Publications by Dimitar Petkov Jetchev

Revisiting Key Decomposition Techniques for FHE: Simpler, Faster and More Generic

Ring-LWE based homomorphic encryption computations in large depth use a combination of two techniques: 1) decomposition of big numbers into small limbs/digits, and 2) efficient cyclotomic multiplications modulo XN+1. It was long believed that the two mecha ...

Springer2025

Cyclic Isogenies For Abelian Varieties With Real Multiplication

Dimitar Petkov Jetchev, Alina Dudeanu, Marius Lorenz Vuille

We study quotients of principally polarized abelian varieties with real multiplication by finite Galois-stable subgroups and describe when these quotients are principally polarizable. We use this character-ization to provide an algorithm to compute explici ...

INDEPENDENT UNIV MOSCOW-IUM2022

CHIMERA: Combining Ring-LWE-based Fully Homomorphic Encryption Schemes

Dimitar Petkov Jetchev

This paper proposes a practical hybrid solution for combining and switching between three popular Ring-LWE-based FHE schemes: TFHE, B/FV and HEAAN. This is achieved by first mapping the different plaintext spaces to a common algebraic structure and then by ...

WALTER DE GRUYTER GMBH2020

Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski

POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN2019

Isogeny graphs of ordinary abelian varieties

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms

Dimitar Petkov Jetchev, Joppe Willem Bos, Alina Dudeanu

De Gruyter, Walter de Gruyter GmbH2014

Liftings of reduction maps for quaternion algebras

Dimitar Petkov Jetchev

We construct liftings of reduction maps from complex multiplication (CM) points to supersingular points for general quaternion algebras and use these liftings to establish a precise correspondence between CM points on indefinite quaternion algebras with a ...

Oxford University Press2013

Hardness of Computing Individual Bits for One-way Functions on Elliptic Curves

Dimitar Petkov Jetchev, Alexandre Raphaël Duc

We prove that if one can predict any of the bits of the input to an elliptic curve based one-way function over a finite field, then we can invert the function. In particular, our result implies that if one can predict any of the bits of the input to a clas ...

Springer2012

Equidistribution of Heegner points and ternary quadratic forms

Dimitar Petkov Jetchev

We prove new equidistribution results for Galois orbits of Heegner points with respect to single reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution ...

Springer Verlag2011