New candidates for multivariate trapdoor functions and new multivariate public key encryption schemes

Abstract: In this thesis we present a new method for building pairs of HFE1 polynomials of high degree, in such a way that the map constructed with this pair is easy to invert. The inversion is accomplished using a low degree polynomial of Hamming weight three, which is derived from a special reduction via Hamming weight three polynomials produced by these two HFE polynomials. This allows us to build new candidates for multivariate trapdoor functions in which we use the pair of HFE polynomials to fabricate the core map. Using this new multivariate trapdoor function we derive an encryption scheme in a similar way as the HFE scheme is created. We show that this encryption scheme is relatively efficient and that it resists the attacks that have threatened the security of HFE. Finally, we propose parameters for a practical implementation of our cryptosystem.

• Autores: Porras Barrera, Jaiberth
• Tipo de recurso: Doctoral thesis
• Fecha de publicación: 2014
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/21674
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/21674; http://bdigital.unal.edu.co/12643/
• Palabra clave: 51 Matemáticas / Mathematics; Polynomials; Low degree polynomial; Polynomial of Hamming; HFE polynomials; Cryptosystem; Polinomios HFE; Polinomios; Polinomio de grado bajo; Polinomios de peso de Hamming; Criptosistema
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional