Secure two-party input-size reduction: Challenges, solutions and applications

•We motivate, formulate, and solve the generic two-party Secure Input-size Reduction.•Our solutions are based on protocols for secure perfect hashing in a two-party setting.•We propose lightweight and perfectly secure protocols with optimal reduced sizes.•We further improve our protocols’ efficiency for security against a PPT adversary.•We give use cases where our protocols result in significant performance improvements.