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Cryptographers’ Track at the RSA Conference

CT-RSA 2015: Topics in Cryptology –- CT-RSA 2015 pp 487–505Cite as

Linearly Homomorphic Encryption from \(\mathsf {DDH}\)

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9048))

Abstract

We design a linearly homomorphic encryption scheme whose security relies on the hardness of the decisional Diffie-Hellman problem. Our approach requires some special features of the underlying group. In particular, its order is unknown and it contains a subgroup in which the discrete logarithm problem is tractable. Therefore, our instantiation holds in the class group of a non maximal order of an imaginary quadratic field. Its algebraic structure makes it possible to obtain such a linearly homomorphic scheme whose message space is the whole set of integers modulo a prime \(p\) and which supports an unbounded number of additions modulo \(p\) from the ciphertexts. A notable difference with previous works is that, for the first time, the security does not depend on the hardness of the factorization of integers. As a consequence, under some conditions, the prime \(p\) can be scaled to fit the application needs.

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Author information

Authors and Affiliations

  1. Institut de Mathématiques de Bordeaux UMR 5251, Université de Bordeaux, 351, cours de la Libération, 33405, Talence cedex, France

    Guilhem Castagnos

  2. CNRS/ENSL/INRIA/UCBL LIP Laboratoire de l’Informatique du Parallélisme, Université Claude Bernard Lyon 1, 46 Allée d’Italie, 69364, Lyon, France

    Fabien Laguillaumie

Authors
  1. Guilhem Castagnos
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  2. Fabien Laguillaumie
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Correspondence to Guilhem Castagnos .

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Editors and Affiliations

  1. Aalto University School of Science, Espoo, Finland

    Kaisa Nyberg

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Castagnos, G., Laguillaumie, F. (2015). Linearly Homomorphic Encryption from \(\mathsf {DDH}\) . In: Nyberg, K. (eds) Topics in Cryptology –- CT-RSA 2015. CT-RSA 2015. Lecture Notes in Computer Science(), vol 9048. Springer, Cham. https://doi.org/10.1007/978-3-319-16715-2_26

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  • DOI: https://doi.org/10.1007/978-3-319-16715-2_26

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  • Online ISBN: 978-3-319-16715-2

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