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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...
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...
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...
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, ...
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...
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...
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...
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...

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