New realizations of somewhere statistically binding hashing and positional accumulators

T. Okamoto, K.Z. Pietrzak, B. Waters, D. Wichs, in:, Springer, 2016, pp. 121–145.

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Conference Paper | Published | English
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Series Title
LNCS
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.
Publishing Year
Date Published
2016-01-08
Volume
9452
Page
121 - 145
Conference
ASIACRYPT: Theory and Application of Cryptology and Information Security
Conference Location
Auckland, New Zealand
Conference Date
2015-11-29 – 2015-12-03
IST-REx-ID

Cite this

Okamoto T, Pietrzak KZ, Waters B, Wichs D. New realizations of somewhere statistically binding hashing and positional accumulators. In: Vol 9452. Springer; 2016:121-145. doi:10.1007/978-3-662-48797-6_6
Okamoto, T., Pietrzak, K. Z., Waters, B., & Wichs, D. (2016). New realizations of somewhere statistically binding hashing and positional accumulators (Vol. 9452, pp. 121–145). Presented at the ASIACRYPT: Theory and Application of Cryptology and Information Security, Auckland, New Zealand: Springer. https://doi.org/10.1007/978-3-662-48797-6_6
Okamoto, Tatsuaki, Krzysztof Z Pietrzak, Brent Waters, and Daniel Wichs. “New Realizations of Somewhere Statistically Binding Hashing and Positional Accumulators,” 9452:121–45. Springer, 2016. https://doi.org/10.1007/978-3-662-48797-6_6.
T. Okamoto, K. Z. Pietrzak, B. Waters, and D. Wichs, “New realizations of somewhere statistically binding hashing and positional accumulators,” presented at the ASIACRYPT: Theory and Application of Cryptology and Information Security, Auckland, New Zealand, 2016, vol. 9452, pp. 121–145.
Okamoto T, Pietrzak KZ, Waters B, Wichs D. 2016. New realizations of somewhere statistically binding hashing and positional accumulators. ASIACRYPT: Theory and Application of Cryptology and Information Security, LNCS, vol. 9452. 121–145.
Okamoto, Tatsuaki, et al. New Realizations of Somewhere Statistically Binding Hashing and Positional Accumulators. Vol. 9452, Springer, 2016, pp. 121–45, doi:10.1007/978-3-662-48797-6_6.
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