. B. Aarv17, B. Applebaum, P. Arkis, P. N. Raykov, and . Vasudevan, Conditional disclosure of secrets: Amplification, closure, amortization, lower-bounds, and separations, CRYPTO 2017, Part I, vol.10401, pp.727-757, 2017.

. S. Abb10, D. Agrawal, X. Boneh, and . Boyen, Efficient lattice (H)IBE in the standard model, EUROCRYPT 2010, vol.6110, pp.553-572, 2010.

. M. Abdp15, F. Abdalla, A. D. Bourse, D. Caro, and . Pointcheval, Simple functional encryption schemes for inner products, PKC 2015, vol.9020, pp.733-751, 2015.

M. Abdalla, F. Bourse, A. De-caro, and D. Pointcheval, Simple Functional Encryption Schemes for Inner Products, Lecture Notes in Computer Science, pp.733-751, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01131971

M. Abdalla, F. Benhamouda, and R. Gay, From Single-Input to Multi-client Inner-Product Functional Encryption, Lecture Notes in Computer Science, vol.11923, pp.552-582, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02135963

. M. Abkw19, F. Abdalla, M. Benhamouda, H. Kohlweiss, and . Waldner, Decentralizing inner-product functional encryption, PKC 2019, Part II, vol.11443, p.17, 2019.

M. Ambrona, G. Barthe, and B. Schmidt, Generic Transformations of Predicate Encodings: Constructions and Applications, Advances in Cryptology ? CRYPTO 2017, vol.10401, pp.36-66, 2017.

S. Agrawal and M. Chase, A Study of Pair Encodings: Predicate Encryption in Prime Order Groups, Theory of Cryptography, vol.9563, pp.259-288, 2015.

S. Agrawal and M. Chase, Simplifying Design and Analysis of Complex Predicate Encryption Schemes, Lecture Notes in Computer Science, vol.9, pp.627-656, 2017.

. M. Acf-+-18, D. Abdalla, D. Catalano, R. Fiore, B. Gay et al., Multi-input functional encryption for inner products: Functionhiding realizations and constructions without pairings, CRYPTO 2018, Part I, vol.10991, pp.597-627, 2018.

. M. Acgu20, D. Abdalla, R. Catalano, B. Gay, and . Ursu, Inner-product functional encryption with fine-grained access control, ASIACRYPT 2020, 2020.

M. Abdalla, R. Gay, M. Raykova, and H. Wee, Multi-input Inner-Product Functional Encryption from Pairings, Lecture Notes in Computer Science, pp.601-626, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01524105

M. Abdalla, J. Gong, and H. Wee, Functional Encryption for Attribute-Weighted Sums from k-Lin, Advances in Cryptology ? CRYPTO 2020, vol.12170, pp.685-716, 2020.
URL : https://hal.archives-ouvertes.fr/hal-02948674

P. Ananth, A. Jain, H. Lin, C. Matt, and A. Sahai, Indistinguishability Obfuscation Without Multilinear Maps: New Paradigms via Low Degree Weak Pseudorandomness and Security Amplification, Advances in Cryptology ? CRYPTO 2019, vol.615, pp.284-332, 2019.

. Ajt99,

M. Ajtai, Generating Hard Instances of the Short Basis Problem, Automata, Languages and Programming, vol.1644, pp.1-9, 1999.

N. Attrapadung and B. Libert, Functional Encryption for Inner Product: Achieving Constant-Size Ciphertexts with Adaptive Security or Support for Negation, Public Key Cryptography ? PKC 2010, vol.6056, pp.384-402, 2010.

S. Agrawal, B. Libert, and D. Stehlé, Fully Secure Functional Encryption for Inner Products, from Standard Assumptions, Advances in Cryptology ? CRYPTO 2016, vol.9816, pp.333-362, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01228559

J. Alwen and C. Peikert, Generating Shorter Bases for Hard Random Lattices, Theory of Computing Systems, vol.48, issue.3, pp.535-553, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00359718

P. Ananth and A. Sahai, Projective Arithmetic Functional Encryption and Indistinguishability Obfuscation from Degree-5 Multilinear Maps, Lecture Notes in Computer Science, pp.152-181, 2017.

