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

Cybersecurity

Table 7 IB-DRE schemes from other LPHF 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)	\(\mathcal {O}\left (n^{0.5}\right)\)	\(\mathcal {O}\left (\frac {\epsilon ^{3}}{\ell ^{4}Q^{2}}\right)\)

∗, |PP|,|Msk| and |c| show the size of public parameters, master secret key and ciphertext, respectively. ℓ is the length of identity and Q is the bound of secret key queries.
^† Assume that η such that \(n^{\eta } > \lceil \log {q} \rceil = \mathcal {O}(\log {n})\), and c is the smallest integer satisfying that n^c≥Q+1.
‡c=c₁+c₂ where c₁, c₂ satisfying \(\phantom {\dot {i}\!}\frac {n^{c_{1}}}{2} \geq Q + 1\) and \(\phantom {\dot {i}\!}n^{-c_{2}} \leq \epsilon \)
§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