Chiara Marcolla

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• PhD
• Lead Cryptographer at Technology Innovation Institute

For any affine-variety code we show how to construct an ideal whose solutions correspond to codewords with any assigned weight. We are able to obtain geometric characterizations for small-weight codewords for some families of Hermitian codes over any F_{q^2}. From these geometric characterizations, we obtain explicit formulas. In particular, we det...

In this paper we present a geometrical characterization for the minimum-weight codewords of the Hermitian codes over the fields Fq2 in the third and fourth phase, namely with distance d > q^2 - q-1. We consider the unique writing uq + l(q + 1) of the distance d with u,l non negative integers, and u<q+1, and prove that the minimum-weight codewords c...

Data privacy concerns are increasing significantly in the context of Internet of Things, cloud services, edge computing, artificial intelligence applications, and other applications enabled by next-generation networks. Homomorphic Encryption addresses privacy challenges by enabling multiple operations to be performed on encrypted messages without d...

Fully Homomorphic Encryption (FHE) is a groundbreaking technology that allows for arbitrary computations to be performed on encrypted data. State-of-the-art schemes such as Brakerski Gentry Vaikuntanathan (BGV) are based on the Learning with Errors over rings (RLWE) assumption, and each ciphertext has an associated error that grows with each homomo...

The Brakerski/Fan-Vercauteren (BFV) scheme is a state-of-the-art scheme in Fully Homomorphic Encryption based on the Ring Learning with Errors (RLWE) problem. Thus, ciphertexts contain an error that increases with each homomorphic operation and has to stay below a certain threshold for correctness. This can be achieved by setting the ciphertext mo...

In this work, we introduce FANNG-MPC, a versatile secure multi-party computation framework capable to offer active security for privacy-preserving machine learning as a service (MLaaS). Derived from the now deprecated SCALE-MAMBA, FANNG is a data-oriented fork, featuring novel set of libraries and instructions for realizing private neural networks,...

The field of fully homomorphic encryption (FHE) has seen many theoretical and computational advances in recent years, bringing the technology closer to practicality than ever before. For this reason, practitioners in related fields, such as machine learning, are increasingly interested in using FHE to provide privacy to their applications. Despite...

The Brakerski–Gentry–Vaikuntanathan (BGV) scheme is a Fully Homomorphic Encryption (FHE) cryptosystem based on the Ring Learning With Error (RLWE) problem. Ciphertexts in this scheme contain an error term that grows with operations and causes decryption failure when it surpasses a certain threshold. Consequently, the parameters of BGV need to be es...

The field of Fully Homomorphic Encryption (FHE) has seen many theoretical and computational advances in recent years, bringing the technology closer to practicality than ever before. For this reason, practitioners from neighbouring fields such as machine learning have sought to understand FHE to provide privacy to their work. Unfortunately, selecti...

In this work, we introduce FANNG-MPC, a versatile secure multi-party computation framework capable to offer active security for privacy-preserving machine learning as a service (MLaaS). Derived from the now deprecated SCALE-MAMBA, FANNG is a data-oriented fork, featuring novel set of libraries and instructions for realizing private neural networks,...

Fully Homomorphic Encryption (FHE) is a groundbreaking technology that allows for arbitrary computations to be performed on encrypted data. State-of-the-art schemes such as Brakerski Gentry Vaikuntanathan (BGV) are based on the Learning with Errors over rings (RLWE) assumption where each ciphertext has an associated error that grows with each homom...

The Brakerski-Gentry-Vaikuntanathan (BGV) scheme is a Fully Homomorphic Encryption (FHE) cryptosystem based on the Ring Learning With Error (RLWE) problem. Ciphertexts in this scheme contain an error term that grows with operations and causes decryption failure when it surpasses a certain threshold. For this reason, the parameters of BGV need to be...

