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Period finding and phase estimation are fundamental in quantum computing. Prior work has established lower bounds on their success probabilities. Such quantum algorithms measure a state $|\hat\ell\rangle$ in an $n$-qubit computational…
Current solutions to quantum vulnerabilities of widely used cryptographic schemes involve migrating users to post-quantum schemes before quantum attacks become feasible. This work deals with protecting quantum procrastinators: users that…
Detection of planted subgraphs in Erd\"os-R\'enyi random graphs has been extensively studied, leading to a rich body of results characterizing both statistical and computational thresholds. However, most prior work assumes a purely random…
Introduced in [CG24], pseudorandom error-correcting codes (PRCs) are a new cryptographic primitive with applications in watermarking generative AI models. These are codes where a collection of polynomially many codewords is computationally…
We introduce a novel post-quantum sanitizable signature scheme constructed upon a chameleon hash function derived from the McEliece cryptosystem. In this design, the designated sanitizer possesses the inherent trapdoor of a Goppa code,…
We report experimental generation of a noisy entangled four-photon state that exhibits a separation between the secure key contents and distillable entanglement, a hallmark feature of the recently established quantum theory of private…
In this thesis, we study algebraic coding theory based McEliece-type cryptosystems over quasi-cyclic codes. The main goal of this thesis is to construct a cryptosystem that resists quantum Fourier sampling making it quantum secure. We…
Entangled states of photons form the backbone of many quantum technologies. Due to the lack of effective photon-photon interactions, the generation of these states is typically probabilistic. In the prevailing but fundamentally limited…
One of the most fundamental problems in distribution testing is the identity testing problem: given samples $x_1,\ldots,x_s$, the goal is to determine whether the samples are drawn from a target distribution $\mathcal{D}$. When…
In this paper, we study the behavior of the true dimension of the subfield subcodes of Hermitian codes. Our motivation is to use these classes of linear codes to improve the parameters of the McEliece cryptosystem, such that key size and…
The Discrete Logarithm Problem is well-known among cryptographers, for its computational hardness that grants security to some of the most commonly used cryptosystems these days. Still, many of these are limited to a small number of…
We bring in here a novel algebraic approach for attacking the McEliece cryptosystem. It consists in introducing a subspace of matrices representing quadratic forms. Those are associated with quadratic relationships for the component-wise…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
Due to recent development in quantum computing, the invention of a large quantum computer is no longer a distant future. Quantum computing severely threatens modern cryptography, as the hard mathematical problems beneath classic public-key…
We propose variations of the class of hidden monomial cryptosystems in order to make it resistant to all known attacks. We use identities built upon a single bivariate polynomial equation with coefficients in a finite field. Indeed, it can…
We analyze the security of quantum cryptography schemes for $d$-level systems using 2 or $d+1$ maximally conjugated bases, under individual eavesdropping attacks based on cloning machines and measurement after the basis reconciliation. We…
Entanglement represents an important resource for quantum information processing, but its generation itself requires physical resources that are limited. We propose a scheme for generating a wide class of entangled qudit-type states of…
Postselected quantum computation is distinguished from regular quantum computation by accepting the output only if measurement outcomes satisfy predetermined conditions. The output must be accepted with nonzero probability. Methods for…
Differentially private data generation techniques have become a promising solution to the data privacy challenge -- it enables sharing of data while complying with rigorous privacy guarantees, which is essential for scientific progress in…
Quantum computing technologies pose a significant threat to the currently employed public-key cryptography protocols. In this paper, we discuss the impact of the quantum threat on public key infrastructures (PKIs), which are used as a part…