<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, we propose a new method of Diffie-Hellman key exchange based on a non-commutative integral closure ring. The key idea of our proposal is that for a given non-commutative ring, we can define the secret key and take it as a common key to encrypt and decrypt the transmitted messages. By doing, we define a new non-commutative structure over the integral closure O<sub>L</sub> of sextic extension L, namely L is an extension of ℚ of degree 6 in the form ℚ(α, β), which is a rational quadratic and monogenic extension over a non-pure and monogenic cubic subfield K = ℚ(β).</p></abstract>

In this paper, we propose a new method of Diffie-Hellman key exchange based on a non-commutative integral closure ring. The key idea of our proposal is that for a given non-commutative ring, we can define the secret key and take it as a common key to encrypt and decrypt the transmitted messages. By doing, we define a new non-commutative structure over the integral closure OL of sextic extension L, namely L is an extension of ℚ of degree 6 in the form ℚ(α, β), which is a rational quadratic and monogenic extension over a non-pure and monogenic cubic subfield K = ℚ(β).

Key Exchange Over Particular Algebraic Closure Ring

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Key Exchange Over Particular Algebraic Closure Ring"}

In this paper, we propose a new method of Diffie-Hellman key exchange based on a non-commutative integral closure ring. The key idea of our proposal is that...

Key Exchange Over Particular Algebraic Closure Ring

Published Online: Mar 23, 2018

Page range: 151 - 162

Received: Mar 25, 2017

DOI: https://doi.org/10.1515/tmmp-2017-0024

Keywords
integral basis, key exchange, fully homomorphic cryptosystems, cryptography

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Key Exchange Over Particular Algebraic Closure Ring

Published Online: Mar 23, 2018

Page range: 151 - 162

Received: Mar 25, 2017

DOI: https://doi.org/10.1515/tmmp-2017-0024

Keywordsintegral basis, key exchange, fully homomorphic cryptosystems, cryptography

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
integral basis, key exchange, fully homomorphic cryptosystems, cryptography