Simple and efficient FE for quadratic functions

This paper presents two functional encryption schemes for quadratic functions (or degree-2 polynomials) achieving simulation-based security in the semi-adaptive model with constant-size secret keys. Prior constructions in the standard model either achieve weaker security model [CRYPTO 17] or require linear-size secret keys (in the message length) [PKC 20]. One of our proposed schemes is comparable to existing schemes in the generic group model in terms of ciphertext size. Technically, we combine Wee’s compiler [TCC 17] with Gay’s paradigm [PKC 20]. However, we avoid (partially) function-hiding inner-product functional encryption used in Gay’s paradigm which makes our work conceptually simpler.