A polynomial-time reduction from bivariate to univariate integral polynomial factorization

1982 ◽  
Author(s):  
Erich Kaltofen
Keyword(s):  
Polynomial Time ◽  
Polynomial Factorization ◽  
Integral Polynomial ◽  
Time Reduction ◽  
Polynomial Time Reduction

scholarly journals On compact k-edge-colorings: A polynomial time reduction from linear to cyclic

2011 ◽  
Vol 8 (3) ◽  
pp. 502-512 ◽  
Author(s):  
Sivan Altinakar ◽  
Gilles Caporossi ◽  
Alain Hertz
Keyword(s):  
Polynomial Time ◽  
Edge Colorings ◽  
Time Reduction ◽  
Polynomial Time Reduction

scholarly journals Strong isomorphism reductions in complexity theory

2011 ◽  
Vol 76 (4) ◽  
pp. 1381-1402 ◽  
Author(s):  
Sam Buss ◽  
Yijia Chen ◽  
Jörg Flum ◽  
Sy-David Friedman ◽  
Moritz Müller
Keyword(s):  
Computational Complexity ◽  
Complexity Theory ◽  
Polynomial Time ◽  
Systematic Study ◽  
Maximal Element ◽  
General Setting ◽  
Partial Ordering ◽  
Time Reduction ◽  
Polynomial Time Reduction

AbstractWe give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classes of structures based on purely comparing for every n the number of nonisomorphic structures of cardinality at most n in both classes. Furthermore, in a more general setting we address the question of the existence of a maximal element in the partial ordering of the degrees.

scholarly journals A polynomial-time reduction algorithm for groups of semilinear or subfield class

2009 ◽  
Vol 322 (3) ◽  
pp. 613-637 ◽  
Author(s):  
Jon F. Carlson ◽  
Max Neunhöffer ◽  
Colva M. Roney-Dougal
Keyword(s):  
Polynomial Time ◽  
Reduction Algorithm ◽  
Time Reduction ◽  
Polynomial Time Reduction

scholarly journals A Polynomial-Time Reduction from the 3SAT Problem to the Generalized String Puzzle Problem

Algorithms ◽  
2012 ◽  
Vol 5 (2) ◽  
pp. 261-272 ◽  
Author(s):  
Chuzo Iwamoto ◽  
Kento Sasaki ◽  
Kenichi Morita
Keyword(s):  
Polynomial Time ◽  
Time Reduction ◽  
Polynomial Time Reduction

scholarly journals MPF Problem over Modified Medial Semigroup Is NP-Complete

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 571 ◽  
Author(s):  
Eligijus Sakalauskas ◽  
Aleksejus Mihalkovich
Keyword(s):  
Power Function ◽  
Polynomial Time ◽  
Cryptographic Protocols ◽  
Binary Field ◽  
Dual Interpretation ◽  
Np Complete ◽  
Matrix Power ◽  
Necessary Constraints ◽  
One Way Function ◽  
Polynomial Time Reduction

This paper is a continuation of our previous publication of enhanced matrix power function (MPF) as a conjectured one-way function. We are considering a problem introduced in our previous paper and prove that tis problem is NP-Complete. The proof is based on the dual interpretation of well known multivariate quadratic (MQ) problem defined over the binary field as a system of MQ equations, and as a general satisfiability (GSAT) problem. Due to this interpretation the necessary constraints to MPF function for cryptographic protocols construction can be added to initial GSAT problem. Then it is proved that obtained GSAT problem is NP-Complete using Schaefer dichotomy theorem. Referencing to this result, GSAT problem by polynomial-time reduction is reduced to the sub-problem of enhanced MPF, hence the latter is NP-Complete as well.

A certain family of subgroups of ℤ𝑛 ⋆ is weakly pseudo-free under the general integer factoring intractability assumption

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Mikhail Anokhin
Keyword(s):  
Polynomial Time ◽  
Random Number ◽  
Abelian Groups ◽  
Computable Function ◽  
Security Parameter ◽  
Odd Order ◽  
The Family ◽  
Uniform Probability Distribution ◽  
Probabilistic Polynomial Time ◽  
Polynomial Time Reduction

Abstract Let {\mathbb{G}_{n}} be the subgroup of elements of odd order in the group {\mathbb{Z}^{\star}_{n}} , and let {\mathcal{U}(\mathbb{G}_{n})} be the uniform probability distribution on {\mathbb{G}_{n}} . In this paper, we establish a probabilistic polynomial-time reduction from finding a nontrivial divisor of a composite number n to finding a nontrivial relation between l elements chosen independently and uniformly at random from {\mathbb{G}_{n}} , where {l\geq 1} is given in unary as a part of the input. Assume that finding a nontrivial divisor of a random number in some set N of composite numbers (for a given security parameter) is a computationally hard problem. Then, using the above-mentioned reduction, we prove that the family {((\mathbb{G}_{n},\mathcal{U}(\mathbb{G}_{n}))\mid n\in N)} of computational abelian groups is weakly pseudo-free. The disadvantage of this result is that the probability ensemble {(\mathcal{U}(\mathbb{G}_{n})\mid n\in N)} is not polynomial-time samplable. To overcome this disadvantage, we construct a polynomial-time computable function {\nu\colon D\to N} (where {D\subseteq\{0,1\}^{*}} ) and a polynomial-time samplable probability ensemble {(\mathcal{G}_{d}\mid d\in D)} (where {\mathcal{G}_{d}} is a distribution on {\mathbb{G}_{\nu(d)}} for each {d\in D} ) such that the family {((\mathbb{G}_{\nu(d)},\mathcal{G}_{d})\mid d\in D)} of computational abelian groups is weakly pseudo-free.

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