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The RSA (Rivest-Shamir-Adleman) cryptosystem is a fundamental algorithm of public key cryptography and is widely used across various information domains. For an RSA modulus represented as $N = pq$, with its factorization remaining unknown, security
vulnerabilities arise when attackers exploit the key equation $ed-k(p-1)(q-1)=1$. To enhance the security, Murru and Saettone introduced cubic Pell RSA --- a variant of RSA based on the cubic Pell equation, where the key equation becomes $ed-k(p^2+p+1)(q^
2+q+1)=1$. In this paper, we further investigate the security implications surrounding the generalized key equation $eu-(p^2+p+1)(q^2+q+1)v=w$. We present a novel attack strategy aimed at recovering the prime factors $p$ and $q$ under specific conditions
satisfied by $u$, $v$, and $w$. Our generalized attack employs lattice-based Coppersmith's techniques and extends several previous attack scenarios, thus deepening the understanding of mathematical cryptanalysis.



## 2024/2082

* Title: ClusterGuard: Secure Clustered Aggregation for Federated Learning with Robustness
* Authors: Yulin Zhao, Zhiguo Wan, Zhangshuang Guan
* [Permalink](https://eprint.iacr.org/2024/2082)
* [Download](https://eprint.iacr.org/2024/2082.pdf)

### Abstract

Federated Learning (FL) enables collaborative model training while preserving data privacy by avoiding the sharing of raw data. However, in large-scale FL systems, efficient secure aggregation and dropout handling remain critical challenges. Existing
state-of-the-art methods, such as those proposed by Liu et al. (UAI'22) and Li et al. (ASIACRYPT'23), suffer from prohibitive communication overhead, implementation complexity, and vulnerability to poisoning attacks. Alternative approaches that utilize
partially connected graph structures (resembling client grouping) to reduce communication costs, such as Bell et al. (CCS'20) and ACORN (USENIX Sec'23), face the risk of adversarial manipulation during the graph construction process.

To address these issues, we propose ClusterGuard, a secure clustered aggregation scheme for federated learning. ClusterGuard leverages Verifiable Random Functions (VRF) to ensure fair and transparent cluster selection and employs a lightweight key-
homomorphic masking mechanism, combined with efficient dropout handling, to achieve secure clustered aggregation. Furthermore, ClusterGuard incorporates a dual filtering mechanism based on cosine similarity and norm to effectively detect and mitigate
poisoning attacks.

Extensive experiments on standard datasets demonstrate that ClusterGuard achieves over 2x efficiency improvement compared to advanced secure aggregation methods. Even with 20% of clients being malicious, the trained model maintains accuracy comparable to
the original model, outperforming state-of-the-art robustness solutions. ClusterGuard provides a more efficient, secure, and robust solution for practical federated learning.



## 2024/2083

* Title: Fully Hybrid TLSv1.3 in WolfSSL on Cortex-M4
* Authors: Mila Anastasova, Reza Azarderakhsh, Mehran Mozaffari Kermani
* [Permalink](https://eprint.iacr.org/2024/2083)
* [Download](https://eprint.iacr.org/2024/2083.pdf)

### Abstract

To provide safe communication across an unprotected medium such as the internet, network protocols are being established. These protocols employ public key techniques to perform key exchange and authentication. Transport Layer Security (TLS) is a widely
used network protocol that enables secure communication between a server and a client. TLS is employed in billions of transactions per second. Contemporary protocols depend on traditional methods that utilize the computational complexity of factorization
or (elliptic curve) logarithm mathematics problems. The ongoing advancement in the processing power of classical computers requires an ongoing increase in the security level of the underlying cryptographic algorithms. This study focuses on the analysis
of Curve448 and Edwards curve Ed448, renowned for their superior security features that offer a 224-bit level of security as part of the TLSv1.3 protocol. The exponential advancement of quantum computers, however, presents a substantial threat to secure
network communication that depends on classical crypto schemes, irrespective of their degree of security. Quantum computers have the capability to resolve these challenges within a feasible timeframe. In order to successfully transition to Post-Quantum
secure network protocols, it is imperative to concurrently deploy both classical and post-quantum algorithms. This is done to fulfill the requirements of both enterprises and governments, while also instilling more assurance in the reliability of the
post-quantum systems. This paper presents a detailed hybrid implementation architecture of the TLSv1.3 network protocol. We showcase the first deployment of Curve448 and Crystals-Kyber for the purpose of key exchanging, and Ed448 and Crystals-Dilithium
for verifying the authenticity of entities and for X.509 Public Key Infrastructure (PKI). We rely upon the widely used OpenSSL library and the specific wolfSSL library for embedded devices to provide our results for server and client applications.