N. Attrapadung, Dual System Encryption via Doubly Selective Security: Framework, Fully Secure Functional Encryption for Regular Languages, and More, Advances in Cryptology ? EUROCRYPT 2014, vol.8441, pp.557-577, 2014.

. Att16,

N. Attrapadung, Dual System Encryption Framework in Prime-Order Groups via Computational Pair Encodings, Advances in Cryptology ? ASIACRYPT 2016, vol.10032, pp.591-623, 2016.

D. Boneh and X. Boyen, Efficient Selective-ID Secure Identity-Based Encryption Without Random Oracles, Advances in Cryptology - EUROCRYPT 2004, vol.3027, pp.223-238, 2004.

. D. Bbg05, X. Boneh, E. Boyen, and . Goh, Hierarchical identity based encryption with constant size ciphertext, EURO-CRYPT 2005, vol.3494, p.17, 2005.

F. Benhamouda, F. Bourse, and H. Lipmaa, CCA-Secure Inner-Product Functional Encryption from Projective Hash Functions, Lecture Notes in Computer Science, vol.10175, pp.36-66, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01613546

. C. Bcfg17, D. Baltico, D. Catalano, R. Fiore, and . Gay, Practical functional encryption for quadratic functions with applications to predicate encryption, CRYPTO 2017, Part I, vol.10401, pp.67-98, 2017.

M. Barbosa, D. Catalano, A. Soleimanian, and B. Warinschi, Efficient Function-Hiding Functional Encryption: From Inner-Products to Orthogonality, Topics in Cryptology ? CT-RSA 2019, pp.127-148, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02363215

D. Boneh and M. K. Franklin, Identity-Based Encryption from the Weil Pairing, Advances in Cryptology ? CRYPTO 2001, vol.2139, pp.213-229, 2001.

. D. Bgg-+-14, C. Boneh, S. Gentry, S. Gorbunov, V. Halevi et al., Fully key-homomorphic encryption, arithmetic circuit ABE and compact garbled circuits, EUROCRYPT 2014, vol.8441, pp.533-556, 2014.

D. Boneh and M. Hamburg, Generalized Identity Based and Broadcast Encryption Schemes, Advances in Cryptology - ASIACRYPT 2008, vol.5350, pp.455-470, 2008.

A. Bishop, A. Jain, and L. Kowalczyk, Function-Hiding Inner Product Encryption, Advances in Cryptology -- ASIACRYPT 2015, vol.9452, pp.470-491, 2015.

. J. Bsw07, A. Bethencourt, B. Sahai, and . Waters, Ciphertext-policy attribute-based encryption, 2007 IEEE Symposium on Security and Privacy, pp.321-334, 2007.

. D. Bsw11, A. Boneh, B. Sahai, and . Waters, Functional encryption: Definitions and challenges, TCC 2011, vol.6597, pp.253-273, 2011.

. Cai98,

J. Cai, A relation of primal-dual lattices and the complexity of shortest lattice vector problem, Theoretical Computer Science, vol.207, issue.1, pp.105-116, 1998.

. J. Cdg-+-18, E. Chotard, . Dufour, R. Sans, D. H. Gay et al., Decentralized multi-client functional encryption for inner product, ASIACRYPT 2018, Part II, vol.11273, pp.703-732, 2018.

. J. Cgw15, R. Chen, H. Gay, and . Wee, Improved dual system ABE in prime-order groups via predicate encodings, EURO-CRYPT 2015, Part II, vol.9057, pp.595-624, 2015.

. J. Cgw18, J. Chen, H. Gong, and . Wee, Improved inner-product encryption with adaptive security and full attribute-hiding, ASIACRYPT 2018, Part II, vol.11273, pp.673-702, 2018.

. D. Chkp10, D. Cash, E. Hofheinz, C. Kiltz, and . Peikert, Bonsai trees, or how to delegate a lattice basis, EUROCRYPT 2010, vol.6110, pp.523-552, 2010.

