Reductions in PPP

Frank Ban, Kamal Jain, Christos H. Papadimitriou, Christos-Alexandros Psomas, Aviad Rubinstein

Abstract: Highlights • We introduce two new problems, Minkowski and Dirichlet . • We show that these two problems belong in the complexity class PPP . • We show that Equal Sums and Dirichlet are reducible to Minkowski . Abstract We show several reductions between problems in the complexity class PPP related to the pigeonhole principle, and harboring several intriguing problems relevant to Cryptography. We define a problem related to Minkowski's theorem and another related to Dirichlet's theorem, and we show them to belong to this class. We also show that Minkowski is very expressive, in the sense that all other non-generic problems in PPP considered here can be reduced to it. We conjecture that Minkowski is PPP -complete.