Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Two general schemes of algebraic cryptography

Two general schemes of algebraic cryptography AbstractIn this paper, we introduce two general schemes of algebraic cryptography.We show that many of the systems and protocols considered in literature that use two-sided multiplications are specific cases of the first general scheme.In a similar way, we introduce the second general scheme that joins systems and protocols based on automorphisms or endomorphisms of algebraic systems.Also, we discuss possible applications of the membership search problem in algebraic cryptanalysis.We show how an efficient decidability of the underlined membership search problem for an algebraic system chosen as the platform can be applied to show a vulnerability of both schemes.Our attacks are based on the linear or on the nonlinear decomposition method, which complete each other.We give a couple of examples of systems and protocols known in the literature that use one of the two introduced schemes with their cryptanalysis.Mostly, these protocols simulate classical cryptographic schemes, such as Diffie–Hellman, Massey–Omura and ElGamal in algebraic setting.Furthermore, we show that, in many cases, one can break the schemes without solving the algorithmic problems on which the assumptions are based. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

Two general schemes of algebraic cryptography

Groups Complexity Cryptology , Volume 10 (2): 16 – Nov 1, 2018

Loading next page...
 
/lp/de-gruyter/two-general-schemes-of-algebraic-cryptography-sAo6qssomd
Publisher
de Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6104
eISSN
1869-6104
DOI
10.1515/gcc-2018-0009
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper, we introduce two general schemes of algebraic cryptography.We show that many of the systems and protocols considered in literature that use two-sided multiplications are specific cases of the first general scheme.In a similar way, we introduce the second general scheme that joins systems and protocols based on automorphisms or endomorphisms of algebraic systems.Also, we discuss possible applications of the membership search problem in algebraic cryptanalysis.We show how an efficient decidability of the underlined membership search problem for an algebraic system chosen as the platform can be applied to show a vulnerability of both schemes.Our attacks are based on the linear or on the nonlinear decomposition method, which complete each other.We give a couple of examples of systems and protocols known in the literature that use one of the two introduced schemes with their cryptanalysis.Mostly, these protocols simulate classical cryptographic schemes, such as Diffie–Hellman, Massey–Omura and ElGamal in algebraic setting.Furthermore, we show that, in many cases, one can break the schemes without solving the algorithmic problems on which the assumptions are based.

Journal

Groups Complexity Cryptologyde Gruyter

Published: Nov 1, 2018

References