We design a linearly homomorphic encryption scheme whose security relies on the
hardness of the decisional Diffie-Hellman problem. Our approach requires some special …

We introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of
the associated oriented and nonoriented ℓ-isogeny supersingular isogeny graphs. As an …

Nowadays, since modern cryptography deals with careful modeling and careful proofs, there
may be two levels of cryptanalysis. One, the traditional breaking or weakness demonstration …

We describe the first polynomial time chosen-plaintext total break of the NICE family of
cryptosystems based on ideal arithmetic in imaginary quadratic orders, introduced in the late …

We present a new algorithm based on binary quadratic forms to factor integers of the form
N= pq 2. Its heuristic running time is exponential in the general case, but becomes …

This paper gives an overview of the state of art in cryptography based on quadratic orders. It
discusses the intractable problems in class groups and the infrastructure of quadratic orders …

In this paper, we investigate the rough order assumption (\(RO_C\)) introduced by Braun,
Damgård, and Orlandi at CRYPTO 23, which posits that class groups of imaginary quadratic …

One of the current challenges in cryptographic research is the development of advanced
cryptographic primitives ensuring a high level of confidence. In this thesis, we focus on their …

This paper introduces an algorithm to efficiently break the Decisional Diffie-Hellman (DDH)
assumption in totally non-maximal imaginary quadratic orders, specifically when $\Delta_1 …

We discuss the discrete logarithm problem over the class group Cl (Δ) of an imaginary
quadratic order \calO_Δ, which was proposed as a public-key cryptosystem by Buchmann …