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Table 3 Theoretical analysis of TRF

From: Predicate encryption against master-key tampering attacks

Reference Description Assumption Size of PP Cost of evaluation
(Faust et al. 2014)** - \(f: \mathbb {Z}_{p}^{t} \times \mathbb {Z}_{p}^{t} \rightarrow \mathbb {Z}_{N}\) \(t|\mathbb {Z}_{p}|\) -
(Qin et al. 2015)*** DDH \(f: \mathbb {H}^{n\times n} \times \mathbb {Z}_{p}^{n} \rightarrow \mathbb {H}^{n}\) \(2|\mathbb {Z}_{p}| +(n^{2}+1)|\mathbb {H}|\) 2n2Exp
(Bellare and Cash 2010) DDH \(f: \mathbb {Z}_{p}^{n+1} \times \{0, 1\}^{n} \rightarrow \mathbb {H}\) \((n+1)|{\mathbb {Z}_{p}}| + |\mathbb {H}|\) 1Exp
  DLIN \(f: (\mathbb {Z}_{p}^{2\times 2})^{n+1} \times \{0, 1\}^{n} \rightarrow \mathbb {H}\) \(4(n+1)|{\mathbb {Z}_{p}}| + |\mathbb {H}|\) 1Exp
(Goyal et al. 2011) q-DHI \(f: \mathbb {Z}_{p} \times \mathbb {Z}_{p} \rightarrow \mathbb {H}\) \(|{\mathbb {Z}_{p}}| + |\mathbb {H}|\) 1Exp
  1. *\(\mathbb {H}\) is a group of prime order p over \(\mathbb {Z}_{N}\). \(|\mathbb {Z}_{p}|\) and \(|\mathbb {H}|\) denote the size of an element in \(\mathbb {Z}_{p}\) and \(\mathbb {H}\), respectively. Exp denotes a modular exponentiation in \(\mathbb {H}\)
  2. **Here we consider the simplest t-wise independent hash function \(f = \sum _{i=0}^{t-1}a_{i}x_{i} \bmod p \bmod N\) where \(\mathbf {a} \xleftarrow {\$} \mathbb {Z}_{p}\)
  3. ***Only partial PP of OT-LF is considered here