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Elementary Remarks on Some Quadratic Based Identity Based Encryption Schemes

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Innovative Security Solutions for Information Technology and Communications (SecITC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14534))

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Abstract

In the design of an identity-based encryption (IBE) scheme, the primary security assumptions center around quadratic residues, bilinear mappings, and lattices. Among these approaches, one of the most intriguing is introduced by Clifford Cocks and is based on quadratic residues. However, this scheme has a significant drawback: a large ciphertext to plaintext ratio. A different approach is taken by Zhao et al., who design an IBE still based on quadratic residues, but with an encryption process reminiscent of the Goldwasser-Micali cryptosystem. In the following pages, we will introduce an elementary method to accelerate Cocks’ encryption process and adapt a space-efficient encryption technique for both Cocks’ and Zhao et al.’s cryptosystems.

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Notes

  1. 1.

    This assumption states that an adversary trying to decide if a random element is from \(J_n\setminus QR_n\) or \(QR_n\) has a negligible success probability.

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Authors and Affiliations

  1. Advanced Technologies Institute, 10 Dinu Vintilă, Bucharest, Romania

    Paul Cotan & George Teşeleanu

  2. Simion Stoilow Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei, Bucharest, Romania

    Paul Cotan & George Teşeleanu

Authors
  1. Paul Cotan
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  2. George Teşeleanu
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Correspondence to George Teşeleanu .

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Editors and Affiliations

  1. Universität der Bundeswehr München, Munich, Germany

    Mark Manulis

  2. Technology Innovation Institute, Abu Dhabi, United Arab Emirates

    Diana Maimuţ

  3. Advanced Technologies Institute, Bucharest, Romania

    George Teşeleanu

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Cotan, P., Teşeleanu, G. (2024). Elementary Remarks on Some Quadratic Based Identity Based Encryption Schemes. In: Manulis, M., Maimuţ, D., Teşeleanu, G. (eds) Innovative Security Solutions for Information Technology and Communications. SecITC 2023. Lecture Notes in Computer Science, vol 14534. Springer, Cham. https://doi.org/10.1007/978-3-031-52947-4_3

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  • DOI: https://doi.org/10.1007/978-3-031-52947-4_3

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  • Print ISBN: 978-3-031-52946-7

  • Online ISBN: 978-3-031-52947-4

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