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Enhancing FHE Over the Integers: Beyond Binary Numbers and Batch Processing

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Cryptology and Network Security with Machine Learning (ICCNSML 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 918))

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Abstract

Fully Homomorphic Encryption (FHE) schemes enable secure computations on encrypted data. Following Gentry’s groundbreaking result, the AGCD problem-based FHE scheme, also known as Fully Homomorphic Encryption over the Integers (FHE-OI), was introduced by Dijk et al. Over the time, several improvements have been made to FHE-OI, including the CS scheme proposed by Cheon and Stehlé. This paper presents two significant enhancements to CS scheme. The first contribution involves extending their FHE scheme to support message space \(\mathbb {Z}_g\), removing the previous constraint limited to binary numbers as described in Cheon and Stehlé’s work. Building upon this advancement, the second enhancement further extends the scheme to encompass batch fully homomorphic encryption. This extension empowers the scheme to efficiently encrypt and perform homomorphic operations on entire vectors of plaintext bits using a single ciphertext, thereby enhancing its applicability and utility in various practical scenarios.

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Authors and Affiliations

  1. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, Uttar Pradesh, 211004, India

    Rohitkumar R. Upadhyay & Sahadeo Padhye

Authors
  1. Rohitkumar R. Upadhyay
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  2. Sahadeo Padhye
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Correspondence to Rohitkumar R. Upadhyay .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Pranveer Singh Institute of Technology, Kanpur, India

    Atul Chaturvedi

  2. Department of Mathematics, Indian Institute of Technology Jammu, Jammu, India

    Sartaj Ul Hasan

  3. Applied Statistics Unit, Indian Statistical Institute, Kolkata, India

    Bimal Kumar Roy

  4. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Boaz Tsaban

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© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Upadhyay, R.R., Padhye, S. (2024). Enhancing FHE Over the Integers: Beyond Binary Numbers and Batch Processing. In: Chaturvedi, A., Hasan, S.U., Roy, B.K., Tsaban, B. (eds) Cryptology and Network Security with Machine Learning. ICCNSML 2023. Lecture Notes in Networks and Systems, vol 918. Springer, Singapore. https://doi.org/10.1007/978-981-97-0641-9_22

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  • DOI: https://doi.org/10.1007/978-981-97-0641-9_22

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-97-0640-2

  • Online ISBN: 978-981-97-0641-9

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