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Completeness of Single-Bit Projection-KDM Security for Public Key Encryption

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Topics in Cryptology –- CT-RSA 2015 (CT-RSA 2015)

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

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Abstract

Applebaum (EUROCRYPT 2011, J. Cryptology 2014) showed that it is possible to convert a public key encryption (PKE) scheme which is key dependent message (KDM) secure with respect to projection functions (also called projection-KDM secure) into a PKE scheme which is KDM secure with respect to any function family that can be computed in fixed polynomial time, without using any other assumption. This result holds in both of the chosen plaintext attack (CPA) and the chosen ciphertext attack (CCA) settings. In the CPA setting, he furthermore showed that even a projection-KDM secure 1-bit PKE scheme is sufficient to construct a KDM secure PKE scheme with respect to polynomial time computable functions. The existence of the latter trivially implies that of the former, and in this sense, he mentioned that single-bit projection-KDM security in the CPA setting and (multi-bit) projection-KDM security in the CCA setting are complete.

In this paper, we show that single-bit projection-KDM security is complete also in the CCA setting. More specifically, as our main technical result, we show how to construct a projection-KDM-CCA secure multi-bit PKE scheme from a projection-KDM-CCA secure 1-bit PKE scheme, without using any other assumption. The combination of our result and Applebaum’s result shows that one can construct a PKE scheme which is KDM-CCA secure with respect to any polynomial time computable functions from a projection-KDM-CCA secure 1-bit PKE scheme, without using additional assumptions.

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Authors and Affiliations

  1. Tokyo Institute of Technology, Meguro, Tokyo, Japan

    Fuyuki Kitagawa & Keisuke Tanaka

  2. National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, Japan

    Fuyuki Kitagawa, Takahiro Matsuda & Goichiro Hanaoka

Authors
  1. Fuyuki Kitagawa
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  2. Takahiro Matsuda
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  3. Goichiro Hanaoka
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  4. Keisuke Tanaka
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Corresponding author

Correspondence to Fuyuki Kitagawa .

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Editors and Affiliations

  1. Aalto University School of Science, Espoo, Finland

    Kaisa Nyberg

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Kitagawa, F., Matsuda, T., Hanaoka, G., Tanaka, K. (2015). Completeness of Single-Bit Projection-KDM Security for Public Key Encryption. 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_11

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  • DOI: https://doi.org/10.1007/978-3-319-16715-2_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16714-5

  • Online ISBN: 978-3-319-16715-2

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