Paper 2021/698
MultiDimensional Sub/SuperRange Signatures
Masahito Ishizaka and Shinsaku Kiyomoto
Abstract
In timespecific signatures (TSS) [Paterson \& Quaglia, SCN'10] [Ishizaka \& Kiyomoto, ISC'20] with $T$ numerical values, each signer is given a secretkey associated with a numerical value $t\in[0,T1]$ and each signature on a message is generated under a numerical range $[L,R]$ s.t. $0\leq L\leq R\leq T1$. 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 multidimensional \textit{sub}range signatures (MDSBRS). As a related primitive, we also propose multidimensional \textit{super}range signatures (MDSPRS). In MDSBRS (resp. MDSPRS) with $D\in\mathbb{N}$ dimensions, each secretkey is associated with a set of $D$ ranges $\{[l_i,r_i]\mid i\in[1,D]\}$ s.t. $0 \leq l_i\leq r_i\leq T_i1$ 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. $0 \leq L_i\leq R_i\leq T_i1$, if and only if total number of keyranges every one $[l_i,r_i]$ of which is a \textit{sub}range (resp. \textit{super}range) of the corresponded signaturerange $[L_i,R_i]$, 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 $d1$. 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.
Metadata
 Available format(s)
 Category
 Publickey cryptography
 Publication info
 Preprint. MINOR revision.
 Keywords
 Multidimensional subrange signaturesMultidimensional superrange signaturesExistential unforgeabilityPerfect privacy
 Contact author(s)
 maishizaka @ kddiresearch jp
 History
 20210528: received
 Short URL
 https://ia.cr/2021/698
 License

CC BY
BibTeX
@misc{cryptoeprint:2021/698, author = {Masahito Ishizaka and Shinsaku Kiyomoto}, title = {MultiDimensional Sub/SuperRange Signatures}, howpublished = {Cryptology {ePrint} Archive, Paper 2021/698}, year = {2021}, url = {https://eprint.iacr.org/2021/698} }