Related papers: Solving discrete logarithms on a 170-bit MNT curve…
We consider the critical problem of distributed learning over data while keeping it private from the computational servers. The state-of-the-art approaches to this problem rely on quantizing the data into a finite field, so that the…
Deep Neural Network (DNN) has been showing great potential in kinds of real-world applications such as fraud detection and distress prediction. Meanwhile, data isolation has become a serious problem currently, i.e., different parties cannot…
We show in some detail how to implement Shor's efficient quantum algorithm for discrete logarithms for the particular case of elliptic curve groups. It turns out that for this problem a smaller quantum computer can solve problems further…
Solving the discrete logarithm problem (DLP) with quantum computers is a fundamental task with important implications. Beyond Shor's algorithm, many researchers have proposed alternative solutions in recent years. However, due to current…
The semidirect discrete logarithm problem (SDLP) in finite groups was proposed as a foundation for post-quantum cryptographic protocols, based on the belief that its non-abelian structure would resist quantum attacks. However, recent…
We describe a novel type of weak cryptographic private key that can exist in any discrete logarithm based public-key cryptosystem set in a group of prime order $p$ where $p-1$ has small divisors. Unlike the weak private keys based on…
Precise suites of benchmarks are required to assess the progress of early fault-tolerant quantum computers at economically impactful applications such as cryptanalysis. Appropriate challenges exist for factoring but those for elliptic curve…
Computing discrete logarithms in finite fields is a main concern in cryptography. The best algorithms in large and medium characteristic fields (e.g., {GF}$(p^2)$, {GF}$(p^{12})$) are the Number Field Sieve and its variants (special,…
Privacy Preserving Data Mining is a method which ensures privacy of individual information during mining. Most important task involves retrieving information from multiple data bases which is distributed. The data once in the data warehouse…
With the increasing deployment of generative machine learning models in privacy-sensitive domains such as healthcare and personalized services, ensuring secure inference has become a critical challenge. Secure multi-party computation (MPC)…
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DLP) into a system of equations. These…
The discrete logarithm problem (DLP) is the basis for several cryptographic primitives. Since Shor's work, it has been known that the DLP can be solved by combining a polynomial-size quantum circuit and a polynomial-time classical…
We describe implementations for solving the discrete logarithm problem in the class group of an imaginary quadratic field and in the infrastructure of a real quadratic field. The algorithms used incorporate improvements over previously-used…
Homomorphic encryption is a very useful gradient protection technique used in privacy preserving federated learning. However, existing encrypted federated learning systems need a trusted third party to generate and distribute key pairs to…
With the development of machine learning, it is difficult for a single server to process all the data. So machine learning tasks need to be spread across multiple servers, turning the centralized machine learning into a distributed one.…
Deep Neural Networks (DNNs) have achieved remarkable progress in various real-world applications, especially when abundant training data are provided. However, data isolation has become a serious problem currently. Existing works build…
Local Differential Privacy (LDP) is the gold standard trust model for privacy-preserving machine learning by guaranteeing privacy at the data source. However, its application to image data has long been considered impractical due to the…
The discrete logarithm problem is a fundamental challenge in number theory with significant implications for cryptographic protocols. In this paper, we investigate the limitations of gradient-based methods for learning the parity bit of the…
Gradient inversion attacks pose significant privacy threats to distributed training frameworks such as federated learning, enabling malicious parties to reconstruct sensitive local training data from gradient communications between clients…
Differential privacy (DP) has arisen as the state-of-the-art metric for quantifying individual privacy when sensitive data are analyzed, and it is starting to see practical deployment in organizations such as the US Census Bureau, Apple,…