## Cryptology ePrint Archive: Report 2020/652

Somewhere Statistically Binding Commitment Schemes with Applications

Prastudy Fauzi and Helger Lipmaa and Zaira Pindado and Janno Siim

Abstract: We define a new primitive that we call a somewhere statistically binding (SSB) commitment scheme, which is a generalization of dual-mode commitments but has similarities with SSB hash functions (Hubacek and Wichs, ITCS 2015) without local opening. In (existing) SSB hash functions, one can compute a hash of a vector $v$ that is statistically binding in one coordinate of $v$. Meanwhile, in SSB commitment schemes, a commitment of a vector $v$ is statistically binding in some coordinates of $v$ and is statistically hiding in the other coordinates. The set of indices where binding holds is predetermined but known only to the commitment key generator. We show that the primitive can be instantiated by generalizing the succinct Extended Multi-Pedersen commitment scheme (González et al., Asiacrypt 2015). We further introduce the notion of functional SSB commitment schemes and, importantly, use it to get an efficient quasi-adaptive NIZK for arithmetic circuits and efficient oblivious database queries.

Category / Keywords: public-key cryptography / Oblivious transfer, QA-NIZK, SSB commitment scheme

Date: received 30 May 2020

Contact author: prastudy fauzi at gmail com,helger lipmaa@gmail com,zaira pindado@upf edu,jannosiim@gmail com

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2020/652

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