This paper comprehensively addresses homomorphic encryption from both theoretical and practical perspectives. The paper delves into the mathematical foundations required to understand fully homomorphic encryption FHE. It consequently covers design fundamentals and security properties of FHE, and describes the main FHE schemes based on various mathe...

Data privacy concerns are increasing significantly in the context of the Internet of Things, cloud services, edge computing, artificial intelligence applications, and other applications enabled by next-generation networks. Homomorphic encryption addresses privacy challenges by enabling multiple operations to be performed on encrypted messages witho...

This paper comprehensively addresses homomorphic encryption from both theoretical and practical perspectives. The paper delves into the mathematical foundations required to understand fully homomorphic encryption FHE. It consequently covers design fundamentals and security properties of FHE, and describes the main FHE schemes based on various mathe...

This paper comprehensively addresses homomorphic encryption from both theoretical and practical perspectives. The paper delves into the mathematical foundations required to understand fully homomorphic encryption FHE. It consequently covers design fundamentals and security properties of FHE, and describes the main FHE schemes based on various mathe...

This paper comprehensively addresses homomorphic encryption from both theoretical and practical perspectives. The paper delves into the mathematical foundations required to understand fully homomorphic encryption FHE. It consequently covers design fundamentals and security properties of FHE, and describes the main FHE schemes based on various mathe...

This paper comprehensively addresses homomorphic encryption from both theoretical and practical perspectives. The paper delves into the mathematical foundations required to understand fully homomorphic encryption FHE. It consequently covers design fundamentals and security properties of FHE, and describes the main FHE schemes based on various mathe...

Multiple approaches have been developed to address data privacy concerns, as cloud services increasingly gain traction. One of these methods is Searchable Encryption (SE), which enables a user to search over encrypted data. When applied to a dynamic dataset, it is important that SE achieves two essential properties upon updating a dynamic dataset:...

Multiple approaches have been developed to address data privacy concerns, as cloud services increasingly gain traction. One of these methods is Searchable Encryption (SE), which enables a user to search over encrypted data. When applied to a dynamic dataset, it is important that SE achieves two essential properties upon updating a dynamic dataset:...

In this work, we propose different techniques that can be used to implement the rank-based key encapsulation methods and public key encryption schemes of the ROLLO, and partially RQC, family of algorithms in a standalone, efficient and constant time library. For simplicity, we focus our attention on one specific instance of this family, ROLLO-I-128...

In addition to their usefulness in proving one’s identity electronically, identification protocols based on zero-knowledge proofs allow designing secure cryptographic signature schemes by means of the Fiat–Shamir transform or other similar constructs. This approach has been followed by many cryptographers during the NIST (National Institute of Stan...

The study of new error correcting codes has raised attention in the last years, especially because of their use in cryptosystems that are resistant to attacks running on quantum computers. In 2006, while leaving a more in-depth analysis for future research, Stakhov gave some interesting ideas on how to exploit Fibonacci numbers to derive an origina...

In this work, we propose different techniques that can be used to implement the ROLLO, and partially RQC, family of algorithms in a standalone, efficient and constant time library. For simplicity, we focus our attention on one specific instance of this family, ROLLO-I-128. For each of these techniques, we present explicit code (with intrinsics when...

The study of new error correcting codes has raised attention in the last years, especially because of their use in cryptosystems that are resistant to attacks running on quantum computers. In 2006, while leaving a more in-depth analysis for future research, Stakhov gave some interesting ideas on how to exploit Fibonacci numbers to derive an origina...

In this paper we present a geometrical characterization for the minimum-weight codewords of the Hermitian codes over the fields $\FQ$ in the third and fourth phase, namely with distance $d \geq q^2-q$. \\ % We consider the unique writing $ \mu q + \lambda (q+1)$ of the distance $d$ with $\mu, \lambda$ non negative integers, and $\mu \leq q$, and pr...

