<abstract xmlns="http://www.w3.org/1999/xhtml"> Families of stable cyclic groups of nonlinear polynomial transformations of affine spaces Kn over general commutative ring K of with n increasing order can be used in the key exchange protocols and El Gamal multivariate cryptosystems related to them. We suggest to use high degree of noncommutativity of affine Cremona group and modify multivariate El Gamal algorithm via conjugations of two polynomials of kind gk and g−1 given by key holder (Alice) or giving them as elements of different transformation groups. Recent results on the existence of families of stable transformations of prescribed degree and density and exponential order over finite fields can be used for the implementation of schemes as above with feasible computational complexity.</abstract>

Families of stable cyclic groups of nonlinear polynomial transformations of affine spaces Kn over general commutative ring K of with n increasing order can be used in the key exchange protocols and El Gamal multivariate cryptosystems related to them. We suggest to use high degree of noncommutativity of affine Cremona group and modify multivariate El Gamal algorithm via conjugations of two polynomials of kind gk and g−1 given by key holder (Alice) or giving them as elements of different transformation groups. Recent results on the existence of families of stable transformations of prescribed degree and density and exponential order over finite fields can be used for the implementation of schemes as above with feasible computational complexity.

On the Families of Stable Multivariate Transformations of Large Order and Their Cryptographical Applications

Tatra Mountains Mathematical Publications

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

Families of stable cyclic groups of nonlinear polynomial transformations of affine spaces Kn over general commutative ring K of with n increasing order can be...

On the Families of Stable Multivariate Transformations of Large Order and Their Cryptographical Applications

Published Online: Mar 23, 2018

Page range: 107 - 117

Received: Aug 13, 2017

DOI: https://doi.org/10.1515/tmmp-2017-0021

Keywords
Multivariate cryptography, stable transformations, key exchange protocols, shifted multivariate ElGamal algorithm, desynchronisation diagram

© 2018

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

On the Families of Stable Multivariate Transformations of Large Order and Their Cryptographical Applications

Published Online: Mar 23, 2018

Page range: 107 - 117

Received: Aug 13, 2017

DOI: https://doi.org/10.1515/tmmp-2017-0021

KeywordsMultivariate cryptography, stable transformations, key exchange protocols, shifted multivariate ElGamal algorithm, desynchronisation diagram

© 2018

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

Keywords
Multivariate cryptography, stable transformations, key exchange protocols, shifted multivariate ElGamal algorithm, desynchronisation diagram