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Experiment for confidentiality (adaptive-predicate IND-CCA Security)
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February
2022, 16(1): 37-72.
doi: 10.3934/amc.2020098
Efficient fully CCA-secure predicate encryptions from pair encodings
| 1. | Applied Statistics Unit, Indian Statistical Institute Kolkata, West Bengal-700108, India |
| 2. | Department of Computer Science and Engineering, Indian Institute of Information Technology, Sri City, Chittoor, Andhra Pradesh - 517 646, India |
Attrapadung (Eurocrypt 2014) proposed a generic framework for fully (adaptively) CPA-secure predicate encryption (PE) based on a new primitive, called pair encodings. Following the CCA conversions of Yamada et al. (PKC 2011, 2012) and Nandi et al. (ePrint Archive: 2015/457, AAECC 2018), one can have CCA-secure PE from CPA-secure PE if the primitive PE has either verifiability or delegation. These traditional approaches degrade the performance of the resultant CCA-secure PE scheme as compared to the primitive CPA-secure PE. As an alternative, we provide a direct fully secure CCA-construction of PE from the pair encoding scheme. This costs an extra computation of group element in encryption, three extra pairing computations and one re-randomization of key in decryption as compared to the CPA-construction of Attrapadung.
Recently, Blömer et al. (CT-RSA 2016) proposed a direct CCA-secure construction of predicate encryptions from pair encodings. Although they did not use the aforementioned traditional approaches, a sort of verifiability checking is still involved in the CCA-decryption. The number of pairing computations for this checking is nearly equal to the number of paring computations in CPA-decryption. Therefore, the performance of our direct CCA-secure PE is far better than Blömer et al.
Mathematics Subject Classification:
Primary: 94A60; Secondary: 68P25.
Citation:
Mridul Nandi, Tapas Pandit. Efficient fully CCA-secure predicate encryptions from pair encodings. Advances in Mathematics of Communications,
2022, 16
(1)
: 37-72.
doi: 10.3934/amc.2020098
![]()
References:
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N. Attrapadung, Dual system encryption via doubly selective security: Framework, fully secure functional encryption for regular languages, and more, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 8441, Springer, 2014,557–577.
doi: 10.1007/978-3-642-55220-5_31. |
| [2] |
N. Attrapadung, Fully secure and succinct attribute based encryption for circuits from multi-linear maps, Cryptology ePrint Archive, Report 2014/772, 2014, http://eprint.iacr.org/. |
| [3] |
N. Attrapadung and B. Libert, Functional encryption for inner product: Achieving constant-size ciphertexts with adaptive security or support for negation, In PKC, Lecture Notes in Comput. Sci., volume 6056, Springer, 2010,384–402.
doi: 10.1007/978-3-642-13013-7_23. |
| [4] |
N. Attrapadung, B. Libert and E. Panafieu, Expressive key-policy attribute-based encryption with constant-size ciphertexts, In PKC, Lecture Notes in Comput. Sci., volume 6571, Springer, 2011, 90–108.
doi: 10.1007/978-3-642-19379-8_6. |
| [5] |
N. Attrapadung and S. Yamada, Duality in ABE: Converting attribute based encryption for dual predicate and dual policy via computational encodings, In CT-RSA, Lecture Notes in Comput. Sci., volume 9048, Springer, 2015, 87–105.
doi: 10.1007/978-3-319-16715-2_5. |
| [6] |
J. Blömer and G. Liske, Construction of fully cca-secure predicate encryptions from pair encoding schemes, In CT-RSA, Lecture Notes in Comput. Sci., volume 9610, Springer, 2016,431–447.
doi: 10.1007/978-3-319-29485-8_25. |
| [7] |
D. Boneh, R. Canetti, S. Halevi and J. Katz,
Chosen-ciphertext security from identity-based encryption, Journal of SIAM, 36 (2007), 1301-1328.
doi: 10.1137/S009753970544713X. |
| [8] |
D. Boneh and M. Franklin, Identity-based encryption from the weil pairing, In CRYPTO, Lecture Notes in Comput. Sci., volume 2139, Springer, 2001,213–229.
doi: 10.1007/3-540-44647-8_13. |
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D. Boneh, E. Goh, and K. Nissim, Evaluating 2-dnf formulas on ciphertexts, In TCC, Lecture Notes in Comput. Sci., volume 3378, Springer, 2005,325–341.
