Dimitar Petkov Jetchev

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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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

Dimitar Petkov Jetchev

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Equidistribution of Heegner points and ternary quadratic forms

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

Cyclic Isogenies For Abelian Varieties With Real Multiplication

Isogeny graphs of ordinary abelian varieties

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

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

Liftings of reduction maps for quaternion algebras

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