Author:
Dowerah Uddipana,Dutta Subhranil,Mitrokotsa Aikaterini,Mukherjee Sayantan,Pal Tapas
Abstract
AbstractPredicate inner product functional encryption (P-IPFE) is essentially attribute-based IPFE (AB-IPFE) which additionally hides attributes associated to ciphertexts. In a P-IPFE, a message $${\textbf {x}}$$
x
is encrypted under an attribute $${\textbf {w}}$$
w
and a secret key is generated for a pair $$({\textbf {y}}, {\textbf {v}})$$
(
y
,
v
)
such that recovery of $$\langle {{\textbf {x}}}, {{\textbf {y}}}\rangle $$
⟨
x
,
y
⟩
requires the vectors $${\textbf {w}}, {\textbf {v}}$$
w
,
v
to satisfy a linear relation. We call a P-IPFE unbounded if it can encrypt unbounded length attributes and message vectors. $$\bullet $$
∙
zero predicate IPFE. We construct the first unbounded zero predicate IPFE (UZP-IPFE) which recovers $$\langle {{\textbf {x}}}, {{\textbf {y}}}\rangle $$
⟨
x
,
y
⟩
if $$\langle {{\textbf {w}}}, {{\textbf {v}}}\rangle =0$$
⟨
w
,
v
⟩
=
0
. This construction is inspired by the unbounded IPFE of Tomida and Takashima (ASIACRYPT 2018) and the unbounded zero inner product encryption of Okamoto and Takashima (ASIACRYPT 2012). The UZP-IPFE stands secure against general attackers capable of decrypting the challenge ciphertext. Concretely, it provides full attribute-hiding security in the indistinguishability-based semi-adaptive model under the standard symmetric external Diffie–Hellman assumption. $$\bullet $$
∙
non-zero predicate IPFE. We present the first unbounded non-zero predicate IPFE (UNP-IPFE) that successfully recovers $$\langle {{\textbf {x}}}, {{\textbf {y}}}\rangle $$
⟨
x
,
y
⟩
if $$\langle {{\textbf {w}}}, {{\textbf {v}}}\rangle \ne 0$$
⟨
w
,
v
⟩
≠
0
. We generically transform an unbounded quadratic FE (UQFE) scheme to weak attribute-hiding UNP-IPFE in both public and secret key setting. Interestingly, our secret key simulation secure UNP-IPFE has succinct secret keys and is constructed from a novel succinct UQFE that we build in the random oracle model. We leave the problem of constructing a succinct public key UNP-IPFE or UQFE in the standard model as an important open problem.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications,Software
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