**Functional Encryption for Quadratic Functions, and Applications to Predicate Encryption**

*Romain Gay*

**Abstract: **We present a functional encryption scheme based on standard assumptions where ciphertexts are associated with a tuple of values \((x_1,\ldots,x_n) \in \mathbb{Z}_p^n\), secret keys are associated with a degree-two polynomial, and the decryption of a ciphertext \(\mathsf{ct}_{(x_1,\ldots,x_n) \in \mathbb{Z}_p^n}\) with a secret key \(\mathsf{sk}_{P \in \mathbb{Z}_p[X_1,\ldots,X_n], \mathsf{deg}(P) \leq 2}\) recovers \(P(x_1,\ldots,x_n)\), where the ciphertext contains only \(O(n)\) group elements. Our scheme, which achieves selective security based on pairings, also yields a new predicate encryption scheme that supports degree-two polynomial evaluation, generalizing both [KSW 08] and [BSW 06].

**Category / Keywords: **functional encryption, quadratic function

**Date: **received 23 Nov 2016, last revised 3 Apr 2017

**Contact author: **rgay at dis ens fr

**Available format(s): **PDF | BibTeX Citation

**Version: **20170403:215111 (All versions of this report)

**Short URL: **ia.cr/2016/1106

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