Let $\mathcal{H}$ be the Hermitian curve defined over a finite field $\mathbb{F}_{q^2}$. Aim of the present paper is to complete the geometrical characterization of the supports of the minimum-weight codewords of the algebraic-geometry codes over H, started in [1]. In that paper we considered the codes with distance $d \geq q^2-q$ and proved that t...

rchitectures relying on a single central authority often offer a great efficiency but suffer of resiliency problems and are quite vulnerable to attacks. In our proposal, a Multiple-Authorities Key-Policy Attribute-Based Encryption scheme is constructed in which the authorities collaborate to achieve shorter keys and parameters, enhancing the effici...

Let $\mathcal{H}$ be the Hermitian curve defined over a finite field $\mathbb{F}_{q^2}$. In this paper we complete the geometrical characterization of the supports of the minimum-weight codewords of the algebraic-geometry codes over $\mathcal{H}$, started in [1]: if $d$ is the distance of the code, the supports are all the sets of $d$ distinct $\ma...

We study the locally recoverable codes on algebraic curves. In the first part of this article, we provide a bound of generalized Hamming weight of these codes. Whereas in the second part, we propose a new family of algebraic geometric LRC codes, that are LRC codes from Norm-Trace curve. Finally, using some properties of Hermitian codes, we improve...

Bilinear groups are often used to create Attribute-Based Encryption (ABE) algorithms. In particular, they have been used to create an ABE system with multi authorities, but limited to the ciphertext-policy instance. Here, for the first time, we propose a multi-authority key-policy ABE system. In our proposal, the authorities may be set up in any mo...

Bilinear groups are often used to create Attribute-Based Encryption (ABE) algo-rithms. In particular, they have been used to create an ABE system with multi authorities, but limited to the ciphertext-policy instance. Here, for the first time, we propose two multi-authority key-policy ABE systems. In our first proposal, the authorities may be set up...

The correctness in decrypting a ciphertext after some operations in the DGVH scheme depends heavily on the dimension of the secret key. In this paper we compute two bounds on the size of the secret key for the DGHV scheme to decrypt correctly a ciphertext after a fixed number of additions and a fixed number of multiplication. Moreover we improve th...

We classify completely the intersections of the Hermitian curve with parabolas in the affine plane. To obtain our results we employ well-known algebraic methods for finite fields and geometric properties of the curve automorphisms. In particular, we provide explicit counting formulas that have also applications to some Hermitian codes.

For any affine-variety code we show how to construct an ideal whose solutions cor-respond to codewords with any assigned weight. We are able to obtain geometric characterizations for small-weight codewords for some families of Hermitian codes over any F_{q^2} . From these geometric characterizations, we obtain explicit formulas. In particular, we d...

We classify completely the intersections of the Hermitian curve with parabolas in the affine plane. To obtain our results we employ well-known algebraic methods for finite fields and geometric properties of the curve automorphisms. In particular, we provide explicit counting formulas that have also applications to some Hermitian codes.

For any affine-variety code we show how to construct an ideal whose solutions correspond to codewords with any assigned weight. We classify completely the intersections of the Hermitian curve with lines and parabolas (in the $\mathbb{F}_{q^2}$ affine plane). Starting from both results, we are able to obtain geometric characterizations for small-wei...

We investigate the geometry of the support of small weight codewords of dual algebraic geometric codes on smooth complete intersections by applying the powerful tools recently developed by Alain Couvreur. In particular, by restricting ourselves to the case of Hermitian codes, we recover and extend previous results obtained by the second named autho...

For any affine-variety code we show how to construct an ideal whose solutions correspond to codewords with any assigned weight. We use our ideal and a geometric characterization to determine the number of small-weight codewords for some families of Hermitian codes over any Fq. In particular, we determine the number of minimum-weight code-words for...

General error locator polynomials are polynomials able to decode any correctable syndrome for a given linear code. Such polynomials are known to exist for all cyclic codes and for a large class of linear codes. We provide some decoding techniques for affine-variety codes using some multidimensional extensions of general error locator polynomials. W...