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A public key cryptosystem based on diophantine equations of degree increasing type

A public key cryptosystem based on diophantine equations of degree increasing type In this paper we propose a new public key cryptosystem based on diophantine equations which we call of degree increasing type. We use an analogous method to the “Algebraic Surface Cryptosystem” (ASC) proposed by Akiyama, Goto and Miyake. There are two main differences between our cryptosystem and ASC. One of them is to twist a plaintext by using some modular arithmetic to increase the number of candidates of the plaintext in order to complicate finding the correct plaintext. Another difference is to use a polynomial of degree increasing type to recover the plaintext uniquely even if the plaintext was twisted. Although we have not been able to give a security proof, we give some discussions on how secure our cryptosystem is against known attacks including the ideal decomposition attack, which can break the one‐wayness of ASC. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Pacific Journal of Mathematics for Industry Springer Journals

A public key cryptosystem based on diophantine equations of degree increasing type

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References (42)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Okumura; licensee Springer.
Subject
Mathematics; Applications of Mathematics; Quantitative Finance; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematical Modeling and Industrial Mathematics; Math Applications in Computer Science
eISSN
2198-4115
DOI
10.1186/s40736-015-0014-4
Publisher site
See Article on Publisher Site

Abstract

In this paper we propose a new public key cryptosystem based on diophantine equations which we call of degree increasing type. We use an analogous method to the “Algebraic Surface Cryptosystem” (ASC) proposed by Akiyama, Goto and Miyake. There are two main differences between our cryptosystem and ASC. One of them is to twist a plaintext by using some modular arithmetic to increase the number of candidates of the plaintext in order to complicate finding the correct plaintext. Another difference is to use a polynomial of degree increasing type to recover the plaintext uniquely even if the plaintext was twisted. Although we have not been able to give a security proof, we give some discussions on how secure our cryptosystem is against known attacks including the ideal decomposition attack, which can break the one‐wayness of ASC.

Journal

Pacific Journal of Mathematics for Industry – Springer Journals

Published: Jun 5, 2015

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