Cryptographic Puzzles and Complex Systems

A puzzle lies behind password authentication (PA) and blockchain proof of work (PoW). A cryptographic hash function is commonly used to implement them. The potential problem with secure hash functions is their complexity and rigidity. We explore the use of complex systems constructs such as a cellular automaton (CA) to provide puzzle functionality. The analysis shows that computational irreducibility and sensitivity to initial state phenomena are enough to create simple puzzle systems that can be used for PA and PoW. Moreover, we present puzzle schemata using CA and n-body problems.

Networks of Picture Processors with Filtering Based on Evaluation Sets as Solvers for Cryptographic Puzzles Based on Random Multivariate Quadratic Equations

Networks of picture processors is a massively distributed and parallel computational model inspired by the evolutionary cellular processes, which offers efficient solutions for NP-complete problems. This bio-inspired model computes two-dimensional strings (pictures) using simple rewriting rules (evolutionary operations). The functioning of this model mimics a community of cells (pictures) that are evolving according to these bio-operations via a selection process that filters valid surviving cells. In this paper, we propose an extension of this model that empowers it with a flexible method that selects the processed pictures based on a quantitative evaluation of its content. In order to show the versatility of this extension, we introduce a solver for a cryptographic proof-of-work based on the hardness of finding a solution to a set of random quadratic equations over the finite field F2. This problem is demonstrated to be NP-hard, even with quadratic polynomials over the field F2, when the number of equations and the number of variables are of roughly the same size. The proposed solution runs in O(n2) computational steps for any size (n,m) of the input pictures. In this context, this paper opens up a wide field of research that looks for theoretical and practical solutions of cryptographic problems via software/hardware implementations based on bio-inspired computational models.

Mitigate DoS and DDoS Attack in Mobile Ad Hoc Networks

This paper proposes a technique to defeat Denial of Service (DoS) and Distributed Denial of Service (DDoS) attacks in Ad Hoc Networks. The technique is divided into two main parts and with game theory and cryptographic puzzles. Introduced first is a new client puzzle to prevent DoS attacks in such networks. The second part presents a multiplayer game that takes place between the nodes of an ad hoc network and based on fundamental principles of game theory. By combining computational problems with puzzles, improvement occurs in the efficiency and latency of the communicating nodes and resistance in DoS and DDoS attacks. Experimental results show the effectiveness of the approach for devices with limited resources and for environments like ad hoc networks where nodes must exchange information quickly.