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Table 2 Comparison of IB-DRE Schemes from Lattices

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

  # of # of # of    Standard
Schemes \(\mathbb {Z}_{q}^{n\times m}\) matrix \(\mathbb {Z}_{q}^{m\times m}\) matrix \(\mathbb {Z}_{q}^{m}\) vector Assumption Security model
  |PP| |Msk| |c|    ?
WB’10 (Wang and Bi 2010) 1 1 3 LWE IND-ID-CPA ROM
Ours:       
IB−DREABB \(\mathcal {O}(n)\) 1 3 LWE IND-ID-CPA \(\checkmark \)
IB−DREZCZ \(\mathcal {O}(\log {Q})\) 1 3 LWE IND-ID-CPA \(\checkmark \)
IB−DREYam \(\omega (\sqrt {n})\) 1 3 LWE IND-ID-CPA \(\checkmark \)
IB−DREMAH ω(log2n) 1 3 LWE IND-ID-CPA \(\checkmark \)
IB−DREAFF ω(logn) 1 3 LWE IND-ID-CPA \(\checkmark \)
  1. , |PP|,|Msk| and |c| show the size of public parameters, master secret key and ciphertext, respectively. Q is the number bound of the secret key queries