G. Castagnos, F. Laguillaumie, and I. Tucker, Practical Fully Secure Unrestricted Inner Product Functional Encryption Modulo p, Lecture Notes in Computer Science, vol.11273, pp.733-764, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01934296

R. J. Connor and M. Schuchard, Blind bernoulli trials: A noninteractive protocol for hidden-weight coin flips, USENIX Security 2019, p.19, 2019.

Y. Chen, L. Zhang, and S. Yiu, Eprint, Cryptology ePrint Archive, 2019.

. P. Ddm16, R. Datta, S. Dutta, and . Mukhopadhyay, Functional encryption for inner product with full function privacy, PKC 2016, Part I, vol.9614, pp.164-195, 2016.

L. Ducas and D. Micciancio, Improved Short Lattice Signatures in the Standard Model, Advances in Cryptology ? CRYPTO 2014, vol.8616, pp.335-352, 2014.

P. Datta, T. Okamoto, and J. Tomida, Full-Hiding (Unbounded) Multi-input Inner Product Functional Encryption from the k-Linear Assumption, Public-Key Cryptography ? PKC 2018, vol.10770, pp.245-277, 2018.

E. , D. Sans, and D. , Unbounded inner-product functional encryption with succinct keys, ACNS 19, vol.11464, p.19, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02357165

R. Gay, Public-Key Encryption, Revisited: Tight Security and Richer Functionalities, vol.34, 2019.
URL : https://hal.archives-ouvertes.fr/tel-02137987

. Gay20,

R. Gay, A New Paradigm for Public-Key Functional Encryption for Degree-2 Polynomials, Lecture Notes in Computer Science, pp.95-120, 2020.

. S. Ggg-+-14, S. D. Goldwasser, V. Gordon, A. Goyal, J. Jain et al., Multi-input functional encryption, EUROCRYPT 2014, vol.8441, p.34, 2014.

. Y. Gikm00, Y. Gertner, E. Ishai, T. Kushilevitz, and . Malkin, Protecting data privacy in private information retrieval schemes, Journal of Computer and System Sciences, vol.60, issue.3, pp.592-629, 2000.

. R. Gjls20, A. Gay, H. Jain, A. Lin, and . Sahai, Eprint, 2019.

. R. Gkw15, I. Gay, H. Kerenidis, and . Wee, Communication complexity of conditional disclosure of secrets and attribute-based encryption, CRYPTO 2015, Part II, vol.9216, pp.485-502, 2015.

. V. Gpsw06, O. Goyal, A. Pandey, B. Sahai, and . Waters, Attribute-based encryption for fine-grained access control of encrypted data, ACM CCS 2006, p.8, 2006.

C. Gentry, C. Peikert, and V. Vaikuntanathan, Trapdoors for hard lattices and new cryptographic constructions, Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08, pp.197-206, 2008.

. S. Gvw13, V. Gorbunov, H. Vaikuntanathan, and . Wee, Attribute-based encryption for circuits, 45th ACM STOC, pp.545-554, 2013.

. S. Gvw15, V. Gorbunov, H. Vaikuntanathan, and . Wee, Predicate encryption for circuits from LWE, CRYPTO 2015, Part II, vol.9216, pp.503-523, 2015.

. A. Jlms19, H. Jain, C. Lin, A. Matt, and . Sahai, How to leverage hardness of constant-degree expanding polynomials overa R to build iO, EUROCRYPT 2019, Part I, vol.11476, p.19, 2019.

A. Jain, H. Lin, and A. Sahai, Eprint, 2019.

S. Kim, K. Lewi, A. Mandal, H. Montgomery, A. Roy et al., Function-Hiding Inner Product Encryption Is Practical, Lecture Notes in Computer Science, vol.11035, pp.544-562, 2018.

. J. Ksw08, A. Katz, B. Sahai, and . Waters, Predicate encryption supporting disjunctions, polynomial equations, and inner products, EUROCRYPT 2008, vol.4965, p.93, 2008.

M. Karchmer and A. Wigderson, On span programs, Proceedings of the Eigth Annual Structure in Complexity Theory Conference, p.16, 1993.

S. Katsumata and S. Yamada, Partitioning via Non-linear Polynomial Functions: More Compact IBEs from Ideal Lattices and Bilinear Maps, Advances in Cryptology ? ASIACRYPT 2016, vol.10032, pp.682-712, 2016.

