Eliana Carozza

Eliana Carozza

Phd student in post quantum cryptography

Posts by Collection

publications

Short Signatures from Regular Syndrome Decoding in the Head

Available on ePrint

Presented at Eurocrypt 2023, 2023

This paper introduces a new candidate post-quantum digital signature scheme based on the regular syndrome decoding (RSD) assumption, a well-established variant of the syndrome decoding problem. The scheme is built using a 5-round zero-knowledge proof system with the MPC-in-the-head paradigm. A key part of the construction is an efficient MPC protocol in the preprocessing model that verifies the correctness of an RSD instance through a share ring-conversion mechanism. The technical analysis is non-trivial and involves combinatorial challenges, such as evaluating soundness in a relaxed model where a cheating prover can use a witness close to a regular vector. The paper also provides a detailed overview of existing attacks against RSD. The resulting signature scheme is competitive with other code-based schemes, with signature sizes ranging from several KB (fast setting, signing in a few milliseconds on a standard laptop) to more compact versions around 15ms for signing.

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Faster Signatures from MPC-in-the-Head

Available on ePrint

Presented at Asiacrypt 2024, 2024

This paper revisits the construction of signature schemes using the MPC-in-the-head paradigm, contributing two key results. First, it is noted that previous schemes relying on this paradigm require a salted version of the GGM puncturable pseudorandom function (PPRF) to prevent collision attacks. A new, efficient PPRF construction is introduced, which is provably secure in the multi-instance setting. The security analysis, performed in the ideal cipher model, forms a core technical contribution. Unlike earlier constructions that depended on a hash function, this approach uses only a fixed-key block cipher, resulting in a 12× to 55× efficiency improvement over recent schemes like Joux and Huth (Crypto’24). This improved PPRF can accelerate various MPC-in-the-head signature schemes. Additionally, a new signature scheme is introduced based on the regular syndrome decoding assumption. It employs a new protocol for the MPC-in-the-head paradigm, significantly reducing communication overhead compared to previous work. The scheme is conceptually straightforward, though its security analysis involves a complex combinatorial analysis.

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On Threshold Signatures from MPC-in-the-Head

Available on ePrint

Presented at , 2024

We investigate the feasibility of constructing threshold signature schemes from the MPC-in-the-head paradigm. Our work addresses the significant challenge posed by recent impossibility results (Doerner et al., Crypto’24), which establish inherent barriers to efficient thresholdization of such schemes without compromising their security or significantly increasing the signature size. We introduce a general methodology to adapt any MPC-in-the-head signature into a threshold-friendly scheme, ensuring that the dependency on the number of users n grows as λ²n + O(1). This represents a substantial improvement over the naive concatenation of independent signatures. We present a threshold signature scheme on top of the scheme of (Carozza, Couteau and Joux, EUROCRYPT’23). Our security analysis introduces the notion of Corruptible Existential Unforgeability under Chosen Message Attacks (CEUF-CMA), which formalizes resilience against adversarial control over parts of the randomness. Our results provide a new perspective on the trade-offs between efficiency and security in threshold settings, opening pathways for future improvements in post-quantum threshold cryptography.

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teaching

Algebra

Assistant, Università degli Studi Roma 3, Mathematic Department, 2021

Informatique

Assistant, Université Paris Cité, Informatic Department, 2024