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Related papers: Pell hyperbolas in DLP-based cryptosystems

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Tuning the hyperparameters of differentially private (DP) machine learning (ML) algorithms often requires use of sensitive data and this may leak private information via hyperparameter values. Recently, Papernot and Steinke (2022) proposed…

Machine Learning · Computer Science 2024-02-14 Antti Koskela , Tejas Kulkarni

In this paper, we present a new identity-based encryption (IBE) scheme using bilinear pairings. Our IBE scheme enjoys the same \textsf{Key Extraction} and \textsf{Decryption} algorithms with the famous IBE scheme of Boneh and Franklin…

Cryptography and Security · Computer Science 2007-05-23 Shengbao Wang

The secure instantiation of the random oracle is one of the major open problems in modern cryptography. We investigate this problem using concepts and methods of algorithmic randomness. In modern cryptography, the random oracle model is…

Cryptography and Security · Computer Science 2019-09-04 Kohtaro Tadaki , Norihisa Doi

The signcryption is a relatively new cryptographic technique that is supposed to fulfill the functionalities of encryption and digital signature in a single logical step. Several signcryption schemes are proposed throughout the years, each…

Cryptography and Security · Computer Science 2012-03-20 M. Toorani , A. A. Beheshti

Proof by coupling is a classical proof technique for establishing probabilistic properties of two probabilistic processes, like stochastic dominance and rapid mixing of Markov chains. More recently, couplings have been investigated as a…

Programming Languages · Computer Science 2017-04-04 Gilles Barthe , Thomas Espitau , Benjamin Grégoire , Justin Hsu , Pierre-Yves Strub

We present a general framework for derandomizing random linear codes with respect to a broad class of properties, known as local properties, which encompass several standard notions such as distance, list-decoding, list-recovery, and…

Information Theory · Computer Science 2025-11-21 Fernando Granha Jeronimo , Nikhil Shagrithaya

We introduce the notion of an $n$-threshold secret petition, in which users add encrypted signatures to a petition, and the signatures are decrypted if and only if at least $n$ signatures have been gathered. This solves the coordination…

Cryptography and Security · Computer Science 2024-08-05 Florian Breuer

We lay the foundations for a blockchain scheme, whose consensus is reached via a proof of work algorithm based on the solution of consecutive discrete logarithm problems over the point group of elliptic curves. In the considered…

Cryptography and Security · Computer Science 2021-11-19 Alessio Meneghetti , Massimiliano Sala , Daniele Taufer

The discrete logarithm in a finite group of large order has been widely applied in public key cryptosystem. In this paper, we will present a probabilistic algorithm for discrete logarithm.

Cryptography and Security · Computer Science 2009-03-21 An-Ping Li

Quantum computers can break the RSA and El Gamal public-key cryptosystems, since they can factor integers and extract discrete logarithms. If we believe that quantum computers will someday become a reality, we would like to have…

Cryptography and Security · Computer Science 2010-10-19 Hang Dinh , Cristopher Moore , Alexander Russell

An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of "hard supersingular curves" that is, equations for supersingular curves for which computing the…

General cryptographic schemes are presented where keys can be one-time or ephemeral. Processes for key exchange are derived. Public key cryptographic schemes based on the new systems are easily established. Authentication and signature…

Cryptography and Security · Computer Science 2020-04-13 Ted Hurley

We show that many known schemes of the public key exchange protocols in the algebraic cryptography, that use two-sided multiplications, are the specific cases of the general scheme of such type. In most cases, such schemes are built on…

Group Theory · Mathematics 2017-09-20 V. A. Roman'kov

Group-based cryptography is a relatively unexplored family in post-quantum cryptography, and the so-called Semidirect Discrete Logarithm Problem (SDLP) is one of its most central problems. However, the complexity of SDLP and its…

Cryptography and Security · Computer Science 2024-06-10 Christopher Battarbee , Delaram Kahrobaei , Ludovic Perret , Siamak F. Shahandashti

The concept of linearity plays a central role in both mathematics and computer science, with distinct yet complementary meanings. In mathematics, linearity underpins functions and vector spaces, forming the foundation of linear algebra and…

Cryptography and Security · Computer Science 2025-10-21 Giulia Giusti

We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent…

Cryptography and Security · Computer Science 2025-07-14 Gennady Khalimov , Yevgen Kotukh

Using the representation of numbers, the methods of decreasing the number of calculation steps for Pell's equation are developed. The formulae relating the natural solution x0 of Pell's equation for A0 with the infinite number of minimal…

Number Theory · Mathematics 2007-05-23 S. N. Arteha

Privacy-preserving machine learning (PPML) based on cryptographic protocols has emerged as a promising paradigm to protect user data privacy in cloud-based machine learning services. While it achieves formal privacy protection, PPML often…

Cryptography and Security · Computer Science 2025-07-22 Wenxuan Zeng , Tianshi Xu , Yi Chen , Yifan Zhou , Mingzhe Zhang , Jin Tan , Cheng Hong , Meng Li

We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann…

Number Theory · Mathematics 2013-02-19 Gaetan Bisson

In this paper we introduce left ideal low-rank parity-check codes by using group algebras and we finally use them to extend ROLLO-I KEM.

Information Theory · Computer Science 2022-10-24 Martino Borello , Paolo Santonastaso , Ferdinando Zullo