One of the primary research challenges in Attribute-Based Encryption
(ABE) is constructing and proving cryptosystems that are adaptively
secure. To date the main paradigm for achieving adaptive security in
ABE is dual system encryption. However, almost all such solutions in
bilinear groups rely on (variants of) either the subgroup decision
problem over composite order groups or the decision linear assumption.
Both of these assumptions are decisional rather than search
assumptions and the target of the assumption is a source or bilinear
group element. This is in contrast to earlier selectively secure ABE
systems which can be proven secure from either the decisional or
search Bilinear Diffie-Hellman assumption. In this work we make
progress on closing this gap by giving a new ABE construction for the
subset functionality and prove security under the Search Bilinear
Diffie-Hellman assumption.
We first provide a framework for
proving adaptive security in Attribute-Based Encryption systems. We
introduce a concept of ABE with deletable attributes where any party
can take a ciphertext encrypted under the attribute string and modify it into a ciphertext encrypted under any string where is derived by replacing any bits of
with symbols (i.e. ``deleting" attributes of ). The
semantics of the system are that any private key for a circuit can
be used to decrypt a ciphertext associated with if none of the
input bits read by circuit are symbols and .
We show a pathway for combining ABE
with deletable attributes with constrained psuedorandom functions to
obtain adaptively secure ABE building upon the recent work of
Tsabary. Our new ABE system will be adaptively
secure and be a ciphertext-policy ABE that supports the same
functionality as the underlying constrained PRF as long as the PRF is
``deletion conforming". Here we also provide a simple constrained PRF
construction that gives subset functionality.
Our approach enables us to access a
broader array of Attribute-Based Encryption schemes support deletion
of attributes. For example, we show that both the Goyal~et
al.~(GPSW) and Boyen ABE schemes can
trivially handle a deletion operation. And, by using a hardcore bit
variant of GPSW scheme we obtain an adaptively secure ABE scheme under
the Search Bilinear Diffie-Hellman assumption in addition to
pseudo random functions in NC1. This gives the first adaptively
secure ABE from a search assumption as all prior work relied on
decision assumptions over source group elements.
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Batch Arguments for NP and More from Standard Bilinear Group Assumptions
Non-interactive batch arguments for NP provide a way to amortize the cost of NP verification across multiple instances. They enable a prover to convince a verifier of multiple NP statements with communication much smaller than the total witness length and verification time much smaller than individually checking each instance.
In this work, we give the first construction of a non-interactive batch argument for NP from standard assumptions on groups with bilinear maps (specifically, from either the subgroup decision assumption in composite-order groups or from the $k$-Lin assumption in prime-order groups for any $k \ge 1$). Previously, batch arguments for NP were only known from LWE, or a combination of multiple assumptions, or from non-standard/non-falsifiable assumptions. Moreover, our work introduces a new direct approach for batch verification and avoids heavy tools like correlation-intractable hash functions or probabilistically-checkable proofs common to previous approaches.
As corollaries to our main construction, we obtain the first publicly-verifiable non-interactive delegation scheme for RAM programs (i.e., a succinct non-interactive argument (SNARG) for P) with a CRS of sublinear size (in the running time of the RAM program), as well as the first aggregate signature scheme (supporting bounded aggregation) from standard assumptions on bilinear maps.
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- NSF-PAR ID:
- 10332075
- Date Published:
- Journal Name:
- Annual International Cryptology Conference (CRYPTO)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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