doi: 10.1007/978-3-540-30576-7_18. |
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D. Boneh and M. Hamburg, Generalized identity-based and broadcast encryption schemes, In ASIACRYPT, Lecture Notes in Comput. Sci., volume 5350, Springer, 2008,455–470.
doi: 10.1007/978-3-540-89255-7_28. |
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D. Boneh and J. Katz, Improved efficiency for CCA-secure cryptosystems built using identity-based encryption, In CT-RSA, Lecture Notes in Comput. Sci., volume 3376, Springer, 2005, 87–103.
doi: 10.1007/978-3-540-30574-3_8. |
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X. Boyen, Q. Mei and B. Waters, Direct chosen ciphertext security from identity-based techniques, In ACM Conference on Computer and Communications Security, ACM, New York, 2005,320–329.
doi: 10.1145/1102120.1102162. |
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R. Canetti, S. Halevi and J. Katz, Chosen-ciphertext security from identity-based encryption, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 3027, Springer, 2004,207–222.
doi: 10.1007/978-3-540-24676-3_13. |
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M. Chase, Multi-authority attribute based encryption, In TCC, Lecture Notes in Comput. Sci., volume 4392, Springer, 2007,515–534.
doi: 10.1007/978-3-540-70936-7_28. |
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C. Chen, Z. Zhang and D. Feng, Efficient ciphertext policy attribute-based encryption with constant-size ciphertext and constant computation-cost, In PROVSEC, Lecture Notes in Comput. Sci., volume 6980, Springer, 2011, 84–101.
doi: 10.1007/978-3-642-24316-5_8. |
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C. Chen, Z. Zhang and D. Feng, Fully secure doubly-spatial encryption under simple assumptions, In PROVSEC, Lecture Notes in Comput. Sci., volume 7496, Springer, 2012,253–263.
doi: 10.1007/978-3-642-33272-2_16. |
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J. Chen and H. Wee,
Doubly spatial encryption from DBDH, Theoret. Comput. Sci., 543 (2014), 79-89.
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C. Cocks, An identity based encryption scheme based on quadratic residues, In Cryptography and Coding, Lecture Notes in Comput. Sci., volume 2260, Springer, 2001,360–363.
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W. Diffie and M. Hellman,
New directions in cryptography, IEEE Transactions on Information Theory, 22 (1976), 644-654.
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K. Emura, A. Miyaji, A. Nomura, K. Omote and M. Soshi, A ciphertext-policy attribute-based encryption scheme with constant ciphertext length, In ISPEC, Lecture Notes in Comput. Sci., volume 5451, Springer, 2009, 13–23.
doi: 10.1504/IJACT.2010.033798. |
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E. Fujisaki and T. Okamoto, Secure integration of asymmetric and symmetric encryption schemes, In CRYPTO, Lecture Notes in Comput. Sci., volume 1666, Springer, 1999,537–554.
doi: 10.1007/3-540-48405-1_34. |
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S. Garg, C. Gentry, S. Halevi, A. Sahai and B. Waters, Attribute-based encryption for circuits from multilinear maps, In CRYPTO, Lecture Notes in Comput. Sci., volume 8043, Springer, 2013,479–499.
doi: 10.1007/978-3-642-40084-1_27. |
| [23] |
C. Gentry and A. Silverberg, Hierarchical ID-based cryptography, In ASIACRYPT, Lecture Notes in Comput. Sci., volume 2501, Springer, 2002,548–566.
doi: 10.1007/3-540-36178-2_34. |
| [24] |
S. Gorbunov, V. Vaikuntanathan and H. Wee., Attribute-based encryption for circuits, In STOC'13–Proceedings of the 2013 ACM Symposium on Theory of Computing, ACM, 2013,545–554.
doi: 10.1145/2488608.2488677. |
| [25] |
V. Goyal, A. Jain, O. Pandey and A. Sahai, Bounded ciphertext policy attribute based encryption, In Automata, Languages and Programming. Part II, Lecture Notes in Comput. Sci., volume 5126, Springer, 2008,579–591.
doi: 10.1007/978-3-540-70583-3_47. |
| [26] |
V. Goyal, O. Pandey, A. Sahai and B. Waters, Attribute-based encryption for fine-grained access control of encrypted data, In ACM Conference on Computer and Communications Security, ACM, 2006, 89–98.
