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Encrypted system identification as-a-service via reliable encrypted matrix inversion

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arXiv 2024年

作者： Adamek, Janis Binfet, Philipp Schlüter, Nils Darup, Moritz Schulze Control and Cyber-physical Systems Group Department of Mechanical Engineering TU Dortmund University Germany

Encrypted computation opens up promising avenues across a plethora of application domains, including machine learning, health-care, finance, and control. Arithmetic homomorphic encryption, in particular, is a natural fit for cloud-based computational services. However, computations are essentially limited to polynomial circuits, while comparisons, transcendental functions, and iterative algorithms are notoriously hard to realize. Against this background, the paper presents an encrypted system identification service enabled by a reliable encrypted solution to least squares problems. More precisely, we devise an iterative algorithm for matrix inversion and present reliable initializations as well as certificates for the achieved accuracy without compromising the privacy of provided I/O-data. The effectiveness of the approach is illustrated with three popular identification tasks. © 2024, CC BY-NC-ND.

关键词： encryption algorithms

MNT Elliptic Curves with Non-Prime Order

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arXiv 2024年

作者： Grześkowiak, Maciej

Miyaji, Nakabayashi, and Takano proposed the algorithm for the construction of prime order pairing-friendly elliptic curves with embedding degrees k = 3, 4, 6. We present a method for generating generalized MNT curves. The order of such pairing-friendly curves is the product of two prime numbers. Copyright © 2024, The Authors. All rights reserved.

关键词： encryption algorithms

Factoring integers via Schnorr’s algorithm assisted with VQE

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arXiv 2024年

作者： Sánchez Cano, Luis Carrascal de las Heras, Ginés Botella Juan, Guillermo del Barrio García, Alberto Iberdrola S.A. Madrid28033 Spain IT Systems and Computation Department Complutense University of Madrid Madrid28040 Spain IBM Quantum IBM Consulting España Madrid28830 Spain Computer Architecture and Automation Department Complutense University of Madrid Madrid28040 Spain

Current asymmetric cryptography is based on the principle that while classical computers can efficiently multiply large integers, the inverse operation, factorization, is significantly more complex. For sufficiently large integers, this factorization process can take in classical computers hundreds or even thousands of years to complete. However, there exist some quantum algorithms that might be able to factor integers theoretically - the theory works properly, but the hardware requirements are far away from what we can build nowadays - and, for instance, Yan, B. et al. ([14]) claim to have constructed a hybrid algorithm which could be able even to challenge RSA-2048 in the near future. This work analyses this article and replicates the experiments they carried out, but with a different quantum method (VQE), being able to factor the number 1961. Copyright © 2024, The Authors. All rights reserved.

关键词： encryption algorithms

The Continuous Logarithm in the Complex Circle for Post-Quantum Cryptographic algorithms

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arXiv 2024年

作者： Gaber, Jaafar University of Marie and Louis Pasteur UTBM CNRS FEMTO-ST Institute BelfortF-90010 France

This paper introduces a novel cryptographic approach based on the continuous logarithm in the complex circle, designed to address the challenges posed by quantum computing. By leveraging its multi-valued and spectral properties, this framework enables the reintroduction of classical algorithms (DH, ECDSA, ElGamal, EC) and elliptic curve variants into the post-quantum landscape. Transitioning from classical or elliptic algebraic structures to the geometric and spectral properties of the complex circle, we propose a robust and adaptable foundation for post-quantum *** Codes 68 Copyright © 2024, The Authors. All rights reserved.

关键词： encryption algorithms

A New Algorithm for Computing Branch Number of Non-Singular Matrices over Finite Fields

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arXiv 2024年

作者： Mishra, P.R. Kumar, Yogesh Samanta, Susanta Gaur, Atul Scientific Analysis Group DRDO Metcalfe House Complex Delhi110054 India R. C. Bose Centre for Cryptology and Security Indian Statistical Institute Kolkata700108 India Department of Mathematics University of Delhi Delhi110007 India

The notion of branch number of a linear transformation is crucial for both linear and differential cryptanalysis. The number of nonzero elements in a state difference or linear mask directly correlates with the active S-Boxes. The differential or linear branch number indicates the minimum number of active S-Boxes in two consecutive rounds of an SPN cipher, specifically for differential or linear cryptanalysis, respectively. This paper presents a new algorithm for computing the branch number of non-singular matrices over finite fields. The algorithm is based on the existing classical method but demonstrates improved computational complexity compared to its predecessor. We conduct a comparative study of the proposed algorithm and the classical approach, providing an analytical estimation of the algorithm's complexity. Our analysis reveals that the computational complexity of our algorithm is the square root of that of the classical approach. © 2024, CC BY.

