and relate it to known computational problems. The…
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