Multivariate public key cryptosystems from Diophantine equations

DOI10.1007/s10623-011-9582-1zbMath1286.94068OpenAlexW2159343703MaRDI QIDQ1936497

Shuhong Gao, Raymond Heindl

Publication date: 5 February 2013

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-011-9582-1

zbMATH Keywords

Gröbner basispolynomial identitymultivariate public key cryptosystemoil-vinegar system

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Uses Software

• FGb
• Magma

Cites Work

• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• The Magma algebra system. I: The user language
• Rainbow, a New Multivariable Polynomial Signature Scheme
• A public key system with signature and master key functions
• Unbalanced Oil and Vinegar Signature Schemes
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Information Security and Privacy
• Public Key Cryptography - PKC 2005
• High Order Linearization Equation (HOLE) Attack on Multivariate Public Key Cryptosystems
• ℓ-Invertible Cycles for $\mathcal{M}$ ultivariate $\mathcal{Q}$ uadratic ( ${\mathcal{MQ}}$ ) Public Key Cryptography
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item