关键词： encryption algorithms

A Practical Exercise in Adapting SIFT Using FHE Primitives

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arXiv 2024年

作者： Balappanawar, Ishwar B. Kommireddy, Bhargav Srinivas IIIT Hyderabad India

An exercise in implementing Scale Invariant Feature Transform using CKKS Fully Homomorphic encryption quickly reveals some glaring limitations in the current FHE paradigm. These limitations include the lack of a standard comparison operator and certain operations that depend on it (like array max, histogram binning etc). We also observe that the existing solutions are either too low level or do not have proper abstractions to implement algorithms like SIFT. In this work, we demonstrate: • Methods of adapting regular code to the FHE setting. • Alternate implementations of standard algorithms (like array max, histogram binning, etc.) to reduce the multiplicative depth. • A novel method of using deferred computations to avoid performing expensive operations such as comparisons in the encrypted domain. Through this exercise, we hope this work acts as a practical guide on how one can adapt algorithms to FHE. © 2024, CC BY.

关键词： encryption algorithms

The complexity of solving a random polynomial system

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arXiv 2023年

作者： Gaggero, Giulia Gorla, Elisa

A multivariate cryptograpic instance in practice is a multivariate polynomialsystem. So the security of a protocol rely on the complexity of solving amultivariate polynomial system. In this paper there is an overview on a generalalgorithm used to solve a multivariate system and the quantity to which thecomplexity of this algorithm depends on: the solving degree. Unfortunately, itis hard to compute. For this reason, it is introduced an invariant: the degreeof regularity. This invariant, under certain condition, give us an upper boundon the solving degree. Then we speak about random polynomial systems and inparticular what "random" means to us. Finally, we give an upper bound on boththe degree of regularity and the solving degree of such random systems. © 2023, CC BY.

关键词： encryption algorithms

Modeling and simulation of common primitive operations used in block ciphers 07

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Modeling and simulation of common primitive operations used ...

Proceedings of the 2007 Summer Computer Simulation Conference

作者： Praveen R. Samala Hamid Vakilzadian Dietmar P. F. Möller University of Nebraska-Lincoln University of Hamburg Germany

ISBN: (纸本)9781565553163

Secure transmission of information is of interest to both public and private sectors. This is especially important with today's increased use of the internet for e-commerce. This research has been motivated by the need for high speed encryption algorithms for the applications that are independent of a particular algorithm and security *** this paper, hardware modeling and simulation of the common primitive operations used by the block ciphers are presented. The primitive operations were selected from the five finalist algorithms of the Advanced encryption Standard (AES [1]) contest. These algorithms are promising for the selection of the new encryption Standard, which was to replace the Data encryption Standard (DES). As Field Programmable Gate Arrays (FPGAs) offer high flexibility and a low cost alternative for implementing these algorithms in Application-Specific Integrated Circuits (ASIC), these primitive operations are implemented in an Altera FPGA to permit user-programmable alternatives for a different encryption/decryption algorithm as opposed to a preselected one by a manufacturer. The results of implementing the Rijndael algorithm using these primitive operations also are presented.

关键词： hardware modeling encryption algorithms discrete event simulation

Encrypted Dynamic Control exploiting Limited Number of Multiplications and a Method using RLWE-based Cryptosystem

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arXiv 2023年

作者： Lee, Joowon Lee, Donggil Kim, Junsoo Shim, Hyungbo ASRI Department of Electrical and Computer Engineering Seoul National University Korea Republic of Department of Electrical Engineering Incheon National University Korea Republic of Department of Electrical and Information Engineering Seoul National University of Science and Technology Korea Republic of

In this paper, we present a method to encrypt dynamic controllers that can be implemented through most homomorphic encryption schemes, including somewhat, leveled fully, and fully homomorphic encryption. To this end, we represent the output of the given controller as a linear combination of a fixed number of previous inputs and outputs. As a result, the encrypted controller involves only a limited number of homomorphic multiplications on every encrypted data, assuming that the output is re-encrypted and transmitted back from the actuator. A guidance for parameter choice is also provided, ensuring that the encrypted controller achieves predefined performance for an infinite time horizon. Furthermore, we propose a customization of the method for Ring Learning With Errors (RLWE)-based cryptosystems, where a vector of messages can be encrypted into a single ciphertext and operated simultaneously, thus reducing computation and communication loads. Unlike previous results, the proposed customization does not require extra algorithms such as rotation, other than basic addition and multiplication. Simulation results demonstrate the effectiveness of the proposed method. Copyright © 2023, The Authors. All rights reserved.

关键词： encryption algorithms