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International Conference on Information Security and Cryptology

ICISC 2018: Information Security and Cryptology – ICISC 2018 pp 3–19Cite as

New Assumptions on Isogenous Pairing Groups with Applications to Attribute-Based Encryption

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11396))

Abstract

We introduce new isogeny-related assumptions called Isog-DDH and Isog-DBDH assumptions. By using the assumptions, we reinforce security of several existing (hierarchical) identity-/attribute-based encryption (HIBE/ABE) schemes. While the existing schemes are proven from the standard DBDH assumption, our reinforced secure ones have two incomparable security proofs: one is proven from the DBDH as well and another is proven from the Isog-DDH assumption which is incomparable with DBDH. As a result, if either DBDH or Isog-DDH assumption holds, the proposed HIBE/ABE schemes are secure. For obtaining our (H)IBE secure in the standard model, we assign a unique (product) group called ID-group to each (H)ID, and introduce a new proof technique, i.e., ID-group partitioning by using isogenies as trapdoors.

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Notes

  1. 1.

    Here, DLIN (resp. DBDH) represents a family of progressively weaker k-Lin (resp. k-BDH) assumptions, e.g., [3, 10, 25] since DLIN = 2-Lin and DBDH is equivalent to 1-BDH.

  2. 2.

    Since logical equivalence \(A \rightarrow C \equiv \lnot A \vee C\) holds for truth variables A, B, C, it holds that \((A \vee B) \rightarrow C \equiv \lnot (A \vee B) \vee C \equiv (\lnot A \vee C) \wedge (\lnot B \vee C) \equiv (A \rightarrow C) \wedge (B \rightarrow C)\). We have \((A \wedge B) \rightarrow C \equiv (A \rightarrow C) \vee (B \rightarrow C)\) in a similar manner (in the case [28]). In our case, \(A=\) “DBDH assumptions holds”, \(B=\) “\(N\)-Isog-DDH assumptions hold”, \(C=\) “our schemes are secure”.

  3. 3.

    The terminology in [21] and in this paper are slightly different. In [21], our (\(N\)-)Isog-DDH assumption is called (\(N\)-)Isog-DBDH assumption and our \(N\)-Isog-DBDH assumption is not defined.

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Authors and Affiliations

  1. Waseda University, Tokyo, Japan

    Takeshi Koshiba

  2. Mitsubishi Electric, Kanagawa, Japan

    Katsuyuki Takashima

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  1. Takeshi Koshiba
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Correspondence to Katsuyuki Takashima .

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  1. Sejong University, Seoul, Korea (Republic of)

    Kwangsu Lee

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Koshiba, T., Takashima, K. (2019). New Assumptions on Isogenous Pairing Groups with Applications to Attribute-Based Encryption. In: Lee, K. (eds) Information Security and Cryptology – ICISC 2018. ICISC 2018. Lecture Notes in Computer Science(), vol 11396. Springer, Cham. https://doi.org/10.1007/978-3-030-12146-4_1

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  • DOI: https://doi.org/10.1007/978-3-030-12146-4_1

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