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Table 7 IB-DRE schemes from other LPHF with high min-entropy

From: (Identity-based) dual receiver encryption from lattice-based programmable hash functions with high min-entropy

Schemes # of   Sample Error Error Reduction
  \(\mathbb {Z}_{q}^{n\times m}\) matrix Modulus width width width cost
  |PP| q σ α q α q  
IB-DRE ZCZ16 \(\mathcal {O}(\log {Q})\) \(\mathcal {O}(n^{6.5+7.5\eta +4c})\) \(\mathcal {O}(n^{2.5+3.5\eta +2c})\) \(\mathcal {O}(n^{3+3\eta +2c})^{\dag }\) \(\mathcal {O}\left (n^{0.5}\right)\) \(\mathcal {O}\left (\frac {\epsilon }{\ell ^{2}Q^{4}}\right)\)
IB-DRE Yam16 \(\omega (\sqrt {n})\) \(\mathcal {O}(n^{5.5+3.5\eta +2c})\) \(\mathcal {O}(n^{2+1.5\eta +c})\) \(\mathcal {O}(n^{2.5+\eta +c})\ddag \) \(\mathcal {O}\left (n^{0.5}\right)\) \(\mathcal {O}\left (\frac {\epsilon ^{5}}{\ell ^{2}Q^{4}}\right)\)
IB-DRE MAH ω(log2n) \(\mathcal {O}(n^{6.5+7.5\eta })\) \(\mathcal {O}(n^{2+3.5\eta })\) \(\mathcal {O}(n^{2.5+3\eta })\) \(\mathcal {O}\left (n^{0.5}\right)\) \(\mathcal {O}\left (\frac {\epsilon ^{2\varphi +1}}{Q^{2\varphi }}\right)\)§
IB-DRE AFF ω(logn) poly(n) poly(n) poly(n) \(\mathcal {O}\left (n^{0.5}\right)\) \(\mathcal {O}\left (\frac {\epsilon ^{3}}{\ell ^{4}Q^{2}}\right)\)
  1. , |PP|,|Msk| and |c| show the size of public parameters, master secret key and ciphertext, respectively. is the length of identity and Q is the bound of secret key queries.
  2. Assume that η such that \(n^{\eta } > \lceil \log {q} \rceil = \mathcal {O}(\log {n})\), and c is the smallest integer satisfying that ncQ+1.
  3. c=c1+c2 where c1, c2 satisfying \(\phantom {\dot {i}\!}\frac {n^{c_{1}}}{2} \geq Q + 1\) and \(\phantom {\dot {i}\!}n^{-c_{2}} \leq \epsilon \)
  4. §φ>1 is the constant which satisfying \(s = 1 - 2^{-\frac {1}{\epsilon }}\), where s{0,1} is the relative distance of the underlying error correcting code. We can take φ as close to 1 as one wants