Polynomial Equivalence Problems: Algorithmic and Theoretical Aspects

DOI10.1007/11761679_3zbMath1140.94337OpenAlexW1806793453MaRDI QIDQ3593087

Jean-Charles Faugère, Ludovic Perret

Publication date: 24 September 2007

Published in: Advances in Cryptology - EUROCRYPT 2006 (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/11761679_3

zbMATH Keywords

Gröbner basescryptanalysisPublic-key cryptographyisomorphism of polynomials (IP)\(F_{5}\) algorithm

Mathematics Subject Classification ID

Cryptography (94A60)

Related Items (17)

Generalization of Isomorphism of Polynomials with Two Secrets and Its Application to Public Key Encryption ⋮ Solving the problem of blockwise isomorphism of polynomials with circulant matrices ⋮ On self-equivalence encodings in white-box implementations ⋮ Security analysis on an ElGamal-like multivariate encryption scheme based on isomorphism of polynomials ⋮ On enumeration of polynomial equivalence classes ⋮ Practical post-quantum signature schemes from isomorphism problems of trilinear forms ⋮ General linear group action on tensors: a candidate for post-quantum cryptography ⋮ Implicit white-box implementations: white-boxing ARX ciphers ⋮ Cryptanalysis of the TRMS Signature Scheme of PKC’05 ⋮ New Differential-Algebraic Attacks and Reparametrization of Rainbow ⋮ Hardness estimates of the code equivalence problem in the rank metric ⋮ Take your MEDS: digital signatures from matrix code equivalence ⋮ Algorithms Based on *-Algebras, and Their Applications to Isomorphism of Polynomials with One Secret, Group Isomorphism, and Polynomial Identity Testing ⋮ Key Recovery on Hidden Monomial Multivariate Schemes ⋮ On enumeration of polynomial equivalence classes and their application to MPKC ⋮ Determining whether a given cryptographic function is a permutation of another given cryptographic function -- a problem in intellectual property ⋮ Polynomial-time algorithms for quadratic isomorphism of polynomials: the regular case

Uses Software

• FGb

Cites Work

• Does co-NP have short interactive proofs ?
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms
• Attacking the Affine Parts of SFLASH
• Advances in Cryptology - CRYPTO 2003
• Comparison Between XL and Gröbner Basis Algorithms
• Coding and Cryptography
• Advances in Cryptology - ASIACRYPT 2003
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