doi: 10.1145/1180405.1180418. |
| [27] |
M. Hamburg, Spatial encryption, Cryptology ePrint Archive, Report 2011/389, 2011, http://eprint.iacr.org/. |
| [28] |
J. Katz, A. Sahai and B. Waters, Predicate encryption supporting disjunctions, polynomial equations, and inner products, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 4965, Springer, 2008,146–162.
doi: 10.1007/978-3-540-78967-3_9. |
| [29] |
A. Lewko and B. Waters, New techniques for dual system encryption and fully secure HIBE with short ciphertexts, In TCC, of Lecture Notes in Comput. Sci., volume 5978, Springer, 2010,455–479.
doi: 10.1007/978-3-642-11799-2_27. |
| [30] |
A. Lewko and B. Waters, Decentralizing attribute-based encryption, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 6632, Springer, 2011,568–588.
doi: 10.1007/978-3-642-20465-4_31. |
| [31] |
A. Lewko, T. Okamoto, A. Sahai, K. Takashima and B. Waters, Fully secure functional encryption: Attribute-based encryption and (hierarchical) inner product encryption, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 6110, Springer, 2010, 62–91.
doi: 10.1007/978-3-642-13190-5_4. |
| [32] |
D. Moriyama and H. Doi,
A fully secure spatial encryption scheme, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 94 (2011), 28-35.
doi: 10.1587/transfun.E94.A.28. |
| [33] |
M. Nandi and T. Pandit, Generic conversions from CPA to CCA secure functional encryption, Cryptology ePrint Archive, Report 2015/457, 2015, http://eprint.iacr.org/. |
| [34] |
M. Nandi and T. Pandit,
Verifiability-based conversion from CPA to CCA-secure predicate encryption, Appl. Algebra Engrg. Comm. Comput., 29 (2018), 77-102.
doi: 10.1007/s00200-017-0330-2. |
| [35] |
M. Nandi and T. Pandit,
Delegation-based conversion from CPA to CCA-secure predicate encryption, International Journal of Applied Cryptography, 4 (2020), 16-35.
doi: 10.1504/ijact.2020.107163. |
| [36] |
T. Okamoto and K. Takashima, Hierarchical predicate encryption for inner-products, In ASIACRYPT, Lecture Notes in Comput. Sci., volume 5912, Springer, 2009,214–231.
doi: 10.1007/978-3-642-10366-7_13. |
| [37] |
T. Okamoto and K. Takashima, Fully secure functional encryption with general relations from the decisional linear assumption, In CRYPTO, Lecture Notes in Comput. Sci., volume 6223, Springer, 2010,191–208.
doi: 10.1007/978-3-642-14623-7_11. |
| [38] |
T. Okamoto and K. Takashima, Achieving short ciphertexts or short secret-keys for adaptively secure general inner-product encryption, In Cryptology and Network Security, Lecture Notes in Comput. Sci., volume 7092, Springer, 2011,138–159.
doi: 10.1007/978-3-642-25513-7_11. |
| [39] |
T. Okamoto and K. Takashima, Adaptively attribute-hiding (hierarchical) inner product encryption, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 7237, Springer, 2012,591–608.
doi: 10.1007/978-3-642-29011-4_35. |
| [40] |
T. Okamoto and K. Takashima, Fully secure unbounded inner-product and attribute-based encryption, In ASIACRYPT, Lecture Notes in Comput. Sci., volume 7658, Springer, 2012,349–366.
doi: 10.1007/978-3-642-34961-4_22. |
| [41] |
R. Rivest, A. Shamir and L. Adleman,
A method for obtaining digital signatures and public-key cryptosystems, Comm. ACM, 21 (1978), 120-126.
doi: 10.1145/359340.359342. |
| [42] |
A. Sahai and B. Waters, Fuzzy identity-based encryption, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 3494, Springer, 2005,457–473.
doi: 10.1007/11426639_27. |
| [43] |
A. Shamir, Identity-based cryptosystems and signature schemes, In CRYPTO, Lecture Notes in Comput. Sci., volume 196, Springer, 1984, 47–53.
doi: 10.1007/3-540-39568-7_5. |
| [44] |
B. Waters, Ciphertext-policy attribute-based encryption: An expressive, efficient, and provably secure realization, In PKC, Lecture Notes in Comput. Sci., volume 6571, Springer, 2011, 53–70.
