Cryptology ePrint Archive: Report 2020/1026

Simple and Efficient FE for Quadratic Functions

Junqing Gong and Haifeng Qian

Abstract: This paper presents the first functional encryption schemes for quadratic functions (or degree-2 polynomials) achieving simulation-based security in the semi-adaptive model with constant-size secret key. The unique prior construction with the same security guarantee by Gay [PKC 20] has secret keys of size linear in the message size. They also enjoy shorter ciphertexts:

- our first scheme is based on bilateral DLIN (decisional linear) assumption as Gay's scheme and the ciphertext is 15% shorter;

- our second scheme based on SXDH assumption and bilateral DLIN assumption is more efficient; it has 67% shorter ciphertext than previous SXDH-based scheme with selective indistinguishability security by Baltico et al. [CRYPTO 17]; the efficiency is comparable to their second scheme in the generic group model.

Technically, we roughly combine Wee's ``secret-key-to-public-key'' compiler [TCC 17] with Gay's paradigm [PKC 20]. We avoid (partial) function-hiding inner-product functional encryption used in Gay's work and make our schemes conceptually simpler.

Category / Keywords: public-key cryptography /

Date: received 25 Aug 2020

Contact author: jqgong at sei ecnu edu cn,hfqian@cs ecnu edu cn

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Version: 20200827:030937 (All versions of this report)

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