. Lew12,

A. B. Lewko, Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting, Advances in Cryptology ? EUROCRYPT 2012, vol.7237, pp.318-335, 2012.

H. Lin, Indistinguishability Obfuscation from SXDH on 5-Linear Maps and Locality-5 PRGs, Advances in Cryptology ? CRYPTO 2017, vol.10401, pp.599-629, 2017.

B. Libert and R. Titiu, Multi-client functional encryption for linear functions in the standard model from LWE, ASIACRYPT 2019, Part III, vol.11923, pp.520-551, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02352139

. T. Lvw17, V. Liu, H. Vaikuntanathan, and . Wee, Conditional disclosure of secrets via non-linear reconstruction, CRYPTO 2017, Part I, vol.10401, p.10, 2017.

A. B. Lewko and B. Waters, New techniques for dual system encryption and fully secure HIBE with short ciphertexts, TCC 2010, vol.5978, p.2, 2010.

D. Micciancio and S. Goldwasser, Complexity of Lattice Problems: a cryptographic perspective, p.12, 2002.

D. Micciancio and C. Peikert, Trapdoors for lattices: Simpler, tighter, faster, smaller, EUROCRYPT 2012, vol.7237, pp.700-718, 2012.

D. Micciancio and O. Regev, Worst-case to average-case reductions based on Gaussian measures, 45th FOCS, pp.372-381, 2004.

. O'n10,

A. , Eprint, Cryptology ePrint Archive, p.9, 2019.

T. Okamoto and K. Takashima, Hierarchical Predicate Encryption for Inner-Products, Advances in Cryptology ? ASIACRYPT 2009, vol.5912, pp.214-231, 2009.

T. Okamoto and K. Takashima, Adaptively Attribute-Hiding (Hierarchical) Inner Product Encryption, Advances in Cryptology ? EUROCRYPT 2012, vol.7237, pp.591-608, 2012.

C. Peikert, Limits on the Hardness of Lattice Problems in \ell _p Norms, Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07), p.6, 2007.

C. Peikert and A. Rosen, Efficient Collision-Resistant Hashing from Worst-Case Assumptions on Cyclic Lattices, Theory of Cryptography, vol.3876, pp.145-166, 2006.

O. Regev, On lattices, learning with errors, random linear codes, and cryptography, Journal of the ACM, vol.56, issue.6, pp.1-40, 2009.

. T. Rpb-+-19, D. Ryffel, F. Pointcheval, E. Bach, R. Dufour-sans et al., Partially encrypted deep learning using functional encryption, Advances in Neural Information Processing Systems, vol.32, pp.4519-4530, 2019.

. Sha84,

A. Shamir, Identity-Based Cryptosystems and Signature Schemes, Advances in Cryptology, vol.196, pp.47-53

A. Sahai and B. R. Waters, Fuzzy Identity-Based Encryption, Lecture Notes in Computer Science, vol.3494, pp.457-473, 2005.

. Springer, The human hippocampus, H.M. Duvernoy Third edition, Springer-Verlag Berlin Heidelberg 2005 (232 pages), Journal of Neuroradiology, vol.32, issue.4, p.288, 2005.

J. Tomida and K. Takashima, Unbounded Inner Product Functional Encryption from Bilinear Maps, Lecture Notes in Computer Science, vol.11273, pp.609-639, 2018.

B. Waters, Dual System Encryption: Realizing Fully Secure IBE and HIBE under Simple Assumptions, Advances in Cryptology - CRYPTO 2009, vol.5677, pp.619-636, 2009.

H. Wee, Dual System Encryption via Predicate Encodings, Theory of Cryptography, vol.8349, pp.616-637, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01094703

H. Wee, Attribute-Hiding Predicate Encryption in Bilinear Groups, Revisited, Theory of Cryptography, vol.10677, pp.206-233, 2017.

. Z. Wfl19, X. Wang, F. Fan, and . Liu, FE for inner products and its application to decentralized ABE, PKC 2019, Part II, vol.11443, pp.97-127, 2019.