doi: 10.1007/978-3-642-19379-8_4. |
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B. Waters, Dual system encryption: Realizing fully secure IBE and HIBE under simple assumptions, In CRYPTO, Lecture Notes in Comput. Sci., volume 5677, Springer, 2009,619–636.
doi: 10.1007/978-3-642-03356-8_36. |
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B. Waters, Ciphertext-policy attribute-based encryption: An expressive, efficient, and provably secure realization, In PKC, Lecture Notes in Comput. Sci., volume 6571, Springer, 2011, 53–70.
doi: 10.1007/978-3-642-19379-8_4. |
| [47] |
B. Waters, Functional encryption for regular languages, In CRYPTO, Lecture Notes in Comput. Sci., volume 7417, Springer, 2012,218–235.
doi: 10.1007/978-3-642-32009-5_14. |
| [48] |
H. Wee, Dual system encryption via predicate encodings, In TCC, Lecture Notes in Comput. Sci., volume 8349, Springer, 2014,616–637.
doi: 10.1007/978-3-642-54242-8_26. |
| [49] |
S. Yamada, N. Attrapadung, G. Hanaoka and N. Kunihiro, Generic constructions for chosen-ciphertext secure attribute based encryption, In PKC, Lecture Notes in Comput. Sci., volume 6571, Springer, 2011, 71–89.
doi: 10.1007/978-3-642-19379-8_5. |
| [50] |
S. Yamada, N. Attrapadung, B. Santoso, J. C. N. Schuldt, Goichiro Hanaoka and Noboru Kunihiro, Verifiable predicate encryption and applications to CCA security and anonymous predicate authentication, In PKC, Lecture Notes in Comput. Sci., volume 7293, Springer, 2012,243–261.
doi: 10.1007/978-3-642-30057-8_15. |
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M. Zhou and Z. Cao, Spatial encryption under simpler assumption, In PROVSEC, Lecture Notes in Comput. Sci., volume 5848, Springer, 2009, 19–31.
doi: 10.1007/978-3-642-04642-1_4. |
show all references
References:
| [1] |
N. Attrapadung, Dual system encryption via doubly selective security: Framework, fully secure functional encryption for regular languages, and more, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 8441, Springer, 2014,557–577.
doi: 10.1007/978-3-642-55220-5_31. |
| [2] |
N. Attrapadung, Fully secure and succinct attribute based encryption for circuits from multi-linear maps, Cryptology ePrint Archive, Report 2014/772, 2014, http://eprint.iacr.org/. |
| [3] |
N. Attrapadung and B. Libert, Functional encryption for inner product: Achieving constant-size ciphertexts with adaptive security or support for negation, In PKC, Lecture Notes in Comput. Sci., volume 6056, Springer, 2010,384–402.
doi: 10.1007/978-3-642-13013-7_23. |
| [4] |
N. Attrapadung, B. Libert and E. Panafieu, Expressive key-policy attribute-based encryption with constant-size ciphertexts, In PKC, Lecture Notes in Comput. Sci., volume 6571, Springer, 2011, 90–108.
doi: 10.1007/978-3-642-19379-8_6. |
| [5] |
N. Attrapadung and S. Yamada, Duality in ABE: Converting attribute based encryption for dual predicate and dual policy via computational encodings, In CT-RSA, Lecture Notes in Comput. Sci., volume 9048, Springer, 2015, 87–105.
doi: 10.1007/978-3-319-16715-2_5. |
| [6] |
J. Blömer and G. Liske, Construction of fully cca-secure predicate encryptions from pair encoding schemes, In CT-RSA, Lecture Notes in Comput. Sci., volume 9610, Springer, 2016,431–447.
doi: 10.1007/978-3-319-29485-8_25. |
| [7] |
D. Boneh, R. Canetti, S. Halevi and J. Katz,
Chosen-ciphertext security from identity-based encryption, Journal of SIAM, 36 (2007), 1301-1328.
doi: 10.1137/S009753970544713X. |
| [8] |
D. Boneh and M. Franklin, Identity-based encryption from the weil pairing, In CRYPTO, Lecture Notes in Comput. Sci., volume 2139, Springer, 2001,213–229.
