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 (evo...

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Vydáno v:	Mathematics (Basel) Ročník 8; číslo 12; s. 2160
Hlavní autoři:	Jiménez, Karina Paola, Gómez-Canaval, Sandra, Villanueva-Polanco, Ricardo, Suazo, Silvia Martín
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Basel MDPI AG 01.12.2020
Témata:	Adaptation bio-inspired computational model Biomimetics combinatorial optimization problems Communication cryptographic proof-of-work Cryptography massively parallel and distributed algorithms Mathematical models Mathematics multivariate quadratic equations Mutation networks of picture processors Pictures Polynomials Processors Quadratic equations Solvers Two dimensional models Valuation
ISSN:	2227-7390, 2227-7390
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Abstract	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.
AbstractList	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 fieldF2. This problem is demonstrated to be NP-hard, even with quadratic polynomials over the fieldF2, when the number of equations and the number of variables are of roughly the same size. The proposed solution runs inO(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. 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 F 2 . This problem is demonstrated to be NP-hard, even with quadratic polynomials over the field F 2 , 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. 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.
Author	Villanueva-Polanco, Ricardo Gómez-Canaval, Sandra Jiménez, Karina Paola Suazo, Silvia Martín
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SubjectTerms	Adaptation bio-inspired computational model Biomimetics combinatorial optimization problems Communication cryptographic proof-of-work Cryptography massively parallel and distributed algorithms Mathematical models Mathematics multivariate quadratic equations Mutation networks of picture processors Pictures Polynomials Processors Quadratic equations Solvers Two dimensional models Valuation
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Title	Networks of Picture Processors with Filtering Based on Evaluation Sets as Solvers for Cryptographic Puzzles Based on Random Multivariate Quadratic Equations
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