---
res:
bibo_abstract:
- "A somewhere statistically binding (SSB) hash, introduced by Hubáček and Wichs
(ITCS ’15), can be used to hash a long string x to a short digest y = H hk (x)
using a public hashing-key hk. Furthermore, there is a way to set up the hash
key hk to make it statistically binding on some arbitrary hidden position i, meaning
that: (1) the digest y completely determines the i’th bit (or symbol) of x so
that all pre-images of y have the same value in the i’th position, (2) it is computationally
infeasible to distinguish the position i on which hk is statistically binding
from any other position i’. Lastly, the hash should have a local opening property
analogous to Merkle-Tree hashing, meaning that given x and y = H hk (x) it should
be possible to create a short proof π that certifies the value of the i’th bit
(or symbol) of x without having to provide the entire input x. A similar primitive
called a positional accumulator, introduced by Koppula, Lewko and Waters (STOC
’15) further supports dynamic updates of the hashed value. These tools, which
are interesting in their own right, also serve as one of the main technical components
in several recent works building advanced applications from indistinguishability
obfuscation (iO).\r\n\r\nThe prior constructions of SSB hashing and positional
accumulators required fully homomorphic encryption (FHE) and iO respectively.
In this work, we give new constructions of these tools based on well studied number-theoretic
assumptions such as DDH, Phi-Hiding and DCR, as well as a general construction
from lossy/injective functions.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Tatsuaki
foaf_name: Okamoto, Tatsuaki
foaf_surname: Okamoto
- foaf_Person:
foaf_givenName: Krzysztof Z
foaf_name: Pietrzak, Krzysztof Z
foaf_surname: Pietrzak
foaf_workInfoHomepage: http://www.librecat.org/personId=3E04A7AA-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Brent
foaf_name: Waters, Brent
foaf_surname: Waters
- foaf_Person:
foaf_givenName: Daniel
foaf_name: Wichs, Daniel
foaf_surname: Wichs
bibo_doi: 10.1007/978-3-662-48797-6_6
bibo_volume: 9452
dct_date: 2016^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: New realizations of somewhere statistically binding hashing and positional
accumulators@
...