Relevant bibliographies by topics / Arithmetization-Oriented

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Arithmetization-Oriented'

Author: Grafiati
Published: 5 October 2024
Last updated: 31 July 2025

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Journal articles on the topic "Arithmetization-Oriented"

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Li, Zhengnan, Baofeng Wu, and Dongdai Lin. "Algebraic-Differential Attacks on a Family of Arithmetization-Oriented Symmetric Ciphers." Journal of Systems Science and Complexity 36, no. 6 (2023): 2681–702. http://dx.doi.org/10.1007/s11424-023-1511-7.

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Lefevre, Charlotte, Mario Marhuenda Beltrán, and Bart Mennink. "To Pad or Not to Pad? Padding-Free Arithmetization-Oriented Sponges." IACR Transactions on Symmetric Cryptology 2025, no. 1 (2025): 97–137. https://doi.org/10.46586/tosc.v2025.i1.97-137.

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The sponge is a popular construction for hashing and keyed hashing, and the duplex for authenticated encryption. They are proven to achieve approximately 2c/2 security, where c is the so-called capacity. This approach generalizes to arithmetizationoriented constructions, that operate on elements from a finite field of size p: in this case, security is guaranteed up to pc/2. However, to hash securely, the sponge needs to injectively pad the message, and likewise, authenticated encryption schemes often flip bits in the inner part to ensure domain separation. While these bit manipulations have li
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Ni, Jianqiang, Jianhui Zhang, Gaoli Wang, Rui Li, and Yanzhao Shen. "Algebraic Attacks against Grendel: An Arithmetization-Oriented Primitive with the Legendre Symbol." Symmetry 15, no. 8 (2023): 1563. http://dx.doi.org/10.3390/sym15081563.

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The rise of modern cryptographic protocols such as Zero-Knowledge proofs and secure Multi-party Computation has led to an increased demand for a new class of symmetric primitives. Unlike traditional platforms such as servers, microcontrollers, and desktop computers, these primitives are designed to be implemented in arithmetical circuits. In terms of security evaluation, arithmetization-oriented primitives are more complex compared to traditional symmetric cryptographic primitives. The arithmetization-oriented permutation Grendel employs the Legendre Symbol to increase the growth of algebraic
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Grassi, Lorenzo, Dmitry Khovratovich, Reinhard Lüftenegger, Christian Rechberger, Markus Schofnegger, and Roman Walch. "Monolith: Circuit-Friendly Hash Functions with New Nonlinear Layers for Fast and Constant-Time Implementations." IACR Transactions on Symmetric Cryptology 2024, no. 3 (2024): 44–83. http://dx.doi.org/10.46586/tosc.v2024.i3.44-83.

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Hash functions are a crucial component in incrementally verifiable computation (IVC) protocols and applications. Among those, recursive SNARKs and folding schemes require hash functions to be both fast in native CPU computations and compact in algebraic descriptions (constraints). However, neither SHA-2/3 nor newer algebraic constructions, such as Poseidon, achieve both requirements. In this work we overcome this problem in several steps. First, for certain prime field domains we propose a new design strategy called Kintsugi, which explains how to construct nonlinear layers of high algebraic d
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Grassi, Lorenzo, Katharina Koschatko, and Christian Rechberger. "Poseidon and Neptune: Gröbner Basis Cryptanalysis Exploiting Subspace Trails." IACR Transactions on Symmetric Cryptology 2025, no. 2 (2025): 34–86. https://doi.org/10.46586/tosc.v2025.i2.34-86.

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At the current state of the art, algebraic attacks are the most efficient method for finding preimages and collisions for arithmetization-oriented hash functions, such as the closely related primitives Poseidon/Poseidon2 and Neptune. In this paper, we revisit Gröbner basis (GB) attacks that exploit subspace trails to linearize some partial rounds, considering both sponge and compression modes.Starting from Poseidon’s original security evaluation, we identified some inaccuracies in the model description that may lead to misestimated round requirements. Consequently, we reevaluate and improve th
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Steiner, Matthias Johann. "Solving Degree Bounds for Iterated Polynomial Systems." IACR Transactions on Symmetric Cryptology 2024, no. 1 (2024): 357–411. http://dx.doi.org/10.46586/tosc.v2024.i1.357-411.

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For Arithmetization-Oriented ciphers and hash functions Gröbner basis attacks are generally considered as the most competitive attack vector. Unfortunately, the complexity of Gröbner basis algorithms is only understood for special cases, and it is needless to say that these cases do not apply to most cryptographic polynomial systems. Therefore, cryptographers have to resort to experiments, extrapolations and hypotheses to assess the security of their designs. One established measure to quantify the complexity of linear algebra-based Gröbner basis algorithms is the so-called solving degree. Cam
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Boeuf, Aurélien, Anne Canteaut, and Léo Perrin. "Propagation of Subspaces in Primitives with Monomial Sboxes: Applications to Rescue and Variants of the AES." IACR Transactions on Symmetric Cryptology 2023, no. 4 (2023): 270–98. http://dx.doi.org/10.46586/tosc.v2023.i4.270-298.

