Two general schemes of algebraic cryptography
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Vitaly Roman’kov
Abstract
In 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.
Funding source: Russian Science Foundation
Award Identifier / Grant number: 16-11-10002
Funding statement: This research was supported by Russian Science Foundation, project 16-11-10002.
Acknowledgements
The author is indebted to the reviewer for useful comments.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Groups whose word problems are not semilinear
- On finitely generated submonoids of virtually free groups
- Two general schemes of algebraic cryptography
- A certain family of subgroups of ℤ𝑛⋆ is weakly pseudo-free under the general integer factoring intractability assumption
- Recognition of 2-dimensional projective linear groups by the group order and the set of numbers of its elements of each order
Articles in the same Issue
- Frontmatter
- Groups whose word problems are not semilinear
- On finitely generated submonoids of virtually free groups
- Two general schemes of algebraic cryptography
- A certain family of subgroups of ℤ𝑛⋆ is weakly pseudo-free under the general integer factoring intractability assumption
- Recognition of 2-dimensional projective linear groups by the group order and the set of numbers of its elements of each order
