Cryptology ePrint Archive: Report 2012/379
All-But-Many Encryption: A New Framework for Fully-Equipped UC Commitments
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)
Short URL: ia.cr/2012/379
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