Why you cannot even hope to use Ore algebras in cryptography

DOI10.1007/s00200-021-00493-9zbMath1469.94089OpenAlexW3126995137MaRDI QIDQ2043853

Michela Ceria, Andrea Visconti, Ferdinando Mora

Publication date: 3 August 2021

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00200-021-00493-9

zbMATH Keywords

key exchangeBuchberger reductionmultivariate Ore extensions

Mathematics Subject Classification ID

Cryptography (94A60) Data encryption (aspects in computer science) (68P25) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Ore rings, multiplicative sets, Ore localization (16U20)

Uses Software

• Plural

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-commutative Gröbner bases in algebras of solvable type
• Why you cannot even hope to use Gröbner bases in cryptography: an eternal golden braid of failures
• Non-commutative elimination in Ore algebras proves multivariate identities
• Computational ideal theory in finitely generated extension rings
• Using Gröbner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence
• Theory of non-commutative polynomials
• Valuations and filtrations
• Buchberger-Zacharias theory of multivariate Ore extensions
• Effective Buchberger-Zacharias-Weispfenning theory of skew polynomial extensions of subbilateral coherent rings
• Gröbner bases in function rings -- a guide for introducing reduction relations to algebraic structures
• Public key cryptography based on semigroup actions
• Buchberger-Weispfenning theory for effective associative rings
• De Nugis Groebnerialium 4
• Cryptanalysis of Cryptosystems Based on Non-commutative Skew Polynomials
• Cryptanalysis of Stickel’s Key Exchange Scheme
• Thompson’s Group and Public Key Cryptography
• One-sided noncommutative Gröbner bases with applications to computing Green's relations

This page was built for publication: Why you cannot even hope to use Ore algebras in cryptography