New realizations of somewhere statistically binding hashing and positional accumulators Conference Paper

Author(s): Okamoto, Tatsuaki; Pietrzak, Krzysztof; Waters, Brent; Wichs, Daniel
Title: New realizations of somewhere statistically binding hashing and positional accumulators
Title Series: LNCS
Affiliation IST Austria
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). The 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.
Keywords: obfuscation; foundations; hashing
Conference Title: ASIACRYPT: Theory and Application of Cryptology and Information Security
Volume: 9452
Conference Dates: November 29 - December 3, 2015
Conference Location: Auckland, New Zealand
ISBN: 978-3-642-17372-1
Publisher: Springer  
Date Published: 2015-01-01
Start Page: 121
End Page: 145
DOI: 10.1007/978-3-662-48797-6_6
Notes: K. Pietrzak—Research supported by ERC starting grant (259668-PSPC). B. Waters—Supported by NSF CNS-1228599 and CNS-1414082. DARPA SafeWare, Google Faculty Research award, the Alfred P. Sloan Fellowship, Microsoft Faculty Fellowship, and Packard Foundation Fellowship. D. Wichs—Research supported by NSF grants CNS-1347350, CNS-1314722, CNS- 1413964.
Open access: yes (repository)
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