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Motivated by progress in the field of zero-knowledge proofs, so-called Arithmetization-Oriented (AO) symmetric primitives have started to appear in the literature, such as MiMC, Poseidon or Rescue. Due to the design constraints implied by this setting, these algorithms are defined using simple operations over large (possibly prime) fields. In particular, many rely on simple low-degree monomials for their non-linear layers, essentially using x ↦ x3 as an S-box.In this paper, we show that the structure of the material injected in each round (be it subkeys in a block cipher or round constants in
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Bak, Antoine, and Léo Perrin. "On the Security of Split-and-Lookup-Based ZK-Friendly Primitives." IACR Transactions on Symmetric Cryptology 2025, no. 2 (2025): 87–123. https://doi.org/10.46586/tosc.v2025.i2.87-123.

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Arithmetization-Oriented hash functions are optimized for their verification to be efficiently implemented within various proof systems, but they are often too slow when evaluated on a regular machine. To solve this problem for some specific protocols, some recent proposals introduced a new type of operations: the Split- And-Lookup. The idea in this case is to “split” prime field elements into smaller integers, e.g. by simply considering their binary representations, and then applying a permutation on each such integer before rebuilding a field element from them. Such operations are fast to ev
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Budaghyan, Lilya, and Mohit Pal. "Arithmetization-oriented APN permutations." Designs, Codes and Cryptography, September 18, 2024. http://dx.doi.org/10.1007/s10623-024-01487-7.

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AbstractRecently, many cryptographic primitives such as homomorphic encryption (HE), multi-party computation (MPC) and zero-knowledge (ZK) protocols have been proposed in the literature which operate on the prime field $${\mathbb {F}}_p$$ F p for some large prime p. Primitives that are designed using such operations are called arithmetization-oriented primitives. As the concept of arithmetization-oriented primitives is new, a rigorous cryptanalysis of such primitives is yet to be done. In this paper, we investigate arithmetization-oriented APN functions. More precisely, we investigate APN perm
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Bariant, Augustin, Clémence Bouvier, Gaëtan Leurent, and Léo Perrin. "Algebraic Attacks against Some Arithmetization-Oriented Primitives." IACR Transactions on Symmetric Cryptology, September 9, 2022, 73–101. http://dx.doi.org/10.46586/tosc.v2022.i3.73-101.

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Recent advanced Zero-Knowledge protocols, along with other high-level constructions such as Multi-Party Computations (MPC), have highlighted the need for a new type of symmetric primitives that are not optimized for speed on the usual platforms (desktop computers, servers, microcontrollers, RFID tags...), but for their ability to be implemented using arithmetic circuits.Several primitives have already been proposed to satisfy this need. In order to enable an efficient arithmetization, they operate over large finite fields, and use round functions that can be modelled using low degree equations
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Dissertations / Theses on the topic "Arithmetization-Oriented"

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Bariant, Augustin. "Analysis of AES-based and arithmetization-oriented symmetric cryptography primitives." Electronic Thesis or Diss., Sorbonne université, 2024. https://accesdistant.sorbonne-universite.fr/login?url=https://theses-intra.sorbonne-universite.fr/2024SORUS182.pdf.

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La cryptographie joue un rôle clé dans la communication numérique, en garantissant que les utilisateurs malveillants ne peuvent pas obtenir des informations sensibles qui ne leur appartiennent pas. En cryptographie symétrique, deux utilisateurs conviennent d'une clé secrète et utilisent un moyen de chiffrement pour communiquer, le plus utilisé étant l'AES. La sécurité des chiffrements symétriques n'est cependant pas mathématiquement prouvable, donc beaucoup d'efforts doivent être consacrés à la cryptanalyse, c'est-à-dire à la recherche des meilleures attaques.Dans ce contexte, cette thèse amél
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Bouvier, Clémence. "Cryptanalysis and design of symmetric primitives defined over large finite fields." Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS367.

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Ces dernières années, de nouvelles primitives de cryptographie symétrique ont été proposées pour être utilisées dans des protocoles avancés comme le calcul multi-partite, en combinaison avec un chiffrement homomorphe ou encore dans divers systèmes de preuve à apport nul de connaissance. De tels protocoles s’inscrivent dans un contexte marqué par le développement du Cloud et des technologies de type Blockchain et doivent ainsi répondre à une préoccupation croissante des utilisateurs en matière de sécurité. Ces protocoles ont mis en avant le besoin de minimiser le nombre de multiplications effec
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Book chapters on the topic "Arithmetization-Oriented"

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Bariant, Augustin, Aurélien Boeuf, Axel Lemoine, et al. "The Algebraic FreeLunch: Efficient Gröbner Basis Attacks Against Arithmetization-Oriented Primitives." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-68385-5_5.

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Bouvier, Clémence, Pierre Briaud, Pyrros Chaidos, et al. "New Design Techniques for Efficient Arithmetization-Oriented Hash Functions: $$\texttt{Anemoi}$$ Permutations and $$\texttt{Jive}$$ Compression Mode." In Advances in Cryptology – CRYPTO 2023. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-38548-3_17.

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Conference papers on the topic "Arithmetization-Oriented"

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Andreeva, Elena, Rishiraj Bhattacharyya, Arnab Roy, and Stefano Trevisani. "On Efficient and Secure Compression Functions for Arithmetization-Oriented Hashing." In 2024 IEEE 37th Computer Security Foundations Symposium (CSF). IEEE, 2024. http://dx.doi.org/10.1109/csf61375.2024.00045.

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