doi: 10.1007/3-540-44647-8_13. |
| [9] |
D. Boneh, E. Goh, and K. Nissim, Evaluating 2-dnf formulas on ciphertexts, In TCC, Lecture Notes in Comput. Sci., volume 3378, Springer, 2005,325–341.
doi: 10.1007/978-3-540-30576-7_18. |
| [10] |
D. Boneh and M. Hamburg, Generalized identity-based and broadcast encryption schemes, In ASIACRYPT, Lecture Notes in Comput. Sci., volume 5350, Springer, 2008,455–470.
doi: 10.1007/978-3-540-89255-7_28. |
| [11] |
D. Boneh and J. Katz, Improved efficiency for CCA-secure cryptosystems built using identity-based encryption, In CT-RSA, Lecture Notes in Comput. Sci., volume 3376, Springer, 2005, 87–103.
doi: 10.1007/978-3-540-30574-3_8. |
| [12] |
X. Boyen, Q. Mei and B. Waters, Direct chosen ciphertext security from identity-based techniques, In ACM Conference on Computer and Communications Security, ACM, New York, 2005,320–329.
doi: 10.1145/1102120.1102162. |
| [13] |
R. Canetti, S. Halevi and J. Katz, Chosen-ciphertext security from identity-based encryption, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 3027, Springer, 2004,207–222.
doi: 10.1007/978-3-540-24676-3_13. |
| [14] |
M. Chase, Multi-authority attribute based encryption, In TCC, Lecture Notes in Comput. Sci., volume 4392, Springer, 2007,515–534.
doi: 10.1007/978-3-540-70936-7_28. |
| [15] |
C. Chen, Z. Zhang and D. Feng, Efficient ciphertext policy attribute-based encryption with constant-size ciphertext and constant computation-cost, In PROVSEC, Lecture Notes in Comput. Sci., volume 6980, Springer, 2011, 84–101.
doi: 10.1007/978-3-642-24316-5_8. |
| [16] |
C. Chen, Z. Zhang and D. Feng, Fully secure doubly-spatial encryption under simple assumptions, In PROVSEC, Lecture Notes in Comput. Sci., volume 7496, Springer, 2012,253–263.
doi: 10.1007/978-3-642-33272-2_16. |
| [17] |
J. Chen and H. Wee,
Doubly spatial encryption from DBDH, Theoret. Comput. Sci., 543 (2014), 79-89.
doi: 10.1016/j.tcs.2014.06.003. |
| [18] |
C. Cocks, An identity based encryption scheme based on quadratic residues, In Cryptography and Coding, Lecture Notes in Comput. Sci., volume 2260, Springer, 2001,360–363.
doi: 10.1007/3-540-45325-3_32. |
| [19] |
W. Diffie and M. Hellman,
New directions in cryptography, IEEE Transactions on Information Theory, 22 (1976), 644-654.
doi: 10.1109/tit.1976.1055638. |
| [20] |
K. Emura, A. Miyaji, A. Nomura, K. Omote and M. Soshi, A ciphertext-policy attribute-based encryption scheme with constant ciphertext length, In ISPEC, Lecture Notes in Comput. Sci., volume 5451, Springer, 2009, 13–23.
doi: 10.1504/IJACT.2010.033798. |
| [21] |
E. Fujisaki and T. Okamoto, Secure integration of asymmetric and symmetric encryption schemes, In CRYPTO, Lecture Notes in Comput. Sci., volume 1666, Springer, 1999,537–554.
doi: 10.1007/3-540-48405-1_34. |
| [22] |
S. Garg, C. Gentry, S. Halevi, A. Sahai and B. Waters, Attribute-based encryption for circuits from multilinear maps, In CRYPTO, Lecture Notes in Comput. Sci., volume 8043, Springer, 2013,479–499.
doi: 10.1007/978-3-642-40084-1_27. |
| [23] |
C. Gentry and A. Silverberg, Hierarchical ID-based cryptography, In ASIACRYPT, Lecture Notes in Comput. Sci., volume 2501, Springer, 2002,548–566.
doi: 10.1007/3-540-36178-2_34. |
| [24] |
S. Gorbunov, V. Vaikuntanathan and H. Wee., Attribute-based encryption for circuits, In STOC'13–Proceedings of the 2013 ACM Symposium on Theory of Computing, ACM, 2013,545–554.
