Table 2 Mapping of the surveyed iterative techniques into the proposed framework.

Ref.²³, 2015

Point P on the curve and a key \(e\)

Using \(e\), find \({K}_{0}\)

Using \(e\), initialize LFSR

LFSR outputs \({C}_{i}\)

\({K}_{i}=X({K}_{i-1}P)+{C}_{i-1}\)

\({S}_{i}={K}_{i}P+{K}_{0}P\)

Convert the x-coordinate of \({S}_{i}\) to binary form

Apply truncation on x-coordinate bits

The LFSR increased the period and introduced randomness in the keystream

Ref.²⁴, 2015

Pick an EC, \(E\), and a generator point \(G\) on E

Point \({U}_{0}\in E({F}_{p})\)

Increment index \(i\)

Use the chaotic map to get the binary sequence \({b}_{i}\)

\({U}_{i}=i\left(1+{b}_{i}\right)G+{U}_{0}\)

Convert the point \({U}_{i}\) into its binary form

Apply the map \({U}_{2\times 2}(x,y)\) or the map \({U}_{3\times 3}(x,y)\) on the point \({U}_{i}\), where \({U}_{\mathrm{k}\times \mathrm{k}}\) takes the rightmost \(k\) bits from \(x\) and \(y\) coordinates

Different chaotic maps can be used

The chaotic map increased the randomness of the bitstream

Ref.²⁵, 2017

Two points \(Y\) and \(G\)

\({SK}_{1}=\) primary key

\(A= {SK}_{i}G\)

\(B=A+Y\)

\(C=B+G\)

\({SK}_{i+1}={y}_{A}+{y}_{B}+{y}_{C}\)

\({Z}_{i}=\left|{x}_{A}\times {x}_{B}\times {x}_{C}\right|\)

Read the value \({Z}_{i}\)

The two points \(Y\) and \(G\) have very high orders

Ref.²⁶, 2019

Point \({P}_{0}\) of order \(n\)

Pick \(r\in [1,n-1]\)

let \({\alpha }_{1}, \dots ,{\alpha }_{p}\) be a basis of \({F}_{{2}^{p}}\)

\({P}_{k}={r}^{k}{P}_{0}\)

\({x}_{k}=X({P}_{k})\)

Writing \({x}_{k}\) =\({{s}_{k}}^{(1)}{\alpha }_{1}+\dots +{{s}_{k}}^{(p)}{\alpha }_{p}\)

Read the sequence \({{s}_{k}}^{(i)} , i=1, \dots , p\)

\(n\) has a large prime order

\(r\) has a large multiplicative order mod n

Ref.²⁷, 2020

Select secure EC

Select point \(P\)

\({S}_{0}=X(P)\)

\(\varphi \) is a truncation function

\(H\) is a hash function

\({S}_{i}={\varphi (x[S}_{i-1}P])\)

\({h}_{i}=\varphi (H\left({S}_{i}\right))\)

Apply \(\varphi \) on the x-coordinate of \({S}_{i-1}P\)

Apply \(\varphi \) on \(H\left({S}_{i}\right)\)

Read lower-order bits from \({h}_{i}\)

The hash function enhanced the statistical properties of the output bits