On Homomorphic Encryption Using Abelian Groups : Classical Security Analysis

Eleni Agathocleous; Vishnupriya Anupindi; Annette Bachmayr; Chloe Martindale; Rahinatou Yuh Njah Nchiwo; Mima Stanojkovski

doi:10.1007/978-3-031-52163-8_1

On Homomorphic Encryption Using Abelian Groups : Classical Security Analysis

Eleni Agathocleous, Vishnupriya Anupindi, Annette Bachmayr, Chloe Martindale^*, Rahinatou Yuh Njah Nchiwo, Mima Stanojkovski

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

Abstract

Leonardi and Ruiz-Lopez recently proposed an additively homomorphic public key encryption scheme based on combining group homomorphisms with noise. Choosing parameters for their primitive requires choosing three groups G, H, and K. In their paper, Leonardi and Ruiz-Lopez claim that when G, H, and K are abelian, then their public key cryptosystem is not quantum secure. In this chapter, we study security for finite abelian groups G, H, and K in the classical case. Moreover, we study quantum attacks on instantiations with solvable groups.

Original language	English
Title of host publication	Women in Numbers Europe IV : Research Directions in Number Theory
Publisher	Springer
Pages	1-27
Number of pages	27
ISBN (Electronic)	978-3-031-52163-8
ISBN (Print)	978-3-031-52162-1
DOIs	https://doi.org/10.1007/978-3-031-52163-8_1
Publication status	Published - 2024
MoE publication type	A3 Book section, Chapters in research books

Publication series

Name	Association for Women in Mathematics Series
Publisher	Springer
Volume	32
ISSN (Print)	2364-5733
ISSN (Electronic)	2364-5741

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10.1007/978-3-031-52163-8_1

https://arxiv.org/abs/2302.12867

Cite this

Agathocleous, E., Anupindi, V., Bachmayr, A., Martindale, C., Nchiwo, R. Y. N., & Stanojkovski, M. (2024). On Homomorphic Encryption Using Abelian Groups : Classical Security Analysis. In Women in Numbers Europe IV : Research Directions in Number Theory (pp. 1-27). (Association for Women in Mathematics Series; Vol. 32). Springer. https://doi.org/10.1007/978-3-031-52163-8_1

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title = "On Homomorphic Encryption Using Abelian Groups : Classical Security Analysis",

abstract = "Leonardi and Ruiz-Lopez recently proposed an additively homomorphic public key encryption scheme based on combining group homomorphisms with noise. Choosing parameters for their primitive requires choosing three groups G, H, and K. In their paper, Leonardi and Ruiz-Lopez claim that when G, H, and K are abelian, then their public key cryptosystem is not quantum secure. In this chapter, we study security for finite abelian groups G, H, and K in the classical case. Moreover, we study quantum attacks on instantiations with solvable groups.",

author = "Eleni Agathocleous and Vishnupriya Anupindi and Annette Bachmayr and Chloe Martindale and Nchiwo, {Rahinatou Yuh Njah} and Mima Stanojkovski",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.",

year = "2024",

doi = "10.1007/978-3-031-52163-8_1",

language = "English",

isbn = "978-3-031-52162-1",

series = "Association for Women in Mathematics Series",

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On Homomorphic Encryption Using Abelian Groups : Classical Security Analysis. / Agathocleous, Eleni; Anupindi, Vishnupriya; Bachmayr, Annette et al.
Women in Numbers Europe IV : Research Directions in Number Theory. Springer, 2024. p. 1-27 (Association for Women in Mathematics Series; Vol. 32).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

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T1 - On Homomorphic Encryption Using Abelian Groups : Classical Security Analysis

AU - Agathocleous, Eleni

AU - Anupindi, Vishnupriya

AU - Bachmayr, Annette

AU - Martindale, Chloe

AU - Nchiwo, Rahinatou Yuh Njah

AU - Stanojkovski, Mima

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AB - Leonardi and Ruiz-Lopez recently proposed an additively homomorphic public key encryption scheme based on combining group homomorphisms with noise. Choosing parameters for their primitive requires choosing three groups G, H, and K. In their paper, Leonardi and Ruiz-Lopez claim that when G, H, and K are abelian, then their public key cryptosystem is not quantum secure. In this chapter, we study security for finite abelian groups G, H, and K in the classical case. Moreover, we study quantum attacks on instantiations with solvable groups.

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On Homomorphic Encryption Using Abelian Groups : Classical Security Analysis

Abstract

Publication series

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Hollanti NT: Number-theoretic well-rounded lattices

Hollanti_ICT: Secure Distributed Computation Schemes with Applications to Digitalized Remote Healthcare

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On Homomorphic Encryption Using Abelian Groups : Classical Security Analysis

Abstract

Publication series

Access to Document

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Projects

Hollanti NT: Number-theoretic well-rounded lattices

Hollanti_ICT: Secure Distributed Computation Schemes with Applications to Digitalized Remote Healthcare

Cite this