Bivariate Polynomials Modulo Composites and Their Applications [chapter]

Dan Boneh, Henry Corrigan-Gibbs
2014 Lecture Notes in Computer Science  
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
more » ... mption leads to (i) a new statistically hiding commitment scheme that composes well with Pedersen commitments, (ii) a conceptually simple cryptographic accumulator, and (iii) an efficient chameleon hash function.
doi:10.1007/978-3-662-45611-8_3 fatcat:3rim4gol2jcqdlzkbbw5t24cjq