$k$-Linear assumption ⇒ ABE

Standard model · KW19 · security loss: polynomial — KW19

Statement

If the $k$-Lin assumption holds in prime-order bilinear groups, there are key-policy and ciphertext-policy ABE schemes for ${\mathrm{NC}}^1$ that are adaptively secure (KP-IND-CPA and CP-IND-CPA) with polynomial security loss. The KP-ABE ciphertext size is linear in the attribute length and independent of the policy size, even when an attribute is used many times in the policy; the CP-ABE scheme has the analogous guarantee — KW19.

Notes

• RW13 give large-universe KP-ABE and CP-ABE in prime-order bilinear groups, selectively secure under two $q$-type assumptions rather than $k$-Lin.