On the Compressibility of NP Instances and Cryptographic Applications

We study compression that preserves the solution to an instance of a problem rather than preserving the instance itself. Our focus is on the compressibility of NP decision problems. We consider NP problems that have long instances but relatively short witnesses. The question is, whether one can efficiently compress an instance and store a shorter representation that maintains the information of whether the original input is in the language or not. We want the length of the compressed instance to be polynomial in the length of the witness and polylog in the length of original input. We discuss the differences between this notion and similar notions from parameterized complexity. Such compression enables succinctly storing instances until a future setting will allow solving them, either via a technological or algorithmic breakthrough or simply until enough time has elapsed. We give a new classification of NP with respect to compression. This classification forms a stratification of ...

• Type: Conference
• Year: 2006
• Where: FOCS
• Authors: Danny Harnik, Moni Naor
• Keywords: FOCS 2006, NP Decision Problems, NP Problems, Original Input, Theoretical Computer Science