doi: 10.1145/2488608.2488677. |
| [25] |
V. Goyal, A. Jain, O. Pandey and A. Sahai, Bounded ciphertext policy attribute based encryption, In Automata, Languages and Programming. Part II, Lecture Notes in Comput. Sci., volume 5126, Springer, 2008,579–591.
doi: 10.1007/978-3-540-70583-3_47. |
| [26] |
V. Goyal, O. Pandey, A. Sahai and B. Waters, Attribute-based encryption for fine-grained access control of encrypted data, In ACM Conference on Computer and Communications Security, ACM, 2006, 89–98.
doi: 10.1145/1180405.1180418. |
| [27] |
M. Hamburg, Spatial encryption, Cryptology ePrint Archive, Report 2011/389, 2011, http://eprint.iacr.org/. |
| [28] |
J. Katz, A. Sahai and B. Waters, Predicate encryption supporting disjunctions, polynomial equations, and inner products, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 4965, Springer, 2008,146–162.
doi: 10.1007/978-3-540-78967-3_9. |
| [29] |
A. Lewko and B. Waters, New techniques for dual system encryption and fully secure HIBE with short ciphertexts, In TCC, of Lecture Notes in Comput. Sci., volume 5978, Springer, 2010,455–479.
doi: 10.1007/978-3-642-11799-2_27. |
| [30] |
A. Lewko and B. Waters, Decentralizing attribute-based encryption, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 6632, Springer, 2011,568–588.
doi: 10.1007/978-3-642-20465-4_31. |
| [31] |
A. Lewko, T. Okamoto, A. Sahai, K. Takashima and B. Waters, Fully secure functional encryption: Attribute-based encryption and (hierarchical) inner product encryption, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 6110, Springer, 2010, 62–91.
doi: 10.1007/978-3-642-13190-5_4. |
| [32] |
D. Moriyama and H. Doi,
A fully secure spatial encryption scheme, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 94 (2011), 28-35.
doi: 10.1587/transfun.E94.A.28. |
| [33] |
M. Nandi and T. Pandit, Generic conversions from CPA to CCA secure functional encryption, Cryptology ePrint Archive, Report 2015/457, 2015, http://eprint.iacr.org/. |
| [34] |
M. Nandi and T. Pandit,
Verifiability-based conversion from CPA to CCA-secure predicate encryption, Appl. Algebra Engrg. Comm. Comput., 29 (2018), 77-102.
doi: 10.1007/s00200-017-0330-2. |
| [35] |
M. Nandi and T. Pandit,
Delegation-based conversion from CPA to CCA-secure predicate encryption, International Journal of Applied Cryptography, 4 (2020), 16-35.
doi: 10.1504/ijact.2020.107163. |
| [36] |
T. Okamoto and K. Takashima, Hierarchical predicate encryption for inner-products, In ASIACRYPT, Lecture Notes in Comput. Sci., volume 5912, Springer, 2009,214–231.
doi: 10.1007/978-3-642-10366-7_13. |
| [37] |
T. Okamoto and K. Takashima, Fully secure functional encryption with general relations from the decisional linear assumption, In CRYPTO, Lecture Notes in Comput. Sci., volume 6223, Springer, 2010,191–208.
doi: 10.1007/978-3-642-14623-7_11. |
| [38] |
T. Okamoto and K. Takashima, Achieving short ciphertexts or short secret-keys for adaptively secure general inner-product encryption, In Cryptology and Network Security, Lecture Notes in Comput. Sci., volume 7092, Springer, 2011,138–159.
doi: 10.1007/978-3-642-25513-7_11. |
| [39] |
T. Okamoto and K. Takashima, Adaptively attribute-hiding (hierarchical) inner product encryption, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 7237, Springer, 2012,591–608.
doi: 10.1007/978-3-642-29011-4_35. |
| [40] |
T. Okamoto and K. Takashima, Fully secure unbounded inner-product and attribute-based encryption, In ASIACRYPT, Lecture Notes in Comput. Sci., volume 7658, Springer, 2012,349–366.
doi: 10.1007/978-3-642-34961-4_22. |
| [41] |
R. Rivest, A. Shamir and L. Adleman,
A method for obtaining digital signatures and public-key cryptosystems, Comm. ACM, 21 (1978), 120-126.
