Welcome to the resource topic for 2021/698
Title:
Multi-Dimensional Sub/Super-Range Signatures
Authors: Masahito Ishizaka, Shinsaku Kiyomoto
Abstract:In time-specific signatures (TSS) [Paterson & Quaglia, SCN’10] [Ishizaka & Kiyomoto, ISC’20] with T numerical values, each signer is given a secret-key associated with a numerical value t\in[0,T-1] and each signature on a message is generated under a numerical range [L,R] s.t. 0\leq L\leq R\leq T-1. A signer with t can correctly generate a signature under [L,R] if t is truly included in [L,R], i.e., t\in[L,R]. As a generalized primitive of TSS, we propose multi-dimensional \textit{sub}-range signatures (MDSBRS). As a related primitive, we also propose multi-dimensional \textit{super}-range signatures (MDSPRS). In MDSBRS (resp. MDSPRS) with D\in\mathbb{N} dimensions, each secret-key is associated with a set of D ranges \{[l_i,r_i]\mid i\in[1,D]\} s.t. 0 \leq l_i\leq r_i\leq T_i-1 and a threshold value d\in[1,D], and it correctly produces a signature on any message under a set of D ranges \{[L_i,R_i]\mid i\in[1,D]\} s.t. 0 \leq L_i\leq R_i\leq T_i-1, if and only if total number of key-ranges every one [l_i,r_i] of which is a \textit{sub}-range (resp. \textit{super}-range) of the corresponded signature-range [L_i,R_i], i.e., L_i\leq l_i\leq r_i\leq R_i (resp. l_i\leq L_i\leq R_i\leq r_i), is more than d-1. We show that, by extending (or generalizing) an existing TSS scheme, we obtain MDSBRS and MDSPRS schemes each one of which is secure, i.e., existentially unforgeable and perfectly (signer-)private, under standard assumption and asymptotically efficient.
ePrint: https://eprint.iacr.org/2021/698
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