## 2024/2084

* Title: Zero Knowledge Memory-Checking Techniques for Stacks and Queues
* Authors: Alexander Frolov
* [Permalink](https://eprint.iacr.org/2024/2084)
* [Download](https://eprint.iacr.org/2024/2084.pdf)

### Abstract

There are a variety of techniques for implementing read/write memory inside of zero-knowledge proofs and validating consistency of memory accesses. These techniques are generally implemented with the goal of implementing a RAM or ROM. In this paper, we
present memory techniques for more specialized data structures: queues and stacks. We first demonstrate a technique for implementing queues in arithmetic circuits that requires 3 multiplication gates and 1 advice value per read and 2 multiplication gates
per write. This is based on using Horner's Rule to evaluate 2 polynomials at random points and check that the values read from the queue are equal to the values written to the queue as vectors. Next, we present a stack scheme based on an optimized
version of the RAM scheme of Yang and Heath that requires 5 multiplication gates and 4 advice values per read and 2 multiplication gates per write. This optimizes the RAM scheme by observing that reads and writes to a stack are already "paired" which
avoids the need for inserting dummy operations for each access as in a stack.
We also introduce a different notion of "multiplexing" or "operation privacy" that is better suited to the use case of stacks and queues. All of the techniques we provide are based on evaluating polynomials at random points and using randomly
evaluated polynomials as universal hash functions to check set/vector equality.



## 2024/2085

* Title: Definition of End-to-end Encryption
* Authors: Mallory Knodel, Sofía Celi, Olaf Kolkman, Gurshabad Grover
* [Permalink](https://eprint.iacr.org/2024/2085)
* [Download](https://eprint.iacr.org/2024/2085.pdf)

### Abstract

This document provides a definition of end-to-end encryption (E2EE). End-to-end encryption is an application of cryptographic mechanisms to provide security and privacy to communication between endpoints. Such communication can include messages, email,
video, audio, and other forms of media. E2EE provides security and privacy through confidentiality, integrity, authenticity and forward secrecy for communication amongst people.



## 2024/2086

* Title: How To Think About End-To-End Encryption and AI: Training, Processing, Disclosure, and Consent
* Authors: Mallory Knodel, Andrés Fábrega, Daniella Ferrari, Jacob Leiken, Betty Li Hou, Derek Yen, Sam de Alfaro, Kyunghyun Cho, Sunoo Park
* [Permalink](https://eprint.iacr.org/2024/2086)
* [Download](https://eprint.iacr.org/2024/2086.pdf)

### Abstract

End-to-end encryption (E2EE) has become the gold standard for securing communications, bringing strong confidentiality and privacy guarantees to billions of users worldwide. However, the current push towards widespread integration of artificial
intelligence (AI) models, including in E2EE systems, raises some serious security concerns.

This work performs a critical examination of the (in)compatibility of AI models and E2EE applications. We explore this on two fronts: (1) the integration of AI “assistants” within E2EE applications, and (2) the use of E2EE data for training AI models.

We analyze the potential security implications of each, and identify conflicts with the security guarantees of E2EE. Then, we analyze legal implications of integrating AI models in E2EE applications, given how AI integration can undermine the
confidentiality that E2EE promises. Finally, we offer a list of detailed recommendations based on our technical and legal analyses, including: technical design choices that must be prioritized to uphold E2EE security; how service providers must
accurately represent E2EE security; and best practices for the default behavior of AI features and for requesting user consent. We hope this paper catalyzes an informed conversation on the tensions that arise between the brisk deployment of AI and the
security offered by E2EE, and guides the responsible development of new AI features.

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