The Dead Cryptographers Society Problem

TL;DR

This paper introduces the Dead Cryptographers Society Problem, analyzing its computational complexity and exploring potential cryptographic applications like key distribution, auctions, and secure communication.

Contribution

It formally defines the DCS problem, proves some complexity results, and discusses its potential cryptographic uses.

Findings

DCS involves determining languages from specific bit-permuting DTMs

Complexity results suggest certain cases are computationally hard

Potential cryptographic applications include secure key exchange and auctions

Abstract

This paper defines The Dead Cryptographers Society Problem - DCS (where several great cryptographers created many polynomial-time Deterministic Turing Machines (DTMs) of a specific type, ran them on their proper descriptions concatenated with some arbitrary strings, deleted them and left only the results from those running, after they died: if those DTMs only permute and sometimes invert the bits on input, is it possible to decide the language formed by such resulting strings within polynomial time?), proves some facts about its computational complexity, and discusses some possible uses on Cryptography, such as into distance keys distribution, online reverse auction and secure communication.