Cryptology ePrint Archive: Report 2018/640

Lower Bounds on Structure-Preserving Signatures for Bilateral Messages

Masayuki Abe and Miguel Ambrona and Miyako Ohkubo and Mehdi Tibouchi

Abstract: Lower bounds for structure-preserving signature (SPS) schemes based on non-interactive assumptions have only been established in the case of unilateral messages, i.e. schemes signing tuples of group elements all from the same source group. In this paper, we consider the case of bilateral messages, consisting of elements from both source groups. We show that, for Type-III bilinear groups, SPSís must consist of at least 6 group elements: many more than the 4 elements needed in the unilateral case, and optimal, as it matches a known upper bound from the literature. We also obtain the first non-trivial lower bounds for SPSís in Type-II groups: a minimum of 4 group elements, whereas constructions with 3 group elements are known from interactive assumptions.

Category / Keywords: public-key cryptography / Structure-Preserving Signatures, Bilateral Messages, Crucial Relation

Original Publication (with minor differences): Conference on Security and Cryptography for Networks (SCN 2018)

Date: received 29 Jun 2018

Contact author: miguel ambrona at imdea org

Available format(s): PDF | BibTeX Citation

Version: 20180706:123744 (All versions of this report)

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