On Noncommutative Cryptography and  homomorphism of stable cubical multivariate transformation groups of infinite dimensional affine spaces

V.  Ustimenko; M.  Klisowski

Paper 2019/593

On Noncommutative Cryptography and homomorphism of stable cubical multivariate transformation groups of infinite dimensional affine spaces

V. Ustimenko and M. Klisowski

Abstract

Noncommutative cryptography is based on applications of algebraic structures like noncommutative groups, semigroups and non-commutative rings. Its inter-section with Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined overfinite commutative rings. Efficiently computed homomorphisms between stable subsemigroups of affine Cremona semigroups can be used in tame homomorphisms protocols schemes and their inverse versions. The implementation scheme with the sequence of subgroups of affine Cremona group, which defines projective limit was already suggested. We present the implementation of other scheme which uses two projective limits which define two different infinite groups and the homomorphism between them. The security of corresponding algorithm is based on a complexity of decomposition problem for an element of affine Cremona semigroup into product of given generators. These algorithms may be used in postquantum technologies.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint. MINOR revision.
Keywords: Multivariate Cryptography stable transformation groups and semigroups wild and tame families of transformations tame homomorphisms key exchange protocols cryptosystems algebraic graphs.
Contact author(s): vasyl @ hektor umcs lublin pl
mklisow @ hektor umcs lublin pl
History: 2019-06-02: received
Short URL: https://ia.cr/2019/593
License: CC BY

BibTeX

@misc{cryptoeprint:2019/593,
      author = {V.  Ustimenko and M.  Klisowski},
      title = {On Noncommutative Cryptography and  homomorphism of stable cubical multivariate transformation groups of infinite dimensional affine spaces},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/593},
      year = {2019},
      url = {https://eprint.iacr.org/2019/593}
}