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Efficient Evaluation of Low Degree Multivariate Polynomials in Ring-LWE Homomorphic Encryption Schemes
homomorphic encryption efficient polynomial evaluation ring lwe
2018/6/27
Homomorphic encryption schemes allow to perform computations over encrypted data. In schemes based on RLWE assumption the plaintext data is a ring polynomial. In many use cases of homomorphic encrypti...
Fully Homomorphic Encryption Using Multivariate Polynomials
public-key cryptography fully homomorphic encryption multivariate cryptography
2017/5/26
Efficient and secure third party computation has many practical applications in cloud computing. We develop new approach for building fully homomorphic encryption (FHE) schemes, by starting with the i...
Determining the Nonexistent Terms of Non-linear Multivariate Polynomials: How to Break Grain-128 More Efficiently
Stream ciphers Grain-128 Polynomial reduction
2017/5/15
In this paper, we propose a reduction technique that can be used to determine the density of IV terms of a complex multivariable boolean polynomial. Using this technique, we revisit the dynamic cube a...
On Functional Decomposition of Multivariate Polynomials with Differentiation and Homogenization
Functional decomposition multivariate polynomial homogeneous polynomials right factor space cryptosystem analysis
2010/11/26
In this paper, we give a theoretical analysis for the algorithms to compute functional decomposition for multivariate polynomials based on differentiation and homogenization which are proposed by Ye, ...
A Digital Signature Based on Multivariate Polynomials over Fq
digital signature multivariate polynomial multivariate algebraic equation Grö bner bases attacks NP complete problems
2010/11/2
We propose the digital signature scheme based on multivariate polynomials over finite fields in this paper. We generate the multivariate a polynomial of high degree F(X) . We construct the digital sig...
Key Agreement Protocols Based on Multivariate Polynomials over Fq
key agreement protocol multivariate polynomials Grö bner bases NP complete problems finite field
2010/10/14
In this paper we propose new key agreement protocols based on multivariate polynomials over finite field Fq. We concretely generate the multivariate polynomial F(X)\in Fq[x1,..,xn] such that F(X)=\sum...
Efficient Methods for Conversion and Solution of Sparse Systems of Low-Degree Multivariate Polynomials over GF(2) via SAT-Solvers
Algebraic Cryptanalysis logical cryptanalysis SAT solvers MQ
2008/9/18
The computational hardness of solving large systems of sparse and low-degree multivariate equations is a necessary condition for the security of most modern symmetric cryptographic schemes.Notably, mo...
An Algorithm for Finding Small Roots of Multivariate Polynomials over the Integers
Algorithm Finding Small Roots Multivariate Polynomials Integers
2008/9/10
In this paper we present a new algorithm for finding small
roots of multivariate polynomials over the integers based on lattice reduction
techniques. Our simpler heuristic method is inspired in algo...