New Realizations of Somewhere Statistically Binding Hashing and Positional Accumulators

A somewhere statistically binding (SSB) hash, introduced by Hub´aˇcek and Wichs (ITCS ’15), can be used to hash a long string x to a short digest y = Hhk(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 preimages 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 = Hhk(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 s...

• Type: Journal
• Year: 2015
• Where: ASIACRYPT
• Authors: Tatsuaki Okamoto, Krzysztof Pietrzak, Brent Waters, Daniel Wichs
• Keywords: ASIACRYPT 2015, Cryptology