From: Efficient functional encryption for inner product with simulation-based security
BJK15(Bishop et al. 2015) | DDM16(Datta et al. 2017) | TAO16(Tomida et al2016) | ZZL17(Zhao et al. 2018) | ZZL18(Zhao et al. 2018) | Ours | |
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MSK | \((8n^2+8)\ell _{\mathbb {Z}_q}\) | \((8n^2+12n+28)\ell _{\mathbb {Z}_q}\) | \((4n^2+18n+20)\ell _{\mathbb {Z}_q}\) | \((6n^2+10n+24)\ell _{\mathbb {Z}_q}\) | \((2n^2+18n+36)\ell _{\mathbb {Z}_q}\) | \((2n^2+14n+20)\ell _{\mathbb {Z}_q}\) |
CT | \((2n+2)\ell _{\mathbb {G}_1}\) | \((4n+8)\ell _{\mathbb {G}_1}\) | \((2n+5)\ell _{\mathbb {G}_1}\) | \((2n+4)\ell _{\mathbb {G}_1}\) | \((n+6)\ell _{\mathbb {G}_1}\) | \((n+5)\ell _{\mathbb {G}_1}\) |
SK | \((2n+2)\ell _{\mathbb {G}_2}\) | \((4n+8)\ell _{\mathbb {G}_2}\) | \((2n+5)\ell _{\mathbb {G}_2}\) | \((2n+4)\ell _{\mathbb {G}_2}\) | \((n+6)\ell _{\mathbb {G}_2}\) | \((n+5)\ell _{\mathbb {G}_2}\) |
KeyGen | 2n+2 | 4n+8 | 2n+5 | 2n+4 | n+6 | n+5 |
Encrypt | 2n+2 | 4n+8 | 2n+5 | 2n+4 | n+6 | n+5 |
Decrypt | 2n+2 | 4n+8 | 2n+5 | 2n+4 | n+6 | n+5 |
Assumption | SXDH | SXDH | XDLIN | SXDH | XDLIN | XDLIN |
Security | IND | IND | IND | SIM | SIM | SIM |