doi: 10.1145/359340.359342. |
| [42] |
A. Sahai and B. Waters, Fuzzy identity-based encryption, In EUROCRYPT, Lecture Notes in Comput. Sci., volume 3494, Springer, 2005,457–473.
doi: 10.1007/11426639_27. |
| [43] |
A. Shamir, Identity-based cryptosystems and signature schemes, In CRYPTO, Lecture Notes in Comput. Sci., volume 196, Springer, 1984, 47–53.
doi: 10.1007/3-540-39568-7_5. |
| [44] |
B. Waters, Ciphertext-policy attribute-based encryption: An expressive, efficient, and provably secure realization, In PKC, Lecture Notes in Comput. Sci., volume 6571, Springer, 2011, 53–70.
doi: 10.1007/978-3-642-19379-8_4. |
| [45] |
B. Waters, Dual system encryption: Realizing fully secure IBE and HIBE under simple assumptions, In CRYPTO, Lecture Notes in Comput. Sci., volume 5677, Springer, 2009,619–636.
doi: 10.1007/978-3-642-03356-8_36. |
| [46] |
B. Waters, Ciphertext-policy attribute-based encryption: An expressive, efficient, and provably secure realization, In PKC, Lecture Notes in Comput. Sci., volume 6571, Springer, 2011, 53–70.
doi: 10.1007/978-3-642-19379-8_4. |
| [47] |
B. Waters, Functional encryption for regular languages, In CRYPTO, Lecture Notes in Comput. Sci., volume 7417, Springer, 2012,218–235.
doi: 10.1007/978-3-642-32009-5_14. |
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H. Wee, Dual system encryption via predicate encodings, In TCC, Lecture Notes in Comput. Sci., volume 8349, Springer, 2014,616–637.
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Figure 3.
The description of the first $ (3q_1 + 6) $ -hybrid games used in the security proof, where alt-keys are answered by $ {\sf AltKeyGen}( {\sf CT}_j, x_j) $ . The rest of the games are described in Figure 4
Figure 4.
The description of the last $ (2\nu + 1) $ -hybrid games used in the security proof, where the key queries are answered in a way similar to $ \mathrm{Game}_{1 \mbox{-} (q_1+1) \mbox{-} 3} $
Table 1.
A comparison between the performance (viz., the number of pairing computations) of the decryption of our construction and that of the construction of Blömer et al
| Additional Decryption Cost (number of pairing) | ||||||
| Blömer et al [6] | ||||||
| PES of [1] | PE Scheme | Features | Verf (V) | Other (O) | Total (V+O) | Our |
| PES 1 | IBE | ER | 4 | 6 | 10 | 2 |
| PES 3 | KP-FE | RL | 2 | |||
| PES 4 | KP-ABE | UnLU | 2 | |||
| PES 5 | KP-ABE | SC | 2 | |||
| PES 6 | KP-DSE | DSE | 2 | |||
| PES 7 | CP-FE | RL | 2 | |||
| PES 8 | KP-ABE | SU | 2 | |||
| PES 9 | KP-ABE | SU | 2 | |||
| PES 10 | CP-ABE | SU | 2 | |||
| PES 11 | CP-ABE | SU | 2 | |||
| PES 12 | KP-ABE | LU | 2 | |||
| PES 13 | CP-ABE | LU | 2 | |||
| PES 14 | DSE | DSE | 2 | |||
| Additional Decryption Cost (number of pairing) | ||||||
| Blömer et al [6] | ||||||
| PES of [1] | PE Scheme | Features | Verf (V) | Other (O) | Total (V+O) | Our |
| PES 1 | IBE | ER | 4 | 6 | 10 | 2 |
| PES 3 | KP-FE | RL | 2 | |||
| PES 4 | KP-ABE | UnLU | 2 | |||
| PES 5 | KP-ABE | SC | 2 | |||
| PES 6 | KP-DSE | DSE | 2 | |||
| PES 7 | CP-FE | RL | 2 | |||
| PES 8 | KP-ABE | SU | 2 | |||
| PES 9 | KP-ABE | SU | 2 | |||
| PES 10 | CP-ABE | SU | 2 | |||
| PES 11 | CP-ABE | SU | 2 | |||
| PES 12 | KP-ABE | LU | 2 | |||
| PES 13 | CP-ABE | LU | 2 | |||
| PES 14 | DSE | DSE | 2 | |||
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