CryptoDB
Mahshid Riahinia
Publications
Year
Venue
Title
2023
EUROCRYPT
Constrained Pseudorandom Functions from Homomorphic Secret Sharing
Abstract
We propose and analyze a simple strategy for constructing 1-key constrained pseudorandom functions (CPRFs) from homomorphic secret sharing. In the process, we obtain the following contributions: first, we identify desirable properties for the underlying HSS scheme for our strategy to work. Second, we show that (most of) recent existing HSS schemes satisfy these properties, leading to instantiations of CPRFs for various constraints and from various assumptions. Notably, we obtain the first (1-key selectively secure, private) CPRFs for inner-product and (1-key selectively secure) CPRFs for NC 1 from the DCR assumption, and more. Last, we revisit two applications of HSS equipped with these additional properties to secure computation: we obtain secure computation in the silent preprocessing model with one party being able to precompute its whole preprocessing material before even knowing the other party, and we construct one-sided statistically secure computation with sublinear communication for restricted forms of computation.
2022
ASIACRYPT
PointProofs, Revisited
Abstract
Vector commitments allow a user to commit to a vector of
length n using a constant-size commitment while being able to locally
open the commitment to individual vector coordinates. Importantly, the
size of position-wise openings should be independent of the dimension
n. Gorbunov, Reyzin, Wee, and Zhang recently proposed PointProofs
(CCS 2020), a vector commitment scheme that supports non-interactive
aggregation of proofs across multiple commitments, allowing to drastically reduce the cost of block propagation in blockchain smart contracts.
Gorbunov et al. provide a security analysis combining the algebraic group
model and the random oracle model, under the weak n-bilinear Diffie-
Hellman Exponent assumption (n-wBDHE) assumption. In this work,
we propose a novel analysis that does not rely on the algebraic group
model. We prove the security in the random oracle model under the n-
Diffie-Hellman Exponent (n-DHE) assumption, which is implied by the
n-wBDHE assumption considered by Gorbunov et al. We further note
that we do not modify their scheme (and thus preserve its efficiency) nor
introduce any additional assumption. Instead, we prove the security of
the scheme as it is via a strictly improved analysis.
Coauthors
- Geoffroy Couteau (1)
- Benoît Libert (1)
- Pierre Meyer (1)
- Alain Passelègue (2)