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**2016/1106**

**Title:**

Functional Encryption for Quadratic Functions, and Applications to Predicate Encryption

**Authors:**
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].

**ePrint:**
https://eprint.iacr.org/2016/1106

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