Cryptology ePrint Archive: Report 2012/379

All-But-Many Encryption: A New Framework for Fully-Equipped UC Commitments

Eiichiro Fujisaki

Abstract: We present a general framework for constructing non-interactive universally composable (UC) commitment schemes that are secure against adaptive adversaries in the non-erasure model under a re-usable common reference string. Previously, such ``fully-equipped'' UC commitment schemes have been known only in [CF01,CLOS02], with strict expansion factor O(k); meaning that to commit L bits, communication strictly requires O(Lk)$ bits, where k denotes the security parameter. Efficient construction of a fully-equipped UC commitment scheme is a long-standing open problem. We introduce new abstraction, called all-but-many encryption (ABME), and prove that it captures fully-equipped UC commitment schemes. We propose the first fully-equipped UC commitment scheme with optimal expansion factor O(1) from our ABME scheme related to the DCR assumption. We also provide an all-but-many lossy trapdoor function (ABM-LTF)[Hof12] from our DCR-based ABME scheme, with a better lossy rate than [Hof12].

Category / Keywords: public-key cryptography / universal composable commitments, all-but-many encryption, and all-but-many lossy trapdoor functions

Original Publication (with major differences): IACR-ASIACRYPT-2014

Date: received 5 Jul 2012, last revised 16 Jun 2016

Contact author: eiichiro fujisaki at gmail com

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Version: 20160616:090115 (All versions of this report)

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