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Multi-dimensional sub/super-range signatures
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DOI：10.1016/j.jisa.2021.103084.png)
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Abstract
En 中文
In time-specific signatures (TSS) (Paterson & Quaglia, SCN'10 and Ishizaka & Kiyomoto, ISC'20) with T numerical values, each signer is given a secret-key associated with a numerical value t is an element of [0, T - 1]and each signature on a message is generated under a numerical range [L, R] s.t. 0 <= L <= R <= 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 is an element of [L, R]. As a generalized primitive of TSS, we propose multi-dimensional sub-range signatures (MDSBRS). As a related primitive, we also propose multi-dimensional super-range signatures (MDSPRS). In MDSBRS (resp. MDSPRS) with D is an element of N dimensions, each secret-key is associated with a set of D ranges {[l(i), r(i)] | i is an element of [1, D]} s.t. 0 <= l(i) <= r(i) <= T-i - 1 and a threshold value d is an element of [1, D], and it correctly produces a signature on any message under a set of D ranges {[L-i , R-i] | i is an element of [1,D]} s.t. 0 <= L-i <= R-i <= T-i - 1, if and only if total number of key-ranges every one [l(i), r(i)] of which is a sub-range (resp.super-range) of the corresponded signature-range [L-i, R-i ], i.e., L-i <= l(i) <= r(i) <= R-i (resp. l(i) <= L-i <= R-i <= 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
Keywords:
Multi-dimensional sub-range signatures
Multi-dimensional super-range signatures
Existential unforgeability
Perfect (signer-)privacy
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