research-article

Arithmetic Cryptography

Authors:

Benny Applebaum,

Jonathan Avron,

Chris BrzuskaAuthors Info & Claims

Journal of the ACM (JACM), Volume 64, Issue 2

Article No.: 10, Pages 1 - 74

https://doi.org/10.1145/3046675

Published: 15 April 2017 Publication History

Abstract

We study the possibility of computing cryptographic primitives in a fully black-box arithmetic model over a finite field F. In this model, the input to a cryptographic primitive (e.g., encryption scheme) is given as a sequence of field elements, the honest parties are implemented by arithmetic circuits that make only a black-box use of the underlying field, and the adversary has a full (non-black-box) access to the field. This model captures many standard information-theoretic constructions.

We prove several positive and negative results in this model for various cryptographic tasks. On the positive side, we show that, under coding-related intractability assumptions, computational primitives like commitment schemes, public-key encryption, oblivious transfer, and general secure two-party computation can be implemented in this model. On the negative side, we prove that garbled circuits, additively homomorphic encryption, and secure computation with low online complexity cannot be achieved in this model. Our results reveal a qualitative difference between the standard Boolean model and the arithmetic model, and explain, in retrospect, some of the limitations of previous constructions.

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https://doi.org/10.1007/s00500-021-06041-4
Ismail SAlmayouf RChehab SAlghamdi SAlmutairi AAlasmari BAltherwy R(2020)Edge IoT-cloud Framework based on Blockchain2020 2nd International Conference on Computer and Information Sciences (ICCIS)10.1109/ICCIS49240.2020.9257647(1-7)Online publication date: 13-Oct-2020
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Index Terms

Arithmetic Cryptography
1. Theory of computation
  1. Computational complexity and cryptography
    1. Cryptographic primitives
    2. Cryptographic protocols

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cover image Journal of the ACM

Journal of the ACM Volume 64, Issue 2

April 2017

277 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/3080497

Editor:
Éva Tardos
Cornell University

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Copyright © 2017 ACM.

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Publication History

Published: 15 April 2017

Accepted: 01 January 2017

Revised: 01 December 2016

Received: 01 April 2015

Published in JACM Volume 64, Issue 2

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Cited By

Applebaum BKonstantini N(2023)Actively Secure Arithmetic Computation and VOLE with Constant Computational OverheadAdvances in Cryptology – EUROCRYPT 202310.1007/978-3-031-30617-4_7(190-219)Online publication date: 15-Apr-2023
https://doi.org/10.1007/978-3-031-30617-4_7
ElRahman SAlluhaidan A(2021)Blockchain technology and IoT-edge framework for sharing healthcare servicesSoft Computing10.1007/s00500-021-06041-4Online publication date: 27-Jul-2021
https://doi.org/10.1007/s00500-021-06041-4
Ismail SAlmayouf RChehab SAlghamdi SAlmutairi AAlasmari BAltherwy R(2020)Edge IoT-cloud Framework based on Blockchain2020 2nd International Conference on Computer and Information Sciences (ICCIS)10.1109/ICCIS49240.2020.9257647(1-7)Online publication date: 13-Oct-2020
https://doi.org/10.1109/ICCIS49240.2020.9257647
Ishai YKushilevitz EOstrovsky RSahai A(2019)Cryptographic SensingAdvances in Cryptology – CRYPTO 201910.1007/978-3-030-26954-8_19(583-604)Online publication date: 18-Aug-2019
https://dl.acm.org/doi/10.1007/978-3-030-26954-8_19

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