31 citations · 42 across the 6 of their papers we have counts for
6 papers
Polynomial-time computing over quadratic maps I: sampling in real algebraic sets
Dima Grigoriev, Dmitrii V. Pasechnik
Given a quadratic map Q : K^n -> K^k defined over a computable subring D of a real closed field K, and a polynomial p(Y_1,...,Y_k) of degree d, we consider the zero set Z=Z(p(Q(X))…
Weak Bezout inequality for D-modules
Dima Grigoriev
Let be linear partial differential operato…
Homomorphic public-key cryptosystems over groups and rings
Dima Grigoriev, Ilia Ponomarenko
We propose a new homomorphic public-key cryptosystem over arbitrary nonidentity finite group based on the difficulty of the membership problem for groups of integer matrices. Besid…
Homomorphic public-key cryptosystems and encrypting boolean circuits
Dima Grigoriev, Ilia Ponomarenko
In this paper homomorphic cryptosystems are designed for the first time over any finite group. Applying Barrington's construction we produce for any boolean circuit of the logarith…
Public-key cryptography and invariant theory
D. Grigoriev
Public-key cryptosystems are suggested based on invariants of groups. We give also an overview of the known cryptosystems which involve groups.
On non-abelian homomorphic public-key cryptosystems
D. Grigoriev, I. Ponomarenko
An important problem of modern cryptography concerns secret public-key computations in algebraic structures. We construct homomorphic cryptosystems being (secret) epimorphisms f:G…