Constructing Subspace Membership Encryption through Inner Product Encryption

Shuichi KATSUMATA; Noboru KUNIHIRO

doi:10.1587/transfun.E100.A.1804

Constructing Subspace Membership Encryption through Inner Product Encryption

Shuichi KATSUMATA, Noboru KUNIHIRO

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Subspace membership encryption (SME), a generalization of inner product encryption (IPE), was recently formalized by Boneh, Raghunathan, and Segev in Asiacrypt 2013. The main motivation for SME was that traditional predicate encryptions did not yield function privacy, a security notion introduced by Boneh et al. in Crypto 2013 that captures the privacy of the predicate associated to the secret key. Although they gave a generic construction of SME based on any IPE, we show that their construction of SME for small attribute space was incorrect and provide an attack that breaks the attribute hiding security, a baseline security notion for predicate encryptions that captures the privacy of the attribute associated with the ciphertext. Then, we propose a generalized construction of SME and prove that the attribute hiding security can not be achieved even in the newly defined setting. Finally, we further extend our generalized construction of SME and propose a SME that achieves the attribute hiding property even when the attribute space is small. In exchange our proposed scheme does not yield function privacy and the construction is rather inefficient. Although we did not succeed in constructing a SME both yielding function privacy and attribute hiding security, ours is the first attribute hiding SME scheme whose attribute space is polynomial in the security parameter, and we formalized a richer framework for constructing SMEs and discovered a trade-off like relationship between the two security notions.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.9 pp.1804-1815

Publication Date: 2017/09/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.1804

Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

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Authors

Shuichi KATSUMATA
the University of Tokyo,National Institute of Advanced Industrial Science and Technology
Noboru KUNIHIRO
the University of Tokyo

Keyword

predicate encryption, subspace membership encryption, function privacy

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Shuichi KATSUMATA, Noboru KUNIHIRO, "Constructing Subspace Membership Encryption through Inner Product Encryption" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 9, pp. 1804-1815, September 2017, doi: 10.1587/transfun.E100.A.1804.
Abstract: Subspace membership encryption (SME), a generalization of inner product encryption (IPE), was recently formalized by Boneh, Raghunathan, and Segev in Asiacrypt 2013. The main motivation for SME was that traditional predicate encryptions did not yield function privacy, a security notion introduced by Boneh et al. in Crypto 2013 that captures the privacy of the predicate associated to the secret key. Although they gave a generic construction of SME based on any IPE, we show that their construction of SME for small attribute space was incorrect and provide an attack that breaks the attribute hiding security, a baseline security notion for predicate encryptions that captures the privacy of the attribute associated with the ciphertext. Then, we propose a generalized construction of SME and prove that the attribute hiding security can not be achieved even in the newly defined setting. Finally, we further extend our generalized construction of SME and propose a SME that achieves the attribute hiding property even when the attribute space is small. In exchange our proposed scheme does not yield function privacy and the construction is rather inefficient. Although we did not succeed in constructing a SME both yielding function privacy and attribute hiding security, ours is the first attribute hiding SME scheme whose attribute space is polynomial in the security parameter, and we formalized a richer framework for constructing SMEs and discovered a trade-off like relationship between the two security notions.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.1804/_p

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@ARTICLE{e100-a_9_1804,
author={Shuichi KATSUMATA, Noboru KUNIHIRO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Constructing Subspace Membership Encryption through Inner Product Encryption},
year={2017},
volume={E100-A},
number={9},
pages={1804-1815},
abstract={Subspace membership encryption (SME), a generalization of inner product encryption (IPE), was recently formalized by Boneh, Raghunathan, and Segev in Asiacrypt 2013. The main motivation for SME was that traditional predicate encryptions did not yield function privacy, a security notion introduced by Boneh et al. in Crypto 2013 that captures the privacy of the predicate associated to the secret key. Although they gave a generic construction of SME based on any IPE, we show that their construction of SME for small attribute space was incorrect and provide an attack that breaks the attribute hiding security, a baseline security notion for predicate encryptions that captures the privacy of the attribute associated with the ciphertext. Then, we propose a generalized construction of SME and prove that the attribute hiding security can not be achieved even in the newly defined setting. Finally, we further extend our generalized construction of SME and propose a SME that achieves the attribute hiding property even when the attribute space is small. In exchange our proposed scheme does not yield function privacy and the construction is rather inefficient. Although we did not succeed in constructing a SME both yielding function privacy and attribute hiding security, ours is the first attribute hiding SME scheme whose attribute space is polynomial in the security parameter, and we formalized a richer framework for constructing SMEs and discovered a trade-off like relationship between the two security notions.},
keywords={},
doi={10.1587/transfun.E100.A.1804},
ISSN={1745-1337},
month={September},}

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TY - JOUR
TI - Constructing Subspace Membership Encryption through Inner Product Encryption
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1804
EP - 1815
AU - Shuichi KATSUMATA
AU - Noboru KUNIHIRO
PY - 2017
DO - 10.1587/transfun.E100.A.1804
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2017
AB - Subspace membership encryption (SME), a generalization of inner product encryption (IPE), was recently formalized by Boneh, Raghunathan, and Segev in Asiacrypt 2013. The main motivation for SME was that traditional predicate encryptions did not yield function privacy, a security notion introduced by Boneh et al. in Crypto 2013 that captures the privacy of the predicate associated to the secret key. Although they gave a generic construction of SME based on any IPE, we show that their construction of SME for small attribute space was incorrect and provide an attack that breaks the attribute hiding security, a baseline security notion for predicate encryptions that captures the privacy of the attribute associated with the ciphertext. Then, we propose a generalized construction of SME and prove that the attribute hiding security can not be achieved even in the newly defined setting. Finally, we further extend our generalized construction of SME and propose a SME that achieves the attribute hiding property even when the attribute space is small. In exchange our proposed scheme does not yield function privacy and the construction is rather inefficient. Although we did not succeed in constructing a SME both yielding function privacy and attribute hiding security, ours is the first attribute hiding SME scheme whose attribute space is polynomial in the security parameter, and we formalized a richer framework for constructing SMEs and discovered a trade-off like relationship between the two security notions.
ER -