A New Heuristic Algorithm Based on Molecular Geometry Optimization and Its Application to the Integer Factorization Problem

2014 ◽  
Author(s):  
Mohit Mishraa ◽  
Utkarsh Chaturvedib ◽  
K.K. Shukla
Keyword(s):  
Heuristic Algorithm ◽  
Geometry Optimization ◽  
Molecular Geometry ◽  
Integer Factorization ◽  
Factorization Problem ◽  
Molecular Geometry Optimization ◽  
Integer Factorization Problem

Reduction of the integer factorization complexity upper bound to the complexity of the Diffie–Hellman problem

2021 ◽  
Vol 31 (1) ◽  
pp. 1-4
Author(s):  
Mikhail A. Cherepnev
Keyword(s):  
Upper Bound ◽  
Polynomial Algorithm ◽  
Integer Factorization ◽  
Factorization Problem ◽  
Diffie Hellman ◽  
Integer Factorization Problem

Abstract We construct a probabilistic polynomial algorithm that solves the integer factorization problem using an oracle solving the Diffie–Hellman problem.

scholarly journals Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lize Gu ◽  
Shihui Zheng
Keyword(s):  
Performance Analysis ◽  
Quantum Algorithm ◽  
Integer Factorization ◽  
Algebraic Structures ◽  
Cryptographic Primitives ◽  
Factorization Problem ◽  
Integer Factorization Problem ◽  
Modern Cryptography ◽  
Nonabelian Groups

To resist known quantum algorithm attacks, several nonabelian algebraic structures mounted upon the stage of modern cryptography. Recently, Baba et al. proposed an important analogy from the integer factorization problem to the factorization problem over nonabelian groups. In this paper, we propose several conjugated problems related to the factorization problem over nonabelian groups and then present three constructions of cryptographic primitives based on these newly introduced conjugacy systems: encryption, signature, and signcryption. Sample implementations of our proposal as well as the related performance analysis are also presented.

scholarly journals Connections on Valuated Binary Tree and Their Applications in Factoring Odd Integers

2021 ◽  
pp. 134-153
Author(s):  
Xingbo Wang ◽  
Jinfeng Luo ◽  
Ying Tian ◽  
Li Ma
Keyword(s):  
Binary Tree ◽  
Numerical Experiments ◽  
Mathematical Reasoning ◽  
Binary Trees ◽  
Integer Factorization ◽  
Parallel Connection ◽  
Central Lines ◽  
Factorization Problem ◽  
Integer Factorization Problem

This paper makes an investigation on geometric relationships among nodes of the valuated binary trees, including parallelism, connection and penetration. By defining central lines and distance from a node to a line, some intrinsic connections are discovered to connect nodes between different subtrees. It is proved that a node out of a subtree can penetrate into the subtree along a parallel connection. If the connection starts downward from a node that is a multiple of the subtree’s root, then all the nodes on the connection are multiples of the root. Accordingly composite odd integers on such connections can be easily factorized. The paper proves the new results with detail mathematical reasoning and demonstrates several numerical experiments made with Maple software to factorize rapidly a kind of big odd integers that are of the length from 59 to 99 decimal digits. It is once again shown that the valuated binary tree might be a key to unlock the lock of the integer factorization problem.

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