Conditional Disclosure of Secrets, Private Information Retrieval, [and] Private Simultaneous Messages

Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 52-53).Private Information Retrieval is the problem of querying two servers to nd a value in a database, while keeping the index private. We extend this problem to Generalized Wildcard PIR, where we instead query an aggregate of the entries whose indices match a pattern, called a generalized wildcard, which species what values each segment of the indices may take. We give a construction for this variant with similar communication to that of the best PIR protocols known. We study information theoretic models in cryptography, namely Private Information Retrieval, Conditional Disclosure of Secrets, and Private Simultaneous Messages. We give extensions of PIR and CDS in the area of generalized wildcards, and give constructions for those extensions. We discuss directions towards more ecient protocols, and raise open questions.by Isaac Grosof.M. Eng

Push-Pull Block Puzzles are Hard

This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question [19]. Push-pull block puzzles are a type of recreational motion planning problem, similar to Sokoban, that involve moving a ‘robot’ on a square grid with 1 × 1 obstacles. The obstacles cannot be traversed by the robot, but some can be pushed and pulled by the robot into adjacent squares. Thin walls prevent movement between two adjacent squares. This work follows in a long line of algorithms and complexity work on similar problems [3– 9, 14, 16, 18]. The 2D push-pull block puzzle shows up in the video games Pukoban as well as The Legend of Zelda: A Link to the Past, giving another proof of hardness for the latter [2]. This variant of block-pushing puzzles is of particular interest because of its connections to reversibility, since any action (e.g., push or pull) can be inverted by another valid action (e.g., pull or push)