Generating Hard Problems of Cellular Automata

by   Souvik Sur, et al.
IIT Kharagpur

We propose two hard problems in cellular automata. In particular the problems are: [DDP^M_n,p] Given two randomly chosen configurations t and s of a cellular automata of length n, find the number of transitions τ between s and t. [SDDP^δ_k,n] Given two randomly chosen configurations s of a cellular automata of length n and x of length k<n, find the configuration t such that k number of cells of t is fixed to x and t is reachable from s within δ transitions. We show that the discrete logarithm problem over the finite field reduces to DDP^M_n,p and the short integer solution problem over lattices reduces to SDDP^δ_k,n. The advantage of using such problems as the hardness assumptions in cryptographic protocols is that proving the security of the protocols requires only the reduction from these problems to the designed protocols. We design one such protocol namely a proof-of-work out of SDDP^δ_k,n.


page 1

page 2

page 3

page 4


Freezing, Bounded-Change and Convergent Cellular Automata

This paper studies three classes of cellular automata from a computation...

On the Cell-based Complexity of Recognition of Bounded Configurations by Finite Dynamic Cellular Automata

This paper studies complexity of recognition of classes of bounded confi...

An evolutionary approach to the identification of Cellular Automata based on partial observations

In this paper we consider the identification problem of Cellular Automat...

Self-stabilisation of cellular automata on tilings

Given a finite set of local constraints, we seek a cellular automaton (i...

Lower Bounds and Hardness Magnification for Sublinear-Time Shrinking Cellular Automata

The minimum circuit size problem (MCSP) is a string compression problem ...

Intrinsic Simulations and Universality in Automata Networks

An automata network (AN) is a finite graph where each node holds a state...

Please sign up or login with your details

Forgot password? Click here to reset