Our scheme only relies on standard assumptions. Specifically we require a pseudorandom number generator, a linear error correcting code and an ideal oblivious transfer functionality. Based on this we prove our scheme secure in the Universal Composability (UC) framework against a static and malicious adversary corrupting any number of parties.
On a practical note, our scheme improves significantly on the non- homomorphic scheme of Cascudo \emph{et al.} Based on their observations in regards to efficiency of using linear error correcting codes for commit- ments we conjecture that our commitment scheme might in practice be more efficient than all existing constructions of UC commitment, even non-homomorphic constructions and even constructions in the random oracle model. In particular, the amortized price of computing one of our commitments is less than that of evaluating a hash function once.
Category / Keywords: Commitments, UC, Homomorphic, Minimal Assumptions, Linear Error Correcting Codes, Erasure Codes. Original Publication (in the same form): IACR-TCC-2016 Date: received 10 Jul 2015, last revised 16 May 2017 Contact author: roberto at cs au dk Available format(s): PDF | BibTeX Citation Note: Added clarification on an error appearing in a previous version of this work. We use the recent notion of interactive proximity testing introduced by Cascudo et al. [CDDDN16] to correct our proof of security. Version: 20170516:070221 (All versions of this report) Short